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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