If R = M/N, is R ≤ M? (1) M 40 (2) 0

Question

If R = M/N, is R ≤ M?

(1) M > 40
(2) 0 < N ≤ 15

Gladiator59 · Answer

R = M/N can we re-written as...
R*N = M

Now, if N = 1 -> R = M.

N>1 -> R <M ... (  R multiplied by something larger than 1 is equal to M means R was less than M to begin with)

So for R ≤ M -> N >= 1

St1. Not sufficient as no info about N.

St2. Not sufficient as N could be less than 1 or greater than 1.

(1) + (2) together gives no more information.

Hence, Option (E) is our choice.

Best,
Gladi

eswarchethu135 · Answer

Statement 1) Let's take M as 45.

R =  \frac{45}{N}

If N = 1, then R = 45 -->  R\leq{M}  --> True

If N =  \frac{1}{3} , then R = 130 -->  R\leq{M}  --> Not True.  INSUFFICIENT

Statement 2) No M value. So clearly  INSUFFICIENT

1) + 2) Both the values of N = 1 and  \frac{1}{3}  fall in the range of  0<N\leq{15} . Still we dont have a unique answer.

OPTION :  E

stoned · Answer

Am I right here? If R = \frac{M}{N} , is R ≤ M ? (1) M > 40 (2) 0 < N ≤ 15 Substituting R = \frac{M}{N} in R ≤ M \frac{M}{N}≤M --> M(\frac{1}{N}-1)≤0 it means either M and \frac{1}{N}-1 have opposite signs or one of them is Zero. Statement 1- M>40 ---> No information about N, therefore not sufficient. Statement 2- 0 < N ≤ 15 ---> No information about M, therefore not sufficient. Statement 1 & 2- M is positive but \frac{1}{N}-1 can be Positive (for 01 ) therfore both Statemens together not sufficent. Answer is E

If R = M/N, is R ≤ M? (1) M > 40 (2) 0 < N ≤ 15

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