simplicaition

1. Simplification
1. The value of
1 1 1 1 1 1 1
3 2 1 1
2 4 4 2 2 3 6
é ùì üæ ö
- - - - -í ýê úç ÷è øî þë û
(1)
1
2
(2)
1
2
2
(3)
1
3
2
(4)
1
9
2
2. Simplify :
2
1
3
1
4
1
5
+
+
+
(1)
7
4
(2)
4
7
(3)
7
5
(4)
3
7
3. The value of
1 17
1 22
3
1
2
7
9
+
+
-
is :
(1)
12
22
(2)
22
5
(3)
5
22
(4) 1
4. Simplify :
( )
4 1
1 10 2
3 2
2
1
5
2
+ - ¸
+
-
(1) 1 (2) 0
(3)
15
2
- (4)
1
2
-
5.
2
2
2 0.39
2
3
2
3
3
+ ´
+
+
is simplified to
(1)
1
3
(2) 2
(3) 6 (4) None of these
6. The value of
995
999 999
999
´ is :
(1) 990809 (2) 998996
(3) 999824 (4) 998999
7.
98
999 99
99
´ is equal to :
(1) 98999 (2) 99899
(3) 99989 (4) 99998
8. The sum ‘5 + 6 + 7 + 8 + ... +19’ is equal to :
(1) 150 (2) 170
(3) 180 (4) 190
9. Given that 12
+ 22
+ 32
... + 202
= 2870, the value of
(22
+ 42
+ 62
+ ... + 402
) is :
(1) 11480 (2) 5740
(3) 28700 (4) 2870
10. Given 13
+ 23
+ 33
... + 103
= 3025, then 23
+ 43
+ 63
+ ... + 203
is equal to
(1) 6050 (2) 9075
(3) 12100 (4) 24200
11. Simplification of
( ) ( )2 2
3.4567 3.4533
0.0034
-
yields the result:
(1) 6.91 (2) 7
(3) 6.81 (4) 7.1
12.
( )5 5 5 5 5
3 3 3 3 3
+ + + ¸
+ + + ¸
is equal to
(1) 1 (2)
3
10
(3)
4
9
(4)
2
5
13. The value of
( ) ( )2 2
2.697 0.498 2.697 0.498
2.697 2.697 0.498 0.498
- + +
´ + ´
is
(1) 4 (2) 2
(3) 2.199 (4) 3.195
14. The simplified value of
1 1 1 1 1
1 1 1 ... 1 1
3 4 5 99 100
æ ö æ ö æ ö æ ö æ ö
- - - - -ç ÷ ç ÷ ç ÷ ç ÷ ç ÷è ø è ø è ø è ø è ø
is
(1)
2
99
(2)
1
25
(3)
1
50
(4)
1
100
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2. 2
CAREER POWER
CAREER POWER, G-7, Roots Tower, Laxmi Nagar, District Centre, Delhi-92, www.careerpower.in
Chapterwise SSC Quantitative Aptitude
15. The value of
0.125 0.027
0.25 0.15 0.09
+
- +
is
(1) 0.2 (2) 0.25
(3) 0.3 (4) 0.8
16.
137 137 137 133 133 133
137 137 137 133 133 133
´ + ´ + ´
´ ´ - ´ ´
is equal to
(1) 4 (2) 270
(3)
1
4
(4)
1
270
17. 0.142857 0.285714+ is equal to
(1) 10 (2) 2
(3)
1
2
(4)
1
3
18. The value of 3 0.2 0.2 0.2 0.04 0.04 0.04
0.4 0.4 0.4 0.08 0.08 0.08
´ ´ + ´ ´
´ ´ + ´ ´
is
(1) 0.5 (2) 0.25
(3) 0.75 (4) 0.125
19.
1 1 1 1 1
1.4 4.7 7.10 10.13 13.16
æ ö
+ + + +ç ÷
è ø
is equal to
(1)
1
3
(2)
5
16
(3)
3
8
(4)
41
7280
20. The simplification of
1 1 1 1
1 1 1 ... 1
2 3 4 100
æ öæ öæ ö æ ö
- - - -ç ÷ç ÷ç ÷ ç ÷
è øè øè ø è ø
result in :
(1) 0.01 (2) 0.001
(3) 1 (4) 0.1
21. If * represents a number, then the value of * in s
3 1
5 3 19
* 2
´ = is :
(1) 7 (2) 4
(3) 6 (4) 2
22. ( ){ }8.7 7.6 6.5 5.4 4.3 2é ù- - - - -ê úë û
is simplified to :
(1) 2.5 (2) 3.5
(3) 4.5 (4) 5.5
23. Simplify :
1
1
2
1
1
2
+
-
¸
4 2 3
7 5 10
æ ö
+ç ÷
è ø
of
1 1
2 3
1 1
2 3
+
-
(1)
2
3
(2)
1
37
2
(3)
3
2
(4)
3
18
8
24. The value of
0.9 0.9 0.9 0.2 0.2 0.2 0.3 0.3
0.9 0.9 0.2 0.2 0.3 0.3 0.9
0.3 3 0.9 0.2 0.3
0.2 0.2 0.3 03 0.9
´ ´ + ´ ´ + ´
´ + ´ + ´ -
´ - ´ ´ ´
´ - ´ - ´
is
(1) 1.4 (2) 0.054
(3) 0.8 (4) 1.0
25. The simplified value of
1 1 1 1 1
1 1 1 .... 1 1
3 4 5 99 100
æ öæ öæ ö æ öæ ö
- - - - -ç ÷ç ÷ ç ÷ ç ÷ç ÷
è øè ø è ø è øè ø
is
(1)
2
99
(2)
1
25
(3)
1
50
(4)
1
100
HINTS & SOLUTIONS
.ANSWER KEY.
1. (1) 2. (1) 3. (4) 4. (2) 5. (4) 6. (2)
7. (1) 8. (3) 9. (1) 10. (4) 11. (1) 12. (4)
13. (2) 14. (3) 15. (4) 16. (3) 17. (3) 18. (1)
19. (2) 20. (1) 21. (1) 22. (3) 23. (3) 24. (1)
25. (3)
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3. 3
CAREER POWER
CAREER POWER, G-7, Roots Tower, Laxmi Nagar, District Centre, Delhi-92, www.careerpower.in
Chapterwise SSC Quantitative Aptitude
1. (1) Expression =
7 9 5 1 3 1 1
2 4 4 2 2 3 6
é ùì üæ ö
- ¸ - - -í ýê úç ÷è øî þë û
=
7 9 5 1 9 2 1
2 4 4 2 6
é ùì - - üæ ö
- ¸ -í ýê úç ÷
è øî þë û
=
7 9 5 1
2 4 4 2
é ùì ü
- ¸ -í ýê ú
î þë û
=
7 9 5 2
2 4 4
é - ùì ü
- ¸ í ýê ú
î þë û
=
7 9 3
2 4 4
é ù
- ¸ê ú
ë û
=
7 9 4
2 4 3
- ´ =
7 7 6 1
3
2 2 2
-
- = =
2. (1) ? =
2
1
3 5
1
9
+
´
+
=
2
1
5
1
3
+
+
=
2 3
1
8
´
+ =
7
4
3. (4)
1 17
1 22
3
1
2
7
9
+
+
-
=
1 17
1 22
3
9
2
7
+
+
-
=
1 17
1 22
3
14 9
7
+
+
-
=
1 17
1 22
3
5
7
+
+
=
1 17
1 22
3
5
7
+
+
=
1
1715 7
65 22
+ + =
5 17
22 22
+ =
22
22
= 1
4. (2)
4 1
1 5
3 2
2
10 1
2
+ - ´
+
-
=
4 5
1
6 2
2
9
+ -
+
=
4 5
1
2 2
2
3
+ -
+
=
4 5
1
8 2
3
+ - = 1 +
4 3 5
8 2
´
-
=
2 3 5
2
+ -
=
2 3 5
2
+ -
= 0
5. (4)
2
2
2 0.39
2
3
11
3
+ ´
+
=
2
2
2 0.39
6
3
11
+ ´
+
=
2
2
2 0.39
33 6
11
+ ´
+
=
2
11 2
2 0.39
39
´
+ ´
=
2 2 2
11 2 39 11 100 11
2 2
39 100 50 50
= =
´ +
+ ´ +
=
100
111
6. (2) The given expreassion =
995
999 999
999
´
=
995
999 999
9999
æ ö
+ ´ç ÷
è ø
= 999 × 999 +
995
999
999
´
= (1000 – 1) 999 + 995
= 999000 – 999 + 995 = 999000 – 4 = 998996
7. (1)
98
999 99
99
æ ö
+ ´ç ÷è ø = 999 × 99 + 98
= (1000 – 1) 99 + 98 = 99000 – 99 + 98 = 98999
8. (3) 1 + 2 + 3 + ... + n =
( )1
2
n n +
5 + 6 + 7 + .... + 19
= (1 + 2 + 3 + .... + 19) – (1 + 2 + 3 + 4)
=
( )19 9 1
2
+
– 10 = 180
9. (1) 22 + 42 + 62 + ... + 402
= 22 (1 2 + 22 + 32 + .... + 202)
= 4 × 2870 = 11480
10. (4) It is given, 13 + 23 + 32 + ... + 103 = 3025
Now, 23 + 43 + 63 + ... + 203
= (1 × 2)3 + (2 × 2)3 + (2 × 3)3 + .... + (2 × 10)3
= 23 [13 + 23 + 33 + ... + 103]
= 8 × 3025 = 24200
11. (1) ?
( ) ( )34567 3.4533 3.4567 3.4533
0.0034
- + +
=
6.9100 0.0034
0.0034
´
= 6.91
12. (4) Expression =
20 5 4 2
9 3 3 10 5
¸
= =
+ ¸
13. (2) Let 2.697 = a and 0.498 = b
Expression =
( ) ( )2 2
2 2
a b a b
a b
- + +
+
=
( )2 2
2 2
2 a b
a b
+
+
= 2
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4. 4
CAREER POWER
CAREER POWER, G-7, Roots Tower, Laxmi Nagar, District Centre, Delhi-92, www.careerpower.in
Chapterwise SSC Quantitative Aptitude
14. (3) Expression
=
1 1 1 1 1
1 1 1 ... 1 1
3 4 5 99 100
æ öæ öæ ö æ öæ ö
- - - - -ç ÷ç ÷ç ÷ ç ÷ç ÷
è øè øè ø è øè ø
=
3 1 4 1 5 1 99 1 100 1
...
3 4 5 99 100
- - - - -æ öæ öæ ö æ öæ ö
ç ÷ç ÷ç ÷ ç ÷ç ÷
è øè øè ø è øè ø
=
2 3 4 98 99
....
3 4 5 99 100
´ ´ ´ ´ ´ =
2 1
100 50
=
15. (4) Expression =
( ) ( )
( ) ( )
3 3
2 2
0.5 0.3
0.5 0.5 0.3 0.3
+
- ´ +
Let 0.5 = a, and 0.3 = b
Expression =
3 3
2 2
a b
a ab b
+
- +
=
( )( )2 2
2 2
a b a ab b
a ab b
+ - +
- +
= 0.5 0.3 0a b+ = + =
16. (3) Let 137 = a and 133 = b
Given expression =
a a a b b b
a a a b b b
´ + ´ + ´
´ ´ - ´ ´
=
2 2
3 3
a ab b
a b
+ +
-
=
( )( )
2 2
2 2
a ab b
a b a ab b
+ +
- + +
=
1
a b-
=
1
137 133-
=
1
4
17. (3) 0.142857 0.285714¸
=
142857 285714
999999 999999
¸ =
142857
285714
=
1
2
18. (1) Let 0.2 = a and 0.04 = b
Expression = 3
2 2 2 2 2 2
a a a b b b
a a a b b b
´ ´ + ´ ´
´ ´ + ´ ´
=
( )
3 3
3 3 3
8
a b
a b
+
+
= 3 1
8
=
1
2
= 0.5
19. (2) Expression =
1 1 1 1 1
1 4 4 7 7 10 10 13 13 16
+ + + +
´ ´ ´ ´ ´
=
1 3 3 3 3 3
3 1 4 4 7 7 10 10 13 13 16
æ ö
+ + + +ç ÷
´ ´ ´ ´ ´è ø
=
1 1 1 1 1 1 1 1 1 1
1
3 4 4 7 7 10 10 13 13 16
æ ö
- + - + - + - + -ç ÷
è ø
=
1 1
1
3 16
æ ö
-ç ÷
è ø
=
1 16 1
3 3
-æ ö
ç ÷
è ø
=
1 15
3 16
´ =
5
16
20. (1)
1 1 1 1
1 1 1 .... 1
2 3 4 100
æ öæ öæ ö æ ö
- - - -ç ÷ç ÷ç ÷ ç ÷
è øè øè ø è ø
=
1 2 3 99
...
2 3 4 100
´ ´ ´ =
1
100
= 0.01
21. (1)
3 7
5
* 2
´ = 19 Þ
3
5
*
=
19 2
7
´
Þ
3
5
*
=
38
7
=
3
5
7
Þ * = 7
22. (3) Expression = ( ){ }8.7 7.6 6.5 5.4 4.3 2é ù- - - - -ê úë û
= ( ){ }8.7 7.6 6.5 5.4 2.3é ù- - - -ê úë û
= { }8.7 7.6 6.5 3.1- - -é ùë û
= { }8.7 7.6 3.1- -é ùë û = 8.7 – 4.2 = 4.5
23. (3)
3
42
1 7
2
¸
4 3
10
+æ ö
ç ÷è ø
of
3 2
6
3 2
6
+
-
=
4 7
3
7 10
æ ö
¸ ç ÷è ø
of
5
6
6
æ ö
´ç ÷è ø
=
4 7
3 5
7 10
æ ö
¸ ´ ´ç ÷è ø
=
3
3 2
2
¸ =
24. (1) Let 0.9 = x, 0.2 = y and 0.3 = z
Then, the given expression
=
3´ ´ + ´ ´ + ´ ´ - ´ ´ ´
´ + ´ + ´ - ´ - ´ - ´
x x x y y y z z z x y z
x x y y z z x y y z z x
=
3 3 3
2 2 2
3+ + -
+ + - - -
x y z xyz
x y z xy yz zx
= x + y + z = 0.9 + 0.2 + 0.3 = 1.4
25. (3)
2 3 4 98 99
...
3 4 5 99 100
´ ´ ´ ´ ´
2 1
100 50
= =
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