number systems Model Questions & Answers, Practice Test for ibps so prelims
If x 959 y is divisible by 44 and y >5, then what are values of the digit x and y ?
Answer: (a)
Here 44 = 11 × 4
∴ the number must be divisible by 4 and 11 respectively.
Test of 4 says that 9y must be divisible by 4 and since y > 5, so y = 6
Again , x 9596 is divisible by 11
so x + 5 + 6 = 9 + 9 ⇒ x = 7
Thus x = 7, y = 6
p,q and r are prime numbers such that p < q < r < 13. In how many cases would (p + q + r) also be a prime number ?
Answer: (a)
The prime numbers less than 13 are 2, 3, 5, 7, 11.
Also, using the condition, p < q < r < 13 and p + q + r is a prime number
Hence, only two possible pairs exist i.e. (3, 5, 11) and (5, 7, 11).
The difference between two numbers is 3 and the difference between their squares is 63. Which is the larger number?
Answer: (c)
Let the larger and smaller numbers be x and y respectively.
Then, x – y = 3 . ...(i)
and, $x^2 – y^2 = 63$
⇒ (x + y) (x – y) = 63
⇒ $(x + y) = 63/3 = 21$ ...(ii)
From equation (i) and (ii),
x = 12
The cost of 5 chairs and 8 tables is Rs. 6,574. What is the cost of 10 chairs and 16 tables?
Answer: (b)
∵ 5 chairs + 8 tables = Rs. 6574
∴ 10 chairs + 16 tables = 6574 × 2 = Rs.43148
The product of two consecutive even numbers is 16128. Which is the larger number?
Answer: (a)
Quicker Approach:
The unit's digit of the number 16128 is 8,
From the given answer choices, 126 × 128 = 16128
∴ Required larger number = 128
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