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A composite number n can be represented as a product of two

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by Max@Math Revolution » Mon Sep 16, 2019 10:51 pm

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[GMAT math practice question]

A composite number n can be represented as a product of two different primes a and b (n=ab). If 100 < nab < 200, what is n-a-b?

A. 4
B. 5
C. 6
D. 7
E. 8
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by Max@Math Revolution » Wed Sep 18, 2019 11:56 pm
=>

Since we have n = ab, we have nab = n^2 and 100 < n^2 < 200.
Perfect squares between 100 and 200 are 11^2 = 121, 12^2 = 144, 13^2 = 169 and 14^2 = 196.
n = 14 is the only one among those numbers, 11, 12, 13 and 14 which is a product of two different prime integers.
Thus we have a=2, b=7 or a=7, b=2.
Thus n - a - b = n - ( a + b ) = 14 - (2 + 7) = 14 - 9 = 5.

Therefore, B is the answer.
Answer: B
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by deloitte247 » Sat Sep 21, 2019 2:23 am
$$Given\ that\ n=ab,\ and\ nab=n^2\ and\ 100<n^2<200$$
Perfect squares between 100 and 200 are $$11^2=121,\ \ 12^2=144,\ \ 13^2=169\ and\ 14^2=196$$

Product of 2 numbers that gives n =>
For 11 = 1 * 11 and 1 is not a prime numbers
For n = 12 = 2 * 6 , 3 * 4 This is not a product of two different prime integers
For n = 13 = 1 * 13 and 1 is not a prime number
For n = 14 = 2 * 7 or 7 * 2 This is a product of two different prime integers

Therefore, we have a = 2; b = 7 or a = 7; b = 2
Hence, n - a - b = 14 - 2 - 7
= 12 - 7
= 5
Answer = option B
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