Nac questions numerical ability

Numerical Ability
Number Systems
Averages & Percentages
Profit and Loss
Time and Work
Ratio
Ages
Clock

Numbers
• The citizens of planet nigiet are 6 fingered and
have thus developed their decimal system in base
6.
• A certain street in nigiet contains 1000 (in base 6)
buildings numbered 1 to 1000.
• How many 3s are used in numbering these
buildings? a) 256 b) 54 c) 192 d) 108
• (N-1)*(BASE)(N-2)
N=NUMBER OF LAST DIGIT=4(1000 contains 4 digits)
• base=6
• (4-1)*62 = 3*36 = 108.

Numbers
• The citizens of planet nigiet are 8 fingered and
have thus developed their decimal system in base
8. A certain street in nigiet contains 1000 (in base
8) buildings numbered 1 to 1000. How many 3s
are used in numbering these buildings? a) 54 b)
64 c) 265 d) 192
• (N-1)*(BASE)(N-2)
• N=NUMBER OF LAST DIGIT=4(1000 contains 4
digits)
• base=8
• (4-1)*8(4-2) =192

NUMBER
• If a and b are odd numbers, then which of the
following is even ?
• A. a + b
• B. a + b + 1
• C. ab
• D. ab + 2
• E. None of these
•
• always add two odd number it gives even number

FRACTIONS
• One-third of the marks obtained by Naveen in maths
is the same as the marks he obtained in English. If the
total marks obtained by him in both the subjects is
160, the marks he obtained in English is:
• A) 40 B) 30 C) 50 D) None of the options
• Let the marks obtained in English be x.
• Marks obtained in Maths = 3x.
• Total marks obtained 4x = 160.
• Hence marks obtained in English x = 40.
• Answer : a) 40

Decimal Number
• In which of the system, decimal number 184 is
equal to 1234?
• 184= 1*x^3 + 2*x^2 + 3*x + 4
• X3 + 2x2 + 3x – 180 = 0.
• Has no integral solution.
• Hence answer choose none of these.

DECIMALS & FRACTIONS
• 892.7 - 573.07 - 95.007 =?
• i) 224.623 ii) 224.777 iii) 233.523 iv)414.637
• Choice 1.

DECIMALS & FRACTIONS
• Which pair of rational numbers lie between
1/5 and 2/5 -
a. 262/1000, 275/1000 b. 362/1000, 562/1000
c. 451/1000, 552/1000 d. 121/1000,131/1000
• BETWEEN 0.2 AND 0.4
• ANS A.

ALGEBRA
• Three consecutive whole numbers are such
that the square of the middle number is
greater than the product of the other two by
1. Find the middle number.
• a. 6 b. 18 c. 12 d. All of these
• Let the numbers be x–1, x, x + 1.
• Since x2 = (x–1) x (x+1) + 1 it is true for any
values of x.

A.M & G.M
• The arithmetic mean of 2 numbers is 34 and
their geometric mean is 16. One of the
numbers will be
• a. 4 b. 16 c. 18 d. 12
• a + b = 68 and ab = 256.
• Hence choice a is correct.

DIVISIBILITY
• What least number must be subtracted from
9400 to get a number exactly divisible by 65?
• a. 40 b. 20 c. 80 d. none of these
• 65 = 5 X 13
• Last digit should be zero or 5.
• 9400–40=9360 divisible by 13 & 5
• 9400–20=9380, 9400–80=9320. none of these
divisible by 13.
• Hence answer is A.

Divisiblity
• 12 divides, ab313ab (in decimal notation, where a,b
are digits>0, the smallest value of a+b is a)7 b)6 c)2 d) 4
• If a number is divisible by 12 then it should be divisible
by 4&3
• for divisible by 4 last [2 digit]no's should be divisible by
4
• Also sum of digits should be divisible by 3.
• Hence 2(a+b)+1 should be 3k and ab = 4m.
• That is a + b = (3k-1)/2 . from the given choices only
first choice is possible k = 5 and smallest should be 7.

Divisibility
• If a number 774958A96B is to be divisible by 8 and 9,
the values of A and B, respectively, will be:
• Using the divisibility rules,
• For 8, the last three digits have to divisible by 8,
therefore the number 774958A96B is divisible by 8 if
96B is divisible by 8.
• 96B is divisible by 8 if it is 960 or 968 thus B is either 0
or 8.
• For 9, the sum of the number has to be divisible by 9,
therefore (55 + A + B) is divisible by 9 if (A + B) is 8.
• Now either of A or B could be 8, but the other has to
be zero.

Divisibility
• 311311311311311311 is divisible by:
a)3 and 11. b)11 but not 3. c)3 but not 11.
d)none of the above.
• a.3 and 11
• the sum of digits is 30 which is divisible by 3
• the differences of odd place digits - even place
is divisible by 11

DIVISIBILITY
• What least number be added to 5200 to get a
number exactly divisible by 180?
(1) 160 (2) 60 (3) 20 (4) 180
• 180 = 5 X 4 X 9.
• 5200 + 160 = 5360 NOT DIVISIBLE BY 9.
• 5200 + 60 = 5260 NOT DIVISIBLE BY 9
• 5200 +20 = 5220 DIVISIBLE BY 9
• 5200 + 180 NOT DIVISIBLE BY 9.

DIVISIBILITY
• A number when divided by 32 leaves the
remainder 29. This number when divided by 8
will leave the remainder (1) 3 (2) 5 (3) 7 (4) 29
• Let the number be 32k + 29.
• 32k + 29 = 32k + 24 + 5
• 8(4k+3) + 5.
• The remainder is 5.

Powers
• The unit digit in the expression
• ( 36234 x 33512 x 39180) – (5429 x 25123 x 31512) will be
• (a) 2 (b) 6 (c) 8 (d) 4
• Power of 6 end in 6
• Fourth power of 3 end in 1
• Even power of 9 end in 1
• Odd power of 4 end in 4
• Ans: 6– 4 = 2.

POWERS
• If x increases linearly, how will a-x behave
(a>1) ?
• a. Increase linearly
• b. Decrease linearly
• c. Increase exponentially
• d. Decrease exponentially
• Since x increases linearly, –x decreases linearly
and a–x decreases exponentially. Ans d.

POWERS
• What is x if
xx
3
3
1
9
81
1
3
27
1 100
Rewrite each term as a power of three, then combine exponents:
12932
4
100
3
333
3
1
3
3
1 xxx
Since the bases are the same, the exponents must be equal:
1293 xx
which has the solution x = –94

LOGARITHM
• What is the value of the following expression:
2 log105 + log104 ?
a. 2 b. 2.5 c. 3 d. None of these
• Log10 25*4 = log10100 = 2.

LCM
• Find the greatest number of five digits, which is
exactly divisible by 7, 10, 15, 21 and 28.
• The number should be exactly divisible by 15 (3,
5), 21 (3, 7), 28 (4, 7).
• Hence, it is enough to check the divisibility for 3,
4, 5 and 7.
• Lcm of 3,4,5 and 7 is 420.
• 105/420 = 238 is quotient
• 238* 420 = 99960 is the only number which
satisfies the given condition.

HCF
• The ratio of two numbers is 3 : 4 and their H.C.F.
is 4.
• Their L.C.M. is: A. 12 B. 16 C. 24 D. 48
• Let the numbers be 3x and 4x.
• Then, their H.C.F. = x.
• So, x = 4(given)
• the numbers are 12 and 16.
• LCM of 12,16 is 48.
• So, ans is OPT (D)

HCF & LCM
• Four different electronic devices make a beep after every 30
minutes, 1 hour, 3/2 hour and 1 hour 45minutes respectively.
• All the devices beeped together at 12 noon.
• They will again beep together at:
• i) 12 Midnight ii) 3 a.m iii) 6 a.m. iv) 9 a.m
Interval after which the devices will beep together
= (L.C.M. of 30, 60, 90, 105) min.
= 1260 min.
= 21 hrs.
So, the devices will again beep together 21 hrs. after 12 noon i.e., at 9 a.m.

Factorization
• The prime factorization of integer N is A*A*B*C where A, B
and C are all distinct prime integers. How many factors
does N have? a)12 b)24 c)4 d)6
• n is A*A*B*C =A^2*B*C
no. of factors=(2+1)(1+1)(1+1)
=12
• A HAS POWER OF 2,B HAS POWER OF 1,C HAS POWER 1
SO PRIME FACTORIZATION CAN BE CALCULATED AS:
IF A^P+B^Q+C^R,THEN
PRIME FACTORIZATION IS (P+1)*(Q+1)*(R+1)
SO IN THIS CASE P=2,Q=1,R=1
SO (2+1)(1+1)(1+1)=12 FACTORS

RACES & GAMES
• An athlete decides to run the same distance
in 1/4th less time that she usually took. By
how percent will she have to increase her
average speed

RACES & GAMES
• In August, a cricket team that played 120 matches won 20% of the
games it played. After a continuous winning streak, this team
raised its average to 52%. How many matches did the team win to
attain this average?
• A) 40 B) 52 C) 68 D) 80
• (24+x) / (120+x) = 0.52, where x is the number of games played and
24 is 20% of 120
• 24 + x = 0.52(120 + x)
24+x = 62.4 + 0.52x
0.48x = 62.4-24
0.48x=38.4
x=38.4/0.48
x=80

PERCENTAGE
• Find the percentage of prime numbers
present between 1 and 100 (including both).
• A) 20 B) 25 C) 24 D) 23
• 2, 3, 5, 7, 11, 13, 17, 19 =8
• 23,29, 31, 37, 41, 43, 47, 53 =8
• 61,67, 71, 73, 79, 83, 89, 97 =8
• 24%

PERCENTAGE
• If 7% of A is 42, then find 27% of A.
• A) 162 B) 62 C) 600 D) 126
• Ans: 162
• Another method
• 7 is prime number and the last digit of given
number is 2. Hence 27% of A also should have
last digit is 2 and so C and D are not possible.
• B is also not possible because it is not divisible by
9(ie 27).

PERCENTAGE
• 4% is equal to one out of every:
• A) 12 B) 20 C) 40 D) 25
• Answer
• 25

PERCENTAGE
• The difference between a discount of 35% and
two successive discounts of 20% and 20% on a
certain bill was Rs. 22. Find the amount of the
bill.
(1) Rs. 1100 (2) Rs. 200 (3) Rs. 2200 (4) Data
inadequate
• Successive 20% discount means 36% discount.
• The difference between 35% and 36% is 1%.
• 1% = 22 means the answer is 2200.

Percentage
• An athlete decides to run the same distance in 1/4th less time that she
usually took.
• By how much percentage will she have to increase her average speed?
• let original speed be s1 and time be t1
• then s1=d/t1 ---eqn 1
• new speed be s2 and time given is 3t1/4
• therefore s2=d/(3t1/4) -----eqn 2
• dividing eqn 2 by eqn 1
• s2=4s1/3
• increased speed = 4s1/3-s1
• =1s1/3
• percent increase=[(1s1/3)/s1]*100
• =33.33%

NEGATIVE POWERS
• What is the value of 0-10?
• i) 0 ii) 1 iii) -10 iv) None of these
• 0.

• 2525 is divided by 24, the remainder is
• 1) 23 2) 22 3) 1 4) 2
• 2525 = (24 + 1)25 = 24K + 1.
• CHOICE 3.

AVERAGE
• The average age of a group of nine men today is
the same as it was six years ago, with one of the
men having been replaced by another much
younger man. The difference in ages of the man
being replaced and the man replacing him is how
many years?
(a) 53 (b) 54 (c) 55 (d) 56
• Six years ago the average is x and now also x. the
number is same. Hence
• No of persons * time elapsed = 9 * 6 = 54.

AGE
• The average age of A and B is 20 years. If C
were to replace A, the average would be 19
and if C were to replace B, the average would
be 21. What are the ages of A, B and C?
(1) 22, 18, 20 (2) 18, 22, 20
(3) 22, 20, 18 (4) 18, 20, 22

RATIO
• If a:b=3:4 and b:c=2:7, then what is the value
of a:b:c?
• A) 3:4:14 B) 3:4:7 C) 6:4:7 D) 6:8:12
• A) 3:4:14

RATIO
• The prices of a refrigerator and a cell phone
are in the ratio 3:2. If the refrigerator costs
Rs. 6000 more than the cell phone, what is
• the price of the cell phone?
• A) Rs. 1200 B) Rs. 12000 C) Rs. 8000 D) Rs.
9000
• Let the price of refrigerator be 3x and
cellphone be 2x.
• X =6000  price of cellphone = 12000.

PROFIT / LOSS
• A man buys a watch for Rs.135. His overhead
expenses were Rs.50. If he sells the watch for
Rs.254, what is his approximate profit/loss in
percent?
• A) 39% profit B) 37% profit C) 37% loss D) 39%
loss
• B) 37% profit
• Wild guess 185 divisible by 37. and S.P > C.P.

PROFIT / LOSS
• After giving a discount of Rs.45 the shopkeeper
still gets a profit of 20%, if the cost price is
Rs.180. Find the mark up percent.
• A) 0.4 B) 0.55 C) 0.45 D) 0.48
• LET THE S.P = X
• C.P = 180. S.P = 180 + 36 = 216.
• M.P = S.P + 45 = 216+45 = 261.
• M.P% = 0.48
PROFIT
COST PRICE
DISCOUNT
MARKED PRICESELLING PRICE

PROFIT / LOSS
• In a shop 80% of the articles are sold at a
profit of 10% and the remaining at a loss of
40%.what is the overall profit/loss?
a.10% profit b.10% loss c.15% profit d. no
profit, no loss
• Option d no profit,no loss
• 80*1.1+20*0.6/100=1

PROFIT / LOSS
• If a pen is being sold at 4% profit instead of 4%
loss the actual profit is Rs 16. What is the
actual cost price of the pen ?
• Let x be the CP.
• (104/100)x - (96/100)x = 16
• Solving we get x = Rs.200.

PROFIT / LOSS
• John buys a cycle for 31 dollars and given a cheque of
amount 35 dollars. Shop Keeper exchanged the cheque
with his neighbor and gave change to John. After 2 days, it
is known that cheque is bounced. Shop keeper paid the
amount to his neighbor. The cost price of cycle is 19 dollars.
What is the profit/loss for shop keeper? a) loss 23 b) gain
23 c) gain 54 d) Loss 54
• CP of cycle = 19$
• SP of cycle = 31$
• Profit = 31$-19$ = 12$
• Again, shopkeeper gave 35$ to neighbour.
• Loss = 35$
• So, net loss = 35$-12$ = 23$

PROFIT & LOSS
-5 x = - 1000 X = 200

• A man can do a job in 25 days. He worked at it
for 15 days and then gave up. After that, B
completed the work in 10 days. Together, both
can finish the job in ________days.
• a) 12 ½days b) 25 days c) 6 days d) 12 days

TIME & WORK
• If 50 people finish a job in 10 days, how long
will it take 20 people to finish the same job?
• A) 25 B) 50 C) 4 D) None of the options
• Answer : A) 25.

TIME – WORK
• Ten men can paint a room in 3 hours. How
many hours would 5 men take to paint the
room, if they work at the same rate?
• A) 6 hours B) 1.5 hours C) 10 hours D) None of
the options
• A) 6 hours.

PIPES & CISTERNS
• Pipe A takes 16 min to fill a tank. Pipes B and C, whose cross-
sectional circumferences are in the ratio 2:3, fill another tank
twice as big as the first. If A has a cross-sectional circumference
that is one-third of C, how long will it take for B and C to fill the
second tank? (Assume the rate at which water flows through a
unit cross-sectional area is same for all the three pipes.)
• a. 66/13 b. 40/13 c. 16/13 d. 32/13
• If A has a cross – sectional circumference is x and area will be
proportional to x2 cross section of C is 3x and area will be
proportional to 9x2 .Hence cross sectional circumference of B will
be (2/3)*3x = 2x so area is proportional to 4x2.
• Pipe A fills in 16 min. Pipe B and C sum of area is proportional to
13x2. will fill the same tank in 16/13 min.
• The second tank is twice big in size require 2 * 16 / 13 = 32/13 min

AGES
• 20) If the ages of a husband and a wife are in
the ratio 5:4 and the sum of their ages is 45,
what is the difference between their ages?
• A) 4 years B) 5 years C) 3 years D) 6 years
• Let the ages be 5x and 4x.
• Sum 9x = 45  x = 5 years.
• Difference between their ages is 5 years.

CLOCK
• Samarth asked his friend: .What will be the
time after 2 hours 30 mins, if the time was
3:45 p.m. half an hour ago?" What should
• be his friend’s reply?
• A) 6:30 p.m. B) 6 p.m. C) 6:45 p.m. D) None of
the options
• Time now = 3:45 + 0:30 = 4:15 min
• After 2:30 time will be 6:45 min.

• Four bells ring at intervals of 10 min, 12 min,
15 min, and 20 min, respectively. If they ring
together at 8 a.m., find out the interval of
time after which they will ring together again.
• a) 9 a.m. b) 10 a.m. c) 11 a.m. d) 1 p.m.

PERMUTATION
• The letters of the word WOMAN are
written in all possible orders and these
words are written out as in a dictionary
,then the rank of the word 'WOMAN' is
• a. 117b. 120 c. 118 d. 119
• 5!=120
120/5=24
• Since W is the last in rank WOMAN is
in the last 24.
• O is in the last rank of the remaining 4
letters. 24/4 = 6
• Therefore WOMAN is in the last 6 in
rank.
• M is between A and N so WOMAN is in
rank 117 or 118.
• A is before N so WOMAN's rank is 117.
There are 120 possible
arrangements of the letters in
WOMAN. Since WOMAN is near the
end, I'll list out the ones after
WOMAN:
WONMA
WONAM
WOMNA
There are only three, so these
account for the 118th, 119th, 120th
words, and it places WOMAN
117th.

PROBABILITY
• What is the probability of getting the sum 5
in two throws of the dice?
• a. 1/12
• b. 1/5
• c. 1/9
• d. None of these

PROBABILITY
• The probability of A solving a problem is 2/3.
The probability of B solving a problem is ¾. If
the same problem is given to both of them,
what is the probability of neither of them
solving it?
(a) 3/4 – 2/3 (b) (1- ¾ ) x 2/3 (c) 1/3 + 1/4
(d) 1/3 x 1/4
•

CUBES
• A 4 inch cube is taken and it is painted in
green colour and then it is cut into 1 inch
cubes. How many cubes are 2 faces painted?
(a) 12 (b) 24 (c) 36 (d) 48

TRAINS
• Two trains start from stations Chennai and
Villupuram spaced 150 km apart at the same time
and speed.
• As the trains start, a bird flies from one train
towards the other and on reaching the second
train; it flies back to the 1st train.
• This is repeated till the trains collide. If the speed
of the train is 75kmph and that of the bird is
100kmph.
• How much did the bird travel till collision?
• (a) 100km (b) 120km (c) 220km (d) 175km

• distance between trains is 150 km.
one train travels 75 km / hr.
other train travels 75 km / hr.
they will meet when the total distance
traveled by both of them is equal to
150 km.
rate * time = distance.
We know that the time that each train
travels will be the same.
We let h = the time each train travels.
train 1 travels 75 km / hr * h hours.
train 2 travels 75km / hr * h hours.
the total distance they travel is 150
km.
75 * h + 75 * h = 150
h = 1
They will meet in 1 hour.
the bird was flying at 100 km/h.
in the same 1 hour the bird flew a
total of 100 km.
bird flies 50 km in one direction, then
travels back 50 km when the trains
meet.

• The difference between the simple interest
and compound interest obtained on a
principal amount at 5% per annum after two
years is Rs.35. What is the principal amount?
• a) Rs.15,000 b) Rs.10,000 c) Rs.14,000 d)
Rs.13,000

ATTENTION TO DETAIL
• Follow the directions given below to answer the questions that follow.
Your answer for each question below would be:
• A. If all the THREE items given in the question are exactly ALIKE
• B. If only the FIRST and SECOND items are exactly ALIKE.
• C. If only the FIRST and THIRD items are exactly ALIKE.
• D. If none of the above
•
• 49 A0067DF667016 A0067DF667016 A0067DF667106
• (a) A (b) B (c) C (d) D
•
• 50 Janmasthami Janmasthhami Jamnasthami
• (a) A (b) B (c) C (d) D
•

• If * stands for +, + stands for -, and - stands for /, then 27/5*8+11-7=?
• (a) 141.4 (b)38.4 (c) 16.4 (d)36.1
•
• If * stands for -, / stands for +, + stands for / and – stands for *, then which
of the following is TRUE?
• A)8/12*4+20-8=18.4 B)12*8/4+20-8= -5.6 C)8*4/12+8-8= -12.2
D)8*8/4+20-8= -4
• (a) A (b) B (c) C (d) D
•
• Identify the correct match 345611242627
• A) 345612414627 B) 345611426227 C)345611624227 D) 345616242227
• (a) A (b) B (c) C (d) D

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