The document contains 12 math word problems where the symbols like +, -, x, / are used with different meanings than their usual meanings. For each problem, the correct meaning of the symbols is determined and the problem is solved to find the right answer. The document tests the ability to solve math problems where the symbols are used in an unconventional way by providing the correct symbolic interpretations.
DESAIN DAN APLIKASI JALAN BETONDI PENDEKAT UTARA JALAN RINGROADTIMUR, PEREM...Debora Elluisa Manurung
Dalam perencanaannya, pelaksanaan jalan beton mengacu pada Petunjuk Perencanaan Jalan Beton Semen yang diterbitkan oleh Departemen Permukiman dan Prasarana Wilayah, Pd T-14-2003. (diadopsi dari AUSTROADS, Pavement Design, A Guide to the Structural Design of Pavements 1992)
Petunjuk penggunaan aplikasi ujian online zya cbt untuk Administrator
Detail aplikasi ada di https://achmadlutfi.wordpress.com/zya-cbt-aplikasi-ujian-online/
di semester dua, ada yang namanya mata kuliah interpretasi ruang. kirain semacam psiko-psiko-aristek gimana gitu kan ternyata engga juga haha. disini hubungannya sama peta + citra satelit. tugas pertama ialah menjiplak peta administrasi sebuah wilayah terus dibikin laporannya. dah gitu. GET STRONGER, PLANNER !
Koreksi geometrik dan geolink er mapper 7.0Rusdianto
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Pengertian Vektor dan Notasi Vektor - Analisis VektorDewi Fitriyani
Pengertian Vektor dan Notasi Vektor Subbab 1.1 dari Mata Kuliah Analisis Vektor.
Disusun Oleh Dewi Fitriyani 16.23.1.0003
Dosen Pengempu Iik Nurhikmayati, M.Pd
Program Studi Pendidikan Matematika
Universitas Majalengka
REPUBLICA
KATHMANDU, March 8: The government has completed final preparation to establish the Department of Railway (DoR) with the vision of developing 4000 km railway line across the country within 20 years.
The Ministry of Physical Planning and Works (MoPPW), which will oversee the DoR upon its formation, recently finalized the Organization and Management (O&M) survey and sent it to the Ministry of General Administration (MoGA) to forward it to the cabinet for approval.
The government decided to form the DoR to speed up the process of constructing different railway project across the country.
Ram Kumar Lamsal, who was involved in preparing O&M survey, said the DoR would have a total of 35 staffers, including three joint-secretaries, seven under-secretaries, 12 section officers and 13 non-gazetted officers. Annual budget for the department has been estimated at Rs 7.5 million.
"The Department of Railway will be formally established once the cabinet approves the O&M survey," said Lamsal, who is heading the Railway Project that is overseeing railway related works under stop-gap basis.
The Ministry of Finance has already given its consent to form the department. Upon formation, the department will oversee construction and management of railway, metro rail, ropeways and cable car lines in the country.
Lamsal, who is also a joint-secretary at MoPPW, said the department has set a vision of increasing railway line to 4,000 km, including the East-West Railway, Kathmandu-Pokhara Railway, Kathmandu-Tibet Railway and railway lines that connect major bordering towns of India and Nepal, within 20 years.
"We have also set a target of building 150 km metro line in the Kathmandu Valley, extend existing ropeway to 1,500 km and establish at least 60 cable car lines within the period," Lamsal told Republica on Monday.
The to-be-formed department will also complete the Detailed Project Report (DPR) of Janakpur-Bardibas railway line and bring the Nepal Railways Company under the purview of the MoPPW. Existing acts specify the Ministry of Labor and Transport Management as the authority to oversee works related to railway.
Paparan Sosialisasi SE PUPR Nomor 18 Tahun 2021 tentang Pedoman Operasional T...Khalid Mustafa
Paparan mengenai SE Nomor 18 Tahun 2021 tentang Pedoman Operasional Tertib Penyelenggaraan Persiapan Pemilihan untuk Pengadaan Jasa Konstruksi di Kementerian PUPR
DESAIN DAN APLIKASI JALAN BETONDI PENDEKAT UTARA JALAN RINGROADTIMUR, PEREM...Debora Elluisa Manurung
Dalam perencanaannya, pelaksanaan jalan beton mengacu pada Petunjuk Perencanaan Jalan Beton Semen yang diterbitkan oleh Departemen Permukiman dan Prasarana Wilayah, Pd T-14-2003. (diadopsi dari AUSTROADS, Pavement Design, A Guide to the Structural Design of Pavements 1992)
Petunjuk penggunaan aplikasi ujian online zya cbt untuk Administrator
Detail aplikasi ada di https://achmadlutfi.wordpress.com/zya-cbt-aplikasi-ujian-online/
di semester dua, ada yang namanya mata kuliah interpretasi ruang. kirain semacam psiko-psiko-aristek gimana gitu kan ternyata engga juga haha. disini hubungannya sama peta + citra satelit. tugas pertama ialah menjiplak peta administrasi sebuah wilayah terus dibikin laporannya. dah gitu. GET STRONGER, PLANNER !
Koreksi geometrik dan geolink er mapper 7.0Rusdianto
Menurut Mather (1987), koreksi geometrik adalah transformasi citra hasil penginderaan jauh sehingga citra tersebut mempunyai sifat-sifat peta dalam bentuk, skala dan proyeksi.
Pengertian Vektor dan Notasi Vektor - Analisis VektorDewi Fitriyani
Pengertian Vektor dan Notasi Vektor Subbab 1.1 dari Mata Kuliah Analisis Vektor.
Disusun Oleh Dewi Fitriyani 16.23.1.0003
Dosen Pengempu Iik Nurhikmayati, M.Pd
Program Studi Pendidikan Matematika
Universitas Majalengka
REPUBLICA
KATHMANDU, March 8: The government has completed final preparation to establish the Department of Railway (DoR) with the vision of developing 4000 km railway line across the country within 20 years.
The Ministry of Physical Planning and Works (MoPPW), which will oversee the DoR upon its formation, recently finalized the Organization and Management (O&M) survey and sent it to the Ministry of General Administration (MoGA) to forward it to the cabinet for approval.
The government decided to form the DoR to speed up the process of constructing different railway project across the country.
Ram Kumar Lamsal, who was involved in preparing O&M survey, said the DoR would have a total of 35 staffers, including three joint-secretaries, seven under-secretaries, 12 section officers and 13 non-gazetted officers. Annual budget for the department has been estimated at Rs 7.5 million.
"The Department of Railway will be formally established once the cabinet approves the O&M survey," said Lamsal, who is heading the Railway Project that is overseeing railway related works under stop-gap basis.
The Ministry of Finance has already given its consent to form the department. Upon formation, the department will oversee construction and management of railway, metro rail, ropeways and cable car lines in the country.
Lamsal, who is also a joint-secretary at MoPPW, said the department has set a vision of increasing railway line to 4,000 km, including the East-West Railway, Kathmandu-Pokhara Railway, Kathmandu-Tibet Railway and railway lines that connect major bordering towns of India and Nepal, within 20 years.
"We have also set a target of building 150 km metro line in the Kathmandu Valley, extend existing ropeway to 1,500 km and establish at least 60 cable car lines within the period," Lamsal told Republica on Monday.
The to-be-formed department will also complete the Detailed Project Report (DPR) of Janakpur-Bardibas railway line and bring the Nepal Railways Company under the purview of the MoPPW. Existing acts specify the Ministry of Labor and Transport Management as the authority to oversee works related to railway.
Paparan Sosialisasi SE PUPR Nomor 18 Tahun 2021 tentang Pedoman Operasional T...Khalid Mustafa
Paparan mengenai SE Nomor 18 Tahun 2021 tentang Pedoman Operasional Tertib Penyelenggaraan Persiapan Pemilihan untuk Pengadaan Jasa Konstruksi di Kementerian PUPR
Esta presentación contiene información acerca de la música, su significado, sus elementos principales y algunos datos curiosos.
"Hay canciones que merecen más volumen del que se les puede dar"
Esta presentación contiene información acerca de la música, su significado, los elementos fundamentales, datos curiosos.
"Hay canciones que merecen más volumen del que se les puede dar"
12 инструментов для бизнеса, которые помогут работать быстрее и эффективнееНовый Сайт
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1of 20Use the formula for the sum of the first n terms of a geom.docxhyacinthshackley2629
1of 20
Use the formula for the sum of the first n terms of a geometric sequence to solve the following.
Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54 . . .
A. 531,440
B. 535,450
C. 535,445
D. 431,440
2 of 20
5.0 Points
The following are defined using recursion formulas. Write the first four terms of each sequence.
a1 = 7 and an = an-1 + 5 for n ≥ 2
A. 8, 13, 21, 22
B. 7, 12, 17, 22
C. 6, 14, 18, 21
D. 4, 11, 17, 20
3 of 20
5.0 Points
How large a group is needed to give a 0.5 chance of at least two people having the same birthday?
A. 13 people
B. 23 people
C. 47 people
D. 28 people
4 of 20
5.0 Points
Write the first six terms of the following arithmetic sequence.
an = an-1 + 6, a1 = -9
A. -9, -3, 3, 9, 15, 21
B. -11, -4, 3, 9, 17, 21
C. -8, -3, 3, 9, 16, 22
D. -9, -5, 3, 11, 15, 27
5 of 20
5.0 Points
Write the first four terms of the following sequence whose general term is given.
an = 3n
A. 3, 9, 27, 81
B. 4, 10, 23, 91
C. 5, 9, 17, 31
D. 4, 10, 22, 41
6 of 20
5.0 Points
If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.
A. ≈ 0.31
B. ≈ 0.42
C. ≈ 0.45
D. ≈ 0.41
7 of 20
5.0 Points
Consider the statement "2 is a factor of n2 + 3n."
If n = 1, the statement is "2 is a factor of __________."
If n = 2, the statement is "2 is a factor of __________."
If n = 3, the statement is "2 is a factor of __________."
If n = k + 1, the statement before the algebra is simplified is "2 is a factor of __________."
If n = k + 1, the statement after the algebra is simplified is "2 is a factor of __________."
A.4; 15; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 8
B.4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 7
C.4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 4
D.4; 15; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 6
8 of 20
5.0 Points
k2 + 3k + 2 = (k2 + k) + 2 ( __________ )
A. k + 5
B. k + 1
C. k + 3
D. k + 2
9 of 20
5.0 Points
The following are defined using recursion formulas. Write the first four terms of each sequence.
a1 = 3 and an = 4an-1 for n ≥ 2
A. 3, 12, 48, 192
B. 4, 11, 58, 92
C. 3, 14, 79, 123
D. 5, 14, 47, 177
10 of 20
5.0 Points
To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?
A. 32,957,326 selections
B. 22,957,480 selections
C. 28,957,680 selections
D. 225,857,480 selections
11 of 20
5.0 Points
Write the first six terms of the following arithmetic sequence.
an = an-1 - 0.4, a1 = 1.6
A. 1.6, 1.2, 0.8, 0.4, 0, -0.4
B. 1.6, 1.4, 0.9, 0.3, 0, -0.3
C. 1.6, 2.2, 1.8, 1.4, 0, -1.4
D. 1.3, 1.5, 0.8, 0.6, 0, -0.6
12 of 20
5.0 Points
You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?
A. 32.
MATHEMATICS BRIDGE COURSE (TEN DAYS PLANNER) (FOR CLASS XI STUDENTS GOING TO ...PinkySharma900491
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1. Slide 1 of 17
Type - 1
Sol. (b).
Using the correct symbols, we have :
Given expression = 16 + 4 × 5 − 72 ÷ 8
= 16 + 20 − 9 = 36 − 9 = 27.
3. If $ means +, # means −, @ means × and * means ÷,
then what is the value of 16 $ 4 @ 5 # 72 * 8 ?
(a) 25 (b) 27 (c) 28 (d) 36
(e) None of these
Sol. (a).
Using the correct symbols, we have :
4. If ÷ means ×, × means +, + means − and − means ÷,
find the value of 16 × 3 + 5 − 2 ÷ 4.
(a) 9 (b) 10 (c) 19
(d) None of these
Sol. (e).
Using the correct symbols, we have :
Given expression = 27 + 81 ÷ 9 − 6
= 27 + 9 − 6 = 36 − 6 = 30.
1. If ‘<’ means ‘minus’, ‘>’ means ‘plus’, ‘=’ means
‘multiplied by’ and ‘$’ means ‘divided by’ then what
would be the value of 27 > 81 $ 9 < 6 ?
(a) 6 (b) 33 (c) 36 (d) 54
(e) None of these
Sol. (d).
Using the correct symbols, we have :
Given expression = 24 × 12 + 18 ÷ 9
= 288 + 2 = 290.
2. If ‘+’ means ‘divided by’, ‘−’ means ‘added to’, ‘×’
means ‘subtracted from’ and ‘÷’ means ‘multiplied
by’, then what is the value of 24 ÷ 12 − 18 + 9 ?
(a) − 25 (b) 0.72 (c) 15.30 (d) 290
(e) None of these
Given expression 16 3 5 2 4
5
16 3 4 19 10 9.
2
= + − ÷ ×
= + − × = − =
2. Slide 2 of 17
Sol. (b).
Using the correct symbols, we have :
Given expression = (3 × 15 + 19) ÷ 8 − 6
= 64 ÷ 8 − 6 = 8 − 6 = 8 − 6 = 2.
7. If × means ÷, − means ×, ÷ means + and + means −,
then (3 − 15 ÷ 19) × 8 + 6 = ?
(a) − 1 (b) 2 (c) 4 (d) 8
Sol. (c).
Using the correct symbols, we have :
Given expression = 12 ÷ 6 − 3 × 2 + 8
= 2 − 6 + 8 = 10 − 6 = 4.
5. If + means ÷, ÷ means −, − means ×, × means +, then
12 + 6 ÷ 3 − 2 × 8 = ?
(a) − 2 (b) 2 (c) 4 (d) 8
Sol. (c).
Using the correct symbols, we have :
Given expression = 15 × 3 – 10 ÷ 5 + 5
= 45 − 2 + 5 = 50 − 2 = 48.
6. If + means −, − means ×, ÷ means + and × means ÷,
then 15 − 3 + 10 × 5 ÷ 5 = ?
(a) 5 (b) 22 (c) 48 (d) 52
Sol. (b).
Using the correct symbols, we have :
8. If × means +, + means ÷, − means × and ÷ means −,
then 8 × 7 − 8 + 40 ÷ 2 = ?
( ) ( ) ( ) ( )
2 3
1 7 8 44
5 5
a b c d
1
Given expression 8 7 8 40 2 8 7 2
5
7 37 2
6 7 .
5 5 5
= + × ÷ − = + × −
= + = =
3. Slide 3 of 17
Sol. (e).
Using the correct symbols, we have :
Given expression = 15 × 2 + 900 ÷ 90 − 100
= 30 + 10 − 100 = − 60.
9. If × means −, + means ÷, − means × and ÷ means +,
then 15 − 2 ÷ 900 + 90 × 100 = ?
(a) 190 (b) 180 (c) 90 (d) 0
(e) None of these
Sol. (a).
Using the correct symbols, we have :
10.
(a) 0 (b) 8 (c) 12 (d) 16
( )
, , ,
36 4 8 4
?
4 8 2 16 1
÷ + − ÷ × − + ×
× − ×
=
+ × + ÷
If means means means and means
then
( )36 4 8 4
Given expression
4 8 2 16 1
32 8 4 4 4
0.
32 32 1 0 1
− ÷ −
=
× − × +
÷ − −
= = =
− + +
4. Slide 4 of 17
Sol. (b).
Given expression = (23 + 45) × 12 = 68 × 12 = 816.
11. (cd × ef) × bc is equal to -
Directions :
In an imaginary language, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are substituted by a, b, c, d, e, f, g, h, i and j. And 10 is
written as ba.
(a) 684 (b) 816 (c) 916 (d) 1564
Sol. (a).
Using the proper notations in (a), we get the statement as :
4 + 5 × 9 ÷ 3 − 4 = 4 + 5 × 3 − 4 = 4 + 15 − 4 = 15.
12. If ‘−’ stands for ‘division’, ‘+’ for ‘multiplication’, ‘÷’
for ‘subtraction’ and ‘×’ for ‘addition’, then which one
of the following equations is correct ?
(a) 4 × 5 + 9 − 3 ÷ 4 = 15
(b) 4 × 5 × 9 + 3 ÷ 4 = 11
(c) 4 − 5 ÷ 9 + 3 × 4 = 20
(d) 4 ÷ 5 + 9 − 3 + 4 = 18
5. Slide 5 of 17
Sol. (c).
Using the proper notations in (c), we get the statement as :
18 ÷ 3 − 6 + 8 + 4 = 12 or 6 − 6 + 8 + 4 = 12
or 12 = 12, which is true.
13. (a) 18 C 3 D 6 B 8 C 4 G 12
(b) 18 A 3 E 6 B 8 G 4 B 12
(c) 18 C 3 G 6 B 8 B 4 D 12
(d) 18 F 3 B 6 E 8 G 4 E 12
Directions :
In each of the following questions, some symbols are represented by letters as shown below :
Now, identify the correct expression in each case.
Sol. (d).
Using the proper notations in (d), we get the statement as :
15 ÷ 5 < 8 ÷ 4 + 6 ÷ 3 or 3 < 2 + 2
or 3 < 4, which is true.
14. (a) 15 B 5 G 8 B 4 G 6 F 3
(b) 15 C 15 B 8 F 4 B 6 C 3
(c) 15 A 5 E 8 C 4 B 6 E 3
(d) 15 C 5 F 8 C 4 B 6 C 3
+ − × ÷ = > <
B G E C D A F
6. Slide 6 of 17
Sol. (c).
Using the proper notations in (c), we get the statement as :
8 − 4 ÷ 2 < 6 + 3 or 6 < 9, which is true.
15. (a) 6 + 3 > 8 = 4 + 2 < 1 (b) 4 > 6 + 2 × 32 + 4 < 1
(c) 8 < 4 + 2 = 6 > 3 (d) 14 + 7 > 3 = 6 + 3 > 2
Directions :
If > denotes +, < denotes −, + denotes ÷, ^ denotes ×, − denotes =, × denotes > and = denotes <, choose the correct
statement in each of the following questions.
7. Slide 7 of 17
Sol. (c).
On interchanging − and ÷ and 4 and 8 in (c), we get the
equation as :
8 − 4 ÷ 2 = 6 or 8 − 2 = 6 or 6 = 6, which is true.
1. Given interchanges :
Signs − and ÷ and numbers 4 and 8.
(a) 6 − 8 ÷ 4 = − 1 (b) 8 − 6 ÷ 4 = 1
(c) 4 ÷ 8 − 2 = 6 (d) 4 − 8 ÷ 6 = 2
Sol. (c).
On interchanging + and × and 4 and 5 in (c), we get the
equation as :
4 + 5 × 20 = 104 or 104 = 104, which is true.
2. Given interchanges :
Signs + and × and numbers 4 and 5.
(a) 5 × 4 + 20 = 40 (b) 5 × 4 + 20 = 85
(c) 5 × 4 + 20 = 104 (d) 5 × 4 + 20 = 95
Directions :
In each of the following questions, if the given interchanges are made in signs and numbers, which one of the four
equations would be correct ?
Sol. (b).
On interchanging + and − and 4 and 8 in (b), we get the
equation as :
8 + 4 − 12 = 0 or 12 − 12 = 0 or 0 = 0, which is true.
3. Given interchanges :
Signs + and − and numbers 4 and 8.
(a) 4 ÷ 8 − 12 = 16 (b) 4 − 8 + 12 = 0
(c) 8 ÷ 4 − 12 = 24 (d) 8 − 4 ÷ 12 = 8
Sol. (b).
On interchanging − and × and 3 and 6 in (b), we get the
equation as :
6 × 3 − 8 = 10 or 18 − 8 = 10 or 10 = 10, which is true.
4. Given interchanges :
Signs − and × and numbers 3 and 6.
(a) 6 − 3 × 2 = 9 (b) 3 − 6 × = 10
(c) 6 × 3 − 4 = 15 (d) 3 × 6 − 4 = 33
Type - 2
8. Slide 8 of 17
Sol. (b).
On interchanging − and ÷, we get the equation as :
5. 5 + 3 × 8 − 12 ÷4 = 3
(a) + and − (b) − and ÷ (c) + and × (d) + and ÷
Directions :
In each of the following questions, the given equation becomes correct due to the interchange of two signs. One of the
four alternatives under it specifies the interchange of signs in the equation which when made will make the equation
correct. Find the correct alternative.
Sol. (a).
On interchanging ÷ and ×, we get :
Given expression = 5 + 6 × 3 − 12 ÷ 2
= 5 + 6 × 3 − 6 = 5 + 18 − 6 = 17.
6. 5 + 6 ÷ 3 − 12 × 2 = 17
(a) ÷ and × (b) + and × (c) + and ÷ (d) + and −
2
5 3 8 12 4 3 or 5 3 4 3
3
or 3 = 3, which is true.
+ × ÷ − = + × − =
Sol. (a).
On interchanging × and +, we get :
Given expression = 2 + 3 × 6 − 12 ÷ 4
= 2 + 3 × 6 − 3 = 2 + 18 − 3 = 17.
7. 2 × 3 + 6 − 12 ÷ 4 = 17
(a) × and + (b) + and − (c) + and ÷ (d) − and ÷
Sol. (b).
On interchanging − and ÷, we get :
Given expression = 16 ÷ 8 − 4 + 5 × 2
= 2 − 4 + 5 × 2 = 2 − 4 + 10 = 8.
8. 16 − 8 ÷ 4 + 5 × 2 = 8
(a) ÷ and × (b) − and ÷ (c) ÷ and + (d) − and ×
9. Slide 9 of 17
Sol. (c).
On interchanging 6 and 4 on L.H.S., we get the statement as :
5 + 3 × 4 − 6 ÷ 2 = 4 × 3 − 10 ÷ 2 + 7
or 5 + 12 − 3 = 12 − 5 + 7
or 14 = 14, which is true.
9. 5 + 3 × 6 − 4 ÷ 2 = 4 × 3 − 10 ÷ 2 + 7
(a) 4, 7 (b) 5, 7 (c) 6, 4 (d) 6, 10
Directions :
In each of the following questions, the two expressions on either side of the sign (=) will have the same value if two
terms on either side or on the same side are interchanged. The correct terms to be interchanged have been given as one
of the four alternatives under the expressions. Find the correct alternative in each case.
Sol. (d).
On interchanging 7 and 6, we get the statement as :
6 × 2 − 3 + 8 ÷ 4 = 5 + 7 × 2 − 24 ÷ 3
or 12 − 3 + 2 = 5 + 14 − 8
or 11 = 11, which is true.
10. 7 × 2 − 3 + 8 ÷ 4 = 5 + 6 × 2 − 24 ÷ 3
(a) 2, 6 (b) 6, 5 (c) 3, 24 (d) 7, 6
Sol. (a).
On interchanging 3 and 5, we get the statement as :
15 + 5 × 4 − 8 ÷ 2 = 8 × 3 + 16 ÷ 2 − 1
or 15 + 20 − 4 = 24 + 8 − 1
or 31 = 31, which is true.
11. 15 + 3 × 4 − 8 ÷ 2 = 8 × 5 + 16 ÷ 2 − 1
(a) 3, 5 (b) 15, 5 (c) 15, 16 (d) 3, 1
Sol. (d).
On interchanging 9 and 5 on R.H.S., we get the statement as :
6 × 3 + 8 ÷ 2 − 1 = 5 − 8 ÷ 4 + 9 × 2
or 18 + 4 − 1 = 5 − 2 + 18
or 21 = 21, which is true.
12. 6 × 3 + 8 ÷ 2 − 1 = 9 − 8 ÷ 4 + 5 × 2
(a) 3, 4 (b) 3, 5 (c) 6, 9 (d) 9, 5
10. Slide 10 of 17
Sol. (c).
On interchanging + and × and 4 and 6, we get the equation as
:
4 + 6 × 2 = 16 or 4 + 12 = 16
or 16 = 16, which is true.
13. 6 × 4 + 2 = 16
(a) + and ×, 2 and 4 (b) + and ×, 2 and 6
(c) + and ×, 4 and 6 (d) None of these
Directions :
In each of the following questions, which one of the four interchanges in signs and numbers would make the given
equation correct ?
Sol. (a).
On interchanging + and ÷ and 2 and 3, we get the equation as :
(2 + 4) ÷ 3 = 2 or 6 ÷ 3 = 2
or 2 = 2, which is true.
14. (3 ÷ 4) + 2 = 2
(a) + and ÷, 2 and 3 (b) + and ÷, 2 and 4
(c) + and ÷, 3 and 4 (d) No interchange, 3 and 4
Sol. (b).
Using the proper operations given in (b), we get the given expression as :
200 + 100 − 300 + 200 ÷ 10 × 2 − 40 = 300 − 300 + 20 × 2 − 40 = 0 + 40 − 40 = 0.
15. Which of the following meanings of the arithmetical signs will yield the value ‘zero’ for the expression given below ?
200× 100 + 300 × 200 − 10 ÷ 2 + 40
(a) + means −, − means ×, × means ÷, ÷ means + (b) + means −, − means ÷, × means +, ÷ means ×
(c) + means ×, − means −, × means ÷, ÷ means + (d) + means ÷, − means +, × means −, ÷ means ×
(e) None of these
11. Slide 11 of 17
Type - 3
Sol. (b).
3. If A + B > C + D, B + E = 2C and C + D > B + E, it
necessarily follows that -
(a) A + B > 2E (b) A + B > 2C
(c) A > C (d) A + B > 2D
Sol. (c).
1. If A > B, B > C and C > D, then which of the following
conclusions is definitely wrong ?
(a) A > D (b) A > C (c) D > A (d) B > D
Sol. (b).
2. If A + D = B + C, A + E = C + D, 2C < A + E and 2A >
B + D, then
(a) A > B > C > D > E (b) B > A > D > C > E
(c) D > B > C > A > E (d) B > C > D > E > A
A B, B C, C D A B C D
A D D
> > > ⇒ > > >
⇒ > ⇒ >
( )
A.
So, is false.c
( )
( )
( )
( )
( ) ( ) ( ) ( )
2C < A+E, A+E = C+D 2C < C+D C < D .....
A+D = B+C, C < D A < B .....
2A > B+D, A < B A > D .....
A+E = C+D, A > D E < C .....
From , , and , we get : B > A > D > C > E.
i
ii
iii
iv
i ii iii iv
⇒ ⇒
⇒
⇒
⇒
A + B > C + D, C + D > B + E, B + E = 2C
A + B > 2C.⇒
12. Slide 12 of 17
Sol. (d).
4. If A + E = B + D, A + B > C + E, A + D = 2B, C + E > B + D, then
(a) A > B > C > D > E (b) C > B > D > A > E (c) C > B > A > E > D (d) C > A > B > D > E
Sol. (a).
Given A + B = 2C ….(i) and C + D = 2A ….(ii)
Adding (i) and (ii), we get : A + B + C + D = 2C + 2A ⇒ B + D = A + C.
5. If A + B = 2C and C + D = 2A, then
(a) A + C = B + D (b) A + C = 2D (c) A + D = B + C (d) A + C = 2B
( )
( )
( )
( )
( ) ( ) ( )
C + E > B + D, B + D = A + E C + E > A + E C > A ....
A + B > C + E, C + E > B + D A + B > B + D A > D ....
A + D = 2B, A > D A > B > D ....
A + E = B + D, A > B E > D ....
From , , and
i
ii
iii
iv
i ii iii
⇒ ⇒
⇒ ⇒
⇒
⇒
( ) , we get : C > A > B > D> E.iv
13. Slide 13 of 17
Sol. (b).
With usual notations, we have :
6. a − b − c implies
(a) a − b + c (b) b + a − c (c) c × b + a (d) b + a ÷ c
Directions :
It being given that :
∆ denotes ‘equal to’ ; denotes ‘not equal to’ ; + denotes ‘greater than’ ; − denotes ‘less than’ ; × denotes ‘not greater
than’ ; ÷ denotes ‘not less than’.
Sol. (c).
With usual notations, we have :
7. a + b − c implies
(a) b − c − a (b) c − b + a (c) c + b − a (d) c × b ÷ a
( )
( )
( )
, which is false.
, which is true.
a a b c a b c
b a b c b a c
c a b c c
< < ⇒ < >
< < ⇒ > <
< < ⇒ >
( )
, which is false.
b a
d a b c b a
>
< < ⇒ > < , which is false.c
( )
( )
( )
( )
, which is false.
, which is false.
, which is true.
a a b c b c a
b a b c c b a
c a b c c b a
d a b c c
> < ⇒ < <
> < ⇒ < >
> < ⇒ > <
> < ⇒ >b < , which is false.a
14. Slide 14 of 17
Sol. (b).
With usual notations, we have :
8. a × b ÷ c implies
(a) a − b + c (b) c × b ÷ a (c) a b c(d) b ÷ a ÷ c
Sol. (d).
With usual notations, we have :
9. a + b + c does not imply
(a) b − a + c (b) c − b − a (c) c − a + b (d) b − a − c
( )a a >b <
( )
, which is not true.
c a b c
b a
⇒ < >
>b < c c⇒ >b <
( )
, which is true.
a
c a >b <
( )
, which is not true.
c a b c
d a
⇒ ≠ ≠
>b < c b⇒ <a < , which is not true.c
( )
( )
( )
( )
, which is false.
, which is false.
, which is false.
, which is true.
a a b c b a c
b a b c c b a
c a b c c a b
d a b c b a c
> > < >
> > < <
> > < >
> > < <
16. Slide 16 of 17
Sol. (b).
12. a α 2b and 2b θ r
(a) a η r (b) a α r (c) a β r (d) a γ r
Directions :
If α means ‘greater than’, β means ‘equal to’ , θ means ‘not less than’, γ means ‘less than’ , δ means ‘not equal to’ and η
means ‘not greater than’, then which of the four alternatives could be α correct or proper inference in each of the
following ?
Sol. (c).
(2x δ y) and (y β 3z)
⇒ 2x ≠ y and y = 3z
⇒ 2x ≠ 3z i.e. 2x δ 3z.
13. 2x δ y and y β 3z
(a) y δ 6x (b) 2x η 3z (c) 2x δ 3z (d) 3z η 3y
( 2 ) and (2 ) 2 and 2a b b r a b bα θ ⇒ > <
2 and 2 . .
r
a b b r a r i e a rα⇒ > ≤ ⇒ >
17. Slide 17 of 17
Sol. (b).
a ∆ b and b + c
⇒ a > b and b is a little more than c.
⇒ a > c
⇒ c > a i.e. c % a.
14. If a ∆ b and b + c, then
(a) a % c (b) c % a (c) c + a (d) Can’t say
Directions :
In the following questions, ∆ means ‘is greater than’, % means ‘is lesser than’, means ‘is equal to’, = means ‘is not
equal to’, + mean ‘is a little more than’ , × means ‘is a little less than’.
Choose the correct alternative in each of the following questions.
Sol. (c).
c = a and a = b
⇒ c ≠ a and a ≠ b
⇒ b ≠ a i.e. b = a.
15. If c = a and a = b, then
(a) b ∆ a (b) c a (c) b = a (d) Can’t say