NIMCET 2018 — Logical Reasoning PYQ

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Question

NIMCET 2018 — Logical Reasoning PYQ

NIMCET | Logical Reasoning | 2018

Let S be the set of integers x such that
i. 100 ≤ x ≤ 200
ii. x is odd and
iii. x is divisible by 3 but not by 7
How many elements does S contain?

Choose the correct answer:

Explanation

Correct Option - 4

Given:
x is odd
x is divisible by 3 but not by 7
100 ≤ x ≤ 200
Calculation:
Numbers that are divisible by 3 and not by 7,
And also 100 ≤ x ≤ 200 are,
⇒ [(by 3) – (by 6) – (by 21) + (by 42)]
Numbers 100 ≤ x ≤ 200 that are divisible by 3,
⇒ 200/3 - 100/3
⇒ 66 – 33
⇒ 33
Numbers 100 ≤ x ≤ 200 that are divisible by 6,
⇒ 200/6 – 100/6
⇒ 33 – 16
⇒ 17
Numbers 100 ≤ x ≤ 200 that are divisible by 21,
⇒ 200/21 – 100/21
⇒ 9 – 4
⇒ 5
Numbers 100 ≤ x ≤ 200 that are divisible by 42,
⇒ 200/42 – 100/42
⇒ 4 – 2
⇒ 2
[(by 3) – (by 6) – (by 21) + (by 42)]
⇒ 33 – 17 – 5 + 2
⇒ 13
∴ S will contain 13 terms.