14
Q:

# The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

 A) 74 B) 94 C) 184 D) 364

Answer:   D) 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.

$\inline \therefore$Required number = (90 x 4) + 4   = 364.

Q:

If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to ?

 A) 13/125 B) 14/57 C) 11/120 D) 16/41

Answer & Explanation Answer: C) 11/120

Explanation:

Let the numbers be a and b.
We know that product of two numbers = Product of their HCF and LCM
Then, a + b = 55 and ab = 5 x 120 = 600.
=> The required sum = (1/a) + (1/b) = (a+b)/ab
=55/600 = 11/120

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1 54
Q:

The largest measuring cylinder that can accurately fill 3 tanks of capacity 98, 182 and 266 litres each, is of capacity ?

 A) 7 lts B) 14 lts C) 98 lts D) 42 lts

Answer & Explanation Answer: B) 14 lts

Explanation:

To know the the measuring cylinder that can fill all the given capacities , they must be divisible by the required number.

98,182,266 all are divisible by 14
So  14 litres  is the largest cylinder that can fill all the given cylinders.

(or)

The other method is take HCF of all given capacities i.e 98, 182 and 266.

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2 71
Q:

If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. What is the sum of the digits of N ?

 A) 6 B) 8 C) 4 D) 9

Answer & Explanation Answer: C) 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 ) = 4

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4 39
Q:

Find the greatest number that will divide 964, 1238 and 1400 leaving remainder of 41,31 and 51 respectively ?

 A) 64 B) 69 C) 71 D) 58

Answer & Explanation Answer: C) 71

Explanation:

To find the greatest number which divides the numbers 964, 1238 and 1400 leaving the remainders 41, 31 and 51 is nothing but the HCF of (964 - 41), (1238 - 31), (1400 - 51).

Therefore, HCF of 923, 1207 and 1349 is 71.

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2 130
Q:

A student can divide her books into groups of 5, 9 and 13. what is the smallest possible number of the books ?

 A) 487 B) 585 C) 635 D) 705

Answer & Explanation Answer: B) 585

Explanation:

The smallest possible number of books = L.C.M of 5, 9 and 13.
Therefore, L.C.M of 5,9 and 13 is = 5 x 9 x 13 = 585.

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4 85