TNPSC Aptitude Study Material for Group 1, 2, 2A, 4, VAO Exams - 1

Question: 1

Find the least number of five digits which when divided by 8, 12, 16 and 20 leaves remainders 1, 5, 9 and 13 respectively.

(A) 10093

(B) 10073

(C) 10013

(D) 10003

Ans: B

Least number of five digits divisible by L.C.M. of 8, 12, 16, 20 is 10080.

∴ Required number = 10080 - 7 = 10073.

Question: 2

Find the greatest number which will divide 3962, 4085 and 4167 leaving the same remainder in each case.

(A) 37

(B) 39

(C) 41

(D) 43

Ans: C

4085 – 3962 = 123

4167 – 4085 = 82

4167 – 3962 = 205

H.C.F. of 123, 82, and 205 is 41.

Question: 3

Find the least number which when divided by 12, leaves a remainder of 7 when divided by 15, leaves a remainder of 10 and when divided by 16, leaves a remainder of 11.

(A) 115

(B) 215

(C) 235

(D) 247

Ans: C

Here (12 - 7) = 5, (15 - 10) = 5 and (16 - 11) = 5.

∴ Required number = (L.C.M. of 12, 15, 16) – 5

= 240 - 5 = 235.

Question: 4

The L.C.M. and ratio of four numbers are 630 and 2 : 3 : 5 : 7 respectively. The difference between the greatest and least numbers is

(A) 14

(B) 15

(C) 21

(D) 24

Ans: B

Let the numbers be 2x, 3x, 5x and 7x respectively.

Then, their L.C.M. = (2 × 3 × 5 × 7) x = 210x.

[∴ 2, 3, 5, 7 are prime numbers]

So, 210x = 630 or x = 3.

∴ The numbers are 6, 9, 15 and 21.

Required difference = 21 - 6 = 15.

Question: 5

The G.C.D. of 1.08, 0.36 and 0.9 is

(A) 0.03

(B) 0.9

(C) 0.18

(D) 0.108

Ans: C

Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18.

∴ H.C.F. of given numbers = 0.18.

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