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What is the greatest number of markers

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What is the greatest number of markers

by Vincen » 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.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » 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!

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