Let m and n be positive integers. Is mn 100?

Question

Let m and n be positive integers. Is mn > 100?
 
(1) m < 100n
(2) m – n = 101

rohit8865 · Answer

(1) if m=n=1 then NO
if m=1 n=1000 then Yes------> not suff

(2) m=100+n
as both are +ve integer numbers m>100
thus mn>100------suff

Ans B

RR88 · Answer

Option B)

Given: m >0 & n >0; Is mn>100 ?

S1 . m<100n
: (m,n) = (100,2); (1,2); . . .
Insufficient

S2 . m - n = 101
: m = 101 + n
: m>100
:m(n)>100(n)>100
:mn>100
Sufficient

BrentGMATPrepNow · Answer

Target question : Is mn > 100? Given : m and n are positive integers. Statement 1 : m < 100n This statement doesn't FEEL sufficient, so let's TEST some values. There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 1 and n = 1. This satisfies statement 1. In this case, mn = (1)(1) = 1. So, mn < 100 Case b: m = 1 and n = 200. This satisfies statement 1. In this case, mn = (1)(200) = 200. So, mn > 100 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2 : m – n = 101 Add n to both sides to get: m = 101 + n Since n is a positive integer, we know that n must be greater than or equal to 1. Since m = 101 + n, we can conclude that m is greater than or equal to 102 . In other words, the SMALLEST value of mn is 102 (when n = 1 and m = 102) So, mn must be greater than or equal to 102. This means we can be certain that mn > 100 Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent

JeffTargetTestPrep · Answer

We are given that m and n are positive and need to determine whether mn > 100.

Statement One Alone:

m < 100n

The information in statement one is not sufficient to answer the question. For instance, if n = 1 and m = 50, then mn IS NOT greater than 100; however, if n = 2 and m = 100, then mn IS greater than 100. We can eliminate answer choices A and D.

Statement Two Alone:

m – n = 101

Using the information in statement two, we see that m = 101 + n. Since both n and m are positive, the minimum value of n is 1 and thus the minimum value of m is 102. We see that in this case, mn = 102 x 1 = 102, which is greater than 100. Since n and m can be greater than 1 and 102, respectively, mn will always be greater than 100. Statement two is sufficient to answer the question.

Answer: B

Let m and n be positive integers. Is mn > 100?

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