number system Model Questions & Answers, Practice Test for ibps rrb po prelims
Consider the following statements:
- There exists a positive real number m such that cos $x = 2^{m + 1}$.
- mn ≥ m + n for all m, n belonging to set of natural numbers.
Answer: (d)
Option (d) is correct.
A canteen requires 4,560 kgs of rice for 30 days. How many kgs, of rice does the canteen require for one week?
Answer: (e)
Required quantity of rice
= ${4560 × 7}/30$ kg = 1064 kg
If $37/13 = 2 + 1/{x + 1/{y + 1/z}}$ where x, y, z are natural numbers, then what is z equal to?
Answer: (a)
$37/13 = 2 + 1/{x + 1/{y + 1/z}}$
⇒ $37/13$ can be expressed as
= $2 + 1/{1 + 2/11} = 2 + 1/{{1 + 1}/{5 + 1/2}}$
Now, this is compared by
$2 + 1/{x + 1/{y + 1/z}} = 2 + 1/{1 + 1/{5 + 1/2}}$
∴ z = 2
The number 2 × 3 × 5 × 7 × 11 + 1
Answer: (c)
2 × 3 × 5 × 7 × 11 gives a number that are, divisible by 2, 3, 5, 7 and 11.
So, (2×3 × 5 × 7 × 11 + 1) gives a number that are not divisible by 2, 3, 5, 7 and 11.
Then, that number is not divisible by 4, 6 8, 9, and 10 as well.
Hence, number '(2 × 3 × 5 × 7 × 11 + 1)' is a prime number.
The sum of three consecutive integers is 39. Which of the following is the largest among the three?
Answer: (e)
Let the three consecutive integers be x, x + 1 and x + 2
According to the question,
x + x + 1 + x + 2 = 39
or, 3x + 3 = 39
or, 3x = 39 - 3 = 36
or, x = $36/3$ = 12
∴ Required largest number = x + 2 = 12 + 2 = 14
Also, from the given alternatives, it could be ascertainal that
12 + 13 + 14 = 39
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