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.
What is the greatest number of markers
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Hi Vincen,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.
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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