number system Model Questions & Answers, Practice Test for ibps so prelims 2023
ibps so prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Ratio & Proportion
Profit & Loss
Time & Work
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Quadratic Equations
A number N when factorized can be written as N = $p_1^4 × p_2^3 × p_3^7$ . Find the number of perfect squares which are factors of N. (The 3 prime numbers $p_1 , p_2 , p_3$ > 2)
Answer: (b)
The powers of $p_1$ can be 0, 2 or 4 i.e., 3, powers of $p_2$ can be 0,2 i.e., 2, Powers of $p_3$ can be 0, 2, 4 or 6 i.e.,4.
Hence, a combination of these powers gives 3 × 2 × 4 i.e., 24 numbers.
So, there are 24 perfect squares that divide N.
Consider the following statements:
- Every natural number is a real number.
- Every real number is a rational number.
- Every integer is a real number.
- Every rational number is a real number
Answer: (a)
Option (b) is correct.
The sum of the squares of two consecutive even numbers is 6500. Which is the smaller number?
Answer: (d)
Let the two numbers be x and (x + 2).
Then, $x^2 + (x + 2)^2$ = 6500
$x^2 + x^2 + 4x + 4 = 6500$
$2x^2 + 4x – 6496 = 0$
$x^2 + 2x – 3248 = 0$
$x^2 + 58x – 56x – 3248 = 0$
(x + 58) (x – 56) = 0
x = 56
The number obtained by interchanging the digits of a two digit number is less than the original number by 63. If the sum of the digits of the number is 11, what is the original number?
Answer: (a)
Suppose the number is 10x + y
∵ (10 x + y) – (10y + x) = 63
9x – 9y = 63
x – y = 7 ⇒ x + y = 11
∴ x = 9, y = 2
So, required number = 92
Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has ?
Answer: (a)
Let total number of goats be x.
Then, total number of hens = (90 – x)
So, x × 4 + (90 – x) × 2 = 248
4x – 2x = 248 – 180
$x = 68/2$ = 34
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