If m and x are positive integers, what is the value of x?

Question

(1) x is a positive multiple of 8m.
(2) x is a factor of 8m.

AR15J · Answer

m and x are positive integers.

Statement 1: x is a positive multiple of 8m.

x=8m*p where p can be any positive integer,

Statement 1 alone is not sufficient as m and p can be any positive integer.

Statement 2: x is a factor of 8m.

8m=x*q where q can be any positive integer.

Statement 2 alone is not sufficient as m and q can be any positive integer.

Combining both statements:

x is a positive multiple of 8m and x is a factor of 8m: It can only be possible when x=8m. For instance, 2 is the multiple of 2 and 2 is a factor of itself i.e. 2

But, m can be any positive integer. Combining both statements do not give us one value of x, so both statements are not sufficient to solve the problem.

Correct answer is E

-------
+1 Kudos if you like the post

yezz · Answer

from 1

x = (8m)k , k is a +ve integer .... insuff x = {8,16,...etc)

from 2

x is 1 or 2 or 4 or 8 or m or 2m or 4m or 8m or m.. insuff

both

x is both a multiple and a factor of 8m , thus x = 8m ... insuff

E

saurabhsavant · Answer

I guess C is the answer,
From 1) x=8,16,24,32...etc
From 2) x = 1, 2, 4, 8, 16..etc depending on the vakue of m

Combining 1 and 2 the statement becomes for waht valu of m is x both a multiple and a factor of 8m...
for m = 1 we get x=8 which a both a multiple and a factor of 8...Am I right?

chetan2u · Answer

Hi
 If a number is both MULTIPLE and FACTOR OF something, the number is that something

so what you get combined is x=8m..
so x will vary with m
insuff

hope it helps

PoojanB · Answer

St 1: x changes with value of m hence st 1 NS
St 2: Again, x can take any of the value from factor of 8m. Hence NS

Combining both the st, we get x=8m which still leaves us with number of possibilities as we don't know the exact value of m.

So the answer is E

If m and x are positive integers, what is the value of x?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If m and x are positive integers, what is the value of x?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards