CAT Aptitude-Numerical Contributed by Model papers updated on Oct 2020
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CAT aptitude questions for practice-Numerical Ability solved question papers.1 What will come in place of question mark(?) in the following questions:- 26 x 451 - ? = 61036523

1 What will come in place of question mark(?) in the following questions:-

 26 x 451 - ? = 61036523
5623
Answer:5623
Explanation:26 x 451 - ? = 6103
--> 11726 - 7 = 6103--> ? = 11726 - 6103 = 5623 6251
4563
None of these

Qn.2 47 x 251 - 3695 = ?
8102
8100
9208
7891
None of these

Qn.3 (12.25 x 4.02 - 14.26) x ? = 699.7
10
20
Answer:20
Explanation:(12.25 x 4.02 - 14.26) x ? = 699.7
=> (49.245 - 14.26) x ? = 699.7=> 34.985 x ? = 699.7 --> 699.7/34.985 = 2015
25
None of these

Qn.4 ? % of 452 = 311,88
67
52
59
71
None of these
Answer:None of these
Explanation:(452 x ?)/100 = 311,88
--> ? = (311,88 x 100)/452 = 69

Qn.5
89% of ? + 365 = 1075.22
798
Answer:798
Explanation:(? x 89)/100 = 1075.22 - 365 = 710.22
--> (710.22 x 100)/89 = 798897
898
752
None of these

Qn.6
3695.12 + 4458.02 - ? = 7592.14
465
651
575
561
Answer:561
Explanation:8153.14 - ? = 7592.14
--> ? = 8153.14 - 7592.14= 561None of these

Qn.7     ? x 35 + 263 = 2680
79
63
75
68
None of these
Answer:None of these
Explanation:? x 35 = 2680 - 265 = 2415
--> ? = 2415/35 = 69

Qn.8     34 = 7^87
56
65
2631
3136
Answer:3136
Explanation: square root of ? - 34 = 22
--> square root of ? = 34 + 22 = 56--> ? = 56 x 56 = 3136None of these

Qn.9     11 x (468 /26) = ? + 13
175
185
Answer:185
Explanation:(11 x 468)/26 = ? + 13
--> 198 = ? + 13--> ? = 198 - 13 = 185211
201
None of these

Qn.10         ?% of 550 - 12% of 150 = 125
54
44
16
36
None of these
Answer:None of these
Explanation:[(550 x ?)/ 100] - [(150 x 12)/100] = 125
--> [(550 x ?)/100] - 18 = 125--> [(550 x ?)/100] = 125 + 18 = 143--> ? = [(143 x 100)/550] = 26


Qn.11     2234 + 84 - 1273 = ? + 123
922
Answer:922
Explanation:--> 1045 = ? + 123
--> ? = 1045 - 123 = 922932
822
832
None of these

Qn.12     ? / 12 x 17 = 238
178
218
128
208
None of these
Answer:None of these
Explanation:( ?/12) x 17 = 238
--> ? = (238 x 12)/17 = 168


Qn.13     135 - 924 / 132 x 6 = ?
93
Answer:93
Explanation:? = 135 - (924/132) x 6
= 135 - 42 = 93103
43
123
None of these

Qn.14     750.46 + 114.09 - 840.04 = ? - 13.09
37.06
63.78
37.60
Answer:37.60
Explanation:750.46 + 114.09 - 840.04 = ? - 13.09
--> 24.51 = ? - 13.09--> ? = 24.51 + 13.09 = 37.6067.38
None of these


Qn.15 64% of 750 / 4 = ? / 5
24
48
300
600
Answer:600
Explanation:(64/100) x (750/4) = ?/5
--> 120 = ?/5--> ? = 120 x 5 = 600None of these

Qn.16
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
14 years
18 years
20 years
22 years
Answer:22 years
Explanation:Let the son's present age be x years.
Then, man's present age = (x + 24) years.Therefore, (x + 24) + 2 = 2(x + 2)--> x + 26 = 2x + 4--> x = 22.None of these

Qn.17
At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
12 years
15 years
Answer:15 years
Explanation:Let the present ages of Arun and Deepak be 4x years and 3x years respectively.
Then, 4x + 6 = 26 <---> 4x = 20x = 5.Therefore, Deepak's age = 3x = 15 years.19 and half
21 years
None of these

Qn.18
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform ?
120 m
240 m
Answer:240 m
Explanation:Speed = 54 x (5/18) m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.Let the length of the platform be x metres.Then, (x + 300)36 = 15---> x + 300 = 540---> x = 240 m.300 m
Data Inadequate
None of these

Qn.19
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train ?
230 m
240 m
260 m
270 m
Answer:270 m
Explanation:Speed = 72 x (5/18) m/sec = 20 m/sec.
Time = 26 sec.Let the length of the train be x metres.Then, (x + 250)/26 = 20---> x + 250 = 520---> x = 270.None of these

Qn.20
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit ?
Rs. 2000
Answer:Rs. 2000
Explanation:Let C.P. be Rs. x.
Then, [(1920 - x)/x]100 = [(x - 1280)/x]100---> 1920 - x = x - 1280---> 2x = 3200---> x = 1600Therefore, Required S.P. = 125% of Rs. 1600= Rs. (125/100) x 1600= Rs 2000.Rs. 2200
Rs. 2400
Data Inadequate
None of these

Qn.21
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize ?
1/10
2/5
2/7
Answer:2/7
Explanation:P (getting a prize) = 10/(10 + 25) = 10/35 = 2/7
5/7
None of these

Qn.22
Two dice are tossed. The probability that the total score is a prime number is:
1/6
5/12
Answer:5/12
Explanation:Clearly, n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.Then E = { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5) }Therefore, n(E) = 15.Therefore, P(E) = n(E)/n(S)= 15/36= 5/121/2
7/9
None of these

Qn.23
If Rs. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4 , then the first part is:
Rs. 182
Rs. 190
Rs. 196
Rs. 204
Answer:Rs. 204
Explanation:Given ratio = 1/2 : 2/3 : 3/4 = 6 : 8 : 9.
Therefore, 1st part = Rs. 782 x (6/23)= Rs. 204None of these

Qn.24
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share ?
Rs. 500
Rs. 1500
Rs. 2000
Answer:Rs. 2000
Explanation:Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000---> x = 1000.Therefore, B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.Rs. 3000
None of these

Qn.25
A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:
100 m
Answer:100 m
Explanation:When B runs 25 m, A runs (45/2) m.
When B runs 1000 m, A runs [(45/2) x (1/25) x 1000]m = 900 m.Therefore, B beats A by 100 m.111 1/9m
25 m
50 m
None of these

Qn.26
If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
Rs. 20
Rs. 21.81
Rs. 22
Rs. 18.33
Answer:Rs. 18.33
Explanation:S.I. on Rs. (110 - 10) for a certain time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.T.D. on Rs. 120 = Rs. (120 - 100) = Rs. 20.T.D. on Rs. 110 = Rs. (20/120) x 110 = Rs. 18.33None of these

Qn.27
A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
gains Rs. 55
gains Rs. 50
Answer:gains Rs. 50
Explanation:S.P. = P.W. of Rs. 2200 due 1 year hence
= Rs. [(2200 x 100)/100 + (10 x 1)]= Rs. 2000.Therefore,Gain = Rs. (2000 - 1950) = Rs. 50.loses Rs. 30
gains Rs. 30
None of these

Qn.28
Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit ?
Rs. 8600
Rs. 8620
Rs. 8820
Answer:Rs. 8820
Explanation:Amount = Rs. {8000 x [1 + (5/100)^2]}
= Rs. {8000 x (21/20) x (21/20)} = Rs. 8820.None of these

Qn.29
The H.C.F. of 9/10 , 12/25 , 18/35 and 21/40 is:
3/5
252/5
3/1400
Answer:3/1400
Explanation:Required H.C.F. = (H.C.F. of 9, 12, 18, 21)/(L.C.M of 10, 25, 35, 40) = 3/1400
63/700
None of these

Qn.30
Which of the following has the most number of divisors ?
99
101
176
Answer:176
Explanation:99 = 1 x 3 x 3 x 11
101 = 1 x 101176 = 1 x 2 x 2 x 2 x 2 x 11182 = 1 x 2 x 7 x 13So, divisors of 99 are 1, 3, 9, 11, 33, 99Divisors of 101 are 1 and 101Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.Hence, 176 has the most number of divisors.182
None of these

Qn.31
On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006 ?
Sunday
Thursday
Tuesday
Friday
Answer:Friday
Explanation:The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.But, 8th Dec, 2007 is Saturday.Therefore, 8th Dec, 2006 is Friday.



Qn.32 A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m^3) is:
4830
5120
Answer:5120
Explanation:Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,h = 8 m.Therefore, Volume of the box = (32 x 20 x 8) m^3 = 5120 m^3.6420
8960

Qn.33
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:
57
67
77
Answer:77
Explanation:Money collected = (59.29 x 100) paise = 5929 paise.
Therefore, Number of members = squareroot(5929) = 77.87

Qn.34
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour ?
9
10
Answer:10
Explanation:Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54) x 60 min = 10 min.12
20

Qn.35
A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:
14 km
15 km
16 km
Answer:16 km
Explanation:Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.So, (x/4) + (61 -x)/9 = 9---> 9x + 4(61 -x) = 9 x 36---> 5x = 80---> x = 16 km.17 km

Qn.36
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number ?
69
78
96
Cannot be determined
Answer:Cannot be determined
Explanation:Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x - y = 3 or y - x = 3.Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.So, the number is either 96 or 69.Hence, the number cannot be determined.None of these

Qn.37
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500 ?
Rs. 4991
Answer:Rs. 4991
Explanation:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Therefore, Required sale = Rs. [ (6500 x 6) - 34009 ]= Rs. (39000 - 34009)= Rs. 4991.Rs. 5991
Rs. 6001
Rs. 6991

Qn.38
The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is :
74
94
184
364
Answer:364
Explanation:L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.Least value of k for which (90k + 4) is divisible by 7 is k = 4.Therefore, Required number = (90 x 4) + 4 = 364.
Qn.39
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
2010
2011
Answer:2011
Explanation:Suppose commodity X will cost 40 paise more than Y after z years.
Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.400.25z = 0.40 + 2.10z = (2.50/0.25) = (250/25) = 10.Therefore, X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.2012
2013

Qn.40
Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
4
Answer:4
Explanation:N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 45
6
8

Qn.41
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
76 kg
76.5 kg
85 kg
Answer:85 kg
Explanation:Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.Data Inadequate
None of these

Qn.42
Difference between the digits of a two digit number is 5 and the digit in the unit's place is six times the digit in the ten's place. What is the number ?
27
72
16
Answer:16
Explanation:Of the given alternatives, required number = 16
Unit's digit = 6 = Ten's digit x 6 and 6 - 1 = 561
None of these

Qn.43
Find the average of the following set of numbers.
132, 148, 164, 128, 120, 136142
136
138
Answer:138
Explanation:Required average : (132 + 148 + 164 + 128 + 120 + 136)/6
= 828/6 = 138144
None of these

Qn.44
Sum of five consecutive even numbers is 380. What is the second number in ascending order ?
76
78
74
Answer:74
Explanation:Sum of five consecutive even numbers = 380
Therefore, Third even number = 380/5 = 76Therefore, Required second number = 76 - 2 = 7472
None of these

Qn.45
Beena and Meena started a boutique investing amounts of Rs. 35,000 and Rs. 56,000 respectively. If Beena's share in the profit earned by them is Rs. 45,000, what is the total profit earned ?
Rs. 81,000
Rs. 1,27,000
Rs. 72,000
Rs. 1,17,000
Answer:Rs. 1,17,000
Explanation:Ratio of the profits of Beena and Meena = 35000 : 56000 = 5 : 8
If the total profit be Rs x, then5x/13 = 45000--> x = (45000 x 13)/5= Rs 117000None of these

Qn.46
Simple interest accrued on an amount in eight years at the rate of 11 p.c.p.a. is Rs. 57,200. What was the principal amount ?
Rs. 72,000
Rs. 82,000
Rs. 75,000
Rs. 65,000
Answer:Rs. 65,000
Explanation:Principal = (SI x 100)/(Time x Rate)
= (57200 x100)/(8 x 11)= Rs 65,000None of these

Qn.47
Nandkishore gives 35% of the money he had to his wife and gave 50% of the money he had to his sons. Remaining amount of Rs. 11,250 he kept for himself What was the total amount of money Nandikishore had ?
Rs. 63,750
Rs 75,000
Answer:Rs 75,000
Explanation:Let Nandkishore had initially Rs. x.
Saving percent = 15%Therefore, x * (15/100) = 11250--> x = (11250 * 100)/15= Rs 75,000Rs. 73,650
Rs. 72,450
None of these

Qn.48
16 men can complete a piece of work in 7 days. In how many days will 28 men complete the same work ?
6 days
8 days
3 days
4 days
Answer:4 days
Explanation:M1 D1 = M2 D2
--> 16 x 7 = 28 x D2--> D2 = (16 x 7)/28 = 4 daysNone of these

Qn.49
Vandana sells an article for Rs. 3240 and earns a profit of 20 %. What is the cost price of the article ?
Rs. 2,800
Rs. 2,820
Rs. 2,750
Rs. 2,700
Answer:Rs. 2,700
Explanation:Cost price of the article
= Rs (100/120) x 3240= Rs 2700None of these

Qn.50
The 56% of a number is less than its 72% by 56. Wh at is 70% of that number ?
300
235
240
350
None of these
Answer:None of these
Explanation:Let the number be x.
Therefore, (72 - 56) * (1/100) * x = 56--> x = (56 * 100)/16 = 350Therefore, 70% of 350= (350 x 70)/100 = 245

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