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Quantitative Reasoning – Practice – How many integers …!

PSA_LEVEL-UP_QNR1) Consider the set of integers {1, 2, 3, …, 5000}. The number of integers that is divisible by neither 3 nor 4 is:

A) 1668
B) 2084
C) 2500
D) 2916

Ans: Number of integers = 5000

Multiples of 3 start with 3*1 and end in 3*1666. Total number of integers divisible by 3= 1666

Multiples of 4 start with 4*1 and end in 4*1250. Total number of integers divisible by 4= 1250

Multiples of 3 and 4 both start with 12*1 and end in 12*416. Total number of integers divisible by 12= 416

Total number of integers divisible by 3 or 4= 1666 + 1250 – 416 = 2916 – 416 = 2500

Out of the given 5000, 2500 are divisible by 3 or 4 and 2500 are not divisible by neither 3 nor 4. Option C.

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