**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

Q**n.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