How many integers between 50 and 100, inclusive, are divisible by 2 or

Question

How many integers between 50 and 100, inclusive, are divisible by 2 or 3?

A. 35
B. 37
C. 42
D. 47
E. 52

Crater · Accepted Answer

Numbers which are divisible by 2:
 \frac{{100-50}}{{2}}+1=26

Numbers which are divisible by 3:
 \frac{{99-51}}{{3}}+1=17

Numbers which are divisible by 6:
 \frac{{96-54}}{{6}}+1=8

Hence, 26+17-8=35, Option (A)

andrenoble · Answer

I believe this is a very poorly worded question. Usually, when we use '2 or 3', we don't exclude those divisible by both. 
Definitely not a GMAT-like phrasing

Bunuel · Answer

The question is well-framed. We are indeed interested in counting the numbers that are divisible by 2 or 3. In this context, we may have numbers that are divisible by both, i.e., divisible by 6, but we intend to count them only once. Since both the count of the numbers divisible by 2 (26) and the count of numbers divisible by 3 (17) include the numbers divisible by 6, we need to subtract the count of numbers divisible by 6 (8) from 26 + 17 to prevent double-counting these numbers. Consequently, we get 26 + 17 - 8 = 35.

Hope it's clear.

Prithvi08 · Answer

Its not mentioned 50 - 100 inclusive. So for 2 I took 98-52/2 + 1 = 24 digits. Hence I got 33 as my overall answer. Was it implied somehow that 50 and 100 are to be considered as well?

Mapat · Answer

Divisible by 2:
{(100-50)/2}+1=26
Divisible by 3:
{(99-51)/3}+1=17
Divisible by both 2 & 3 i.e 6:
{(96-54)/6}+1=8
Since numbers divisible by 2 or 3 also divisible by 6
Henceforth divisible by  only 2 :26-8=18
Divisible by  only 3 :17-8=9

Thus total  integers:18+19+8=35

Posted from my mobile device

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How many integers between 50 and 100, inclusive, are divisible by 2 or

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How many integers between 50 and 100, inclusive, are divisible by 2 or

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