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Q:

Find the number which multiplied by 15 is increased by 56 ?

A) 6	B) 4
C) 3	D) 12

Answer & Explanation Answer: B) 4

Explanation:

Let the number be x. Then,

15x - x = 56

x = 4

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Q:

The probability that a number selected at random from the first 100 natural numbers is a composite number is ?

A) 3/2	B) 2/3
C) 1/2	D) 34/7

Answer & Explanation Answer: A) 3/2

Explanation:

The number of exhaustive events = 100 C₁ = 100.

We have 25 primes from 1 to 100.

Number of favourable cases are 75.

Required probability = 75/50 = 3/2.

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Q:

How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ?

A) 7	B) 9
C) 11	D) 5

Answer & Explanation Answer: B) 9

Explanation:

LCM of 2, 3, 7 is 42.

=> (700 – 300)/42 = 9 22/42 => 9 Numbers.

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Q:

In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case ?

A) 693	B) 741
C) 528	D) 654

Answer & Explanation Answer: C) 528

Explanation:

Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.

Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k

As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)

x = ([(1200)(30)(3)] / (25)(2.5)) - 1200 => x = 528.

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Filed Under: Ratios and Proportions
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Q:

A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?

A) 115	B) 117
C) 116	D) 114

Answer & Explanation Answer: B) 117

Explanation:

Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.

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Filed Under: Area
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Q:

The least number of four digits which is divisible by 4, 6, 8 and 10 is ?

A) 1107	B) 1080
C) 1100	D) 1208

Answer & Explanation Answer: B) 1080

Explanation:

LCM of 4, 6, 8 and 10 = 120
120) 1000 (8
960
------
40

The least number of four digits which is divisible by 4, 6, 8 and 10 => 1000 + 120 - 40 = 1080.

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Q:

The number of permutations of the letters of the word 'MESMERISE' is ?

A) 9!/(2!)^{2}x3!	B) 9! x 2! x 3!
C) 0	D) None

Answer & Explanation Answer: A) 9!/(2!)^{2}x3!

Explanation:

n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = $\frac{9!}{(2!)^{2} \times 3!}$

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Q:

If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?

A) 1	B) 1/2
C) 0	D) 3/5

Answer & Explanation Answer: B) 1/2

Explanation:

The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.

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