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## What is the greatest number of markers

This topic has 1 expert reply and 0 member replies

### Top Member

Vincen Legendary Member
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#### What is the greatest number of markers

Fri Sep 15, 2017 7:37 pm
What is the greatest number of markers that can be purchased for $18? (1) 4 markers or 6 pens or 12 pencils can be purchased for$36

(2) If the cost of each marker is increased by $3, 5 less markers can be purchased for$180

The OA is D.

Really statement (2) alone is sufficient? Can anyone explain it to me.

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Sat Sep 16, 2017 3:50 am
Vincen wrote:
What is the greatest number of markers that can be purchased for $18? (1) 4 markers or 6 pens or 12 pencils can be purchased for$36

(2) If the cost of each marker is increased by $3, 5 less markers can be purchased for$180

The OA is D.

Really statement (2) alone is sufficient? Can anyone explain it to me.
Hi Vincen,

Yes, Statement 2 itself is also sufficient.

Say the price of a marker is $x. Thus, in$180, one can buy 180/x numbers of markers.

Given that the new price is $(x+3), one would buy five fewer markers than before. Thus, Number of markers before = Number of markers after + 5 180/x = 180/(x + 3) + 5 => 180/x - 180/(x + 3) = 5 180[{(x+3) - x}/x(x+3)] = 5 36[{x + 3 - x}/x(x+3)] = 1; '180' is camcelled by '5.' 36[3/x(x+3)] = 1 x(x + 3) = 36 x 3 x(x + 3) = 12 x 3 x 3 x(x + 3) = 9 x 12 => x =$9

Thus, one can buy $18/$9 = 2 numbers of markers. Sufficient.

Hope this helps!

-Jay
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