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03 Feb 2015, 10:01
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
56% (01:44) correct
44%
(01:31)
wrong
based on 484
sessions
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Danny bought some packets of pens, each packet at a cost of $4, and some packets of pencils, each packet at a cost of $3. What is the ratio of the number of packets of pens to the number of packets of pencils purchased?
(1) He paid $24 for the entire purchase.
(2) He spent equal amounts of money on pens and pencils.
(1) He paid $24 for the entire purchase.
(2) He spent equal amounts of money on pens and pencils.
04 Feb 2015, 12:41
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If the number of packets of pens =x
If the number of Packets of pencils = y
We need to find x:y
Statement 1:
Total cost is given by: 4x + 3y = 24
the only integral values of (x,y) that satisfies the above equation is (3,4) and (6,0) but since it is mentioned that he did buy some packets of pencils we have to assume that y > 0. Hence x:y = 3:4 -- Sufficient
Statement 2
it is given that 4x=3y
hence x:y=3:4 -- Sufficient
Hence D
If the number of Packets of pencils = y
We need to find x:y
Statement 1:
Total cost is given by: 4x + 3y = 24
the only integral values of (x,y) that satisfies the above equation is (3,4) and (6,0) but since it is mentioned that he did buy some packets of pencils we have to assume that y > 0. Hence x:y = 3:4 -- Sufficient
Statement 2
it is given that 4x=3y
hence x:y=3:4 -- Sufficient
Hence D
General Discussion
03 Feb 2015, 12:18
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The problem states Danny both "some" pens and "some" pencils, so he bought at least one packet of each.
Statement 1 [SUFFICIENT] - As the packets must be represented as integers, the only combination that satisfies this statement is 3 packets of pens and 4 packets of pencils => $4(3) + $3(4) = $24 and the ratio of pens to pencils is 3:4
Statement 2 [INSUFFICIENT] - This just means that half of the total amount spent is a multiple of 3 and 4. This still leaves many possible totals ($24, $48, $96) so there are still many possible combinations.
The correct answer is A.
Statement 1 [SUFFICIENT] - As the packets must be represented as integers, the only combination that satisfies this statement is 3 packets of pens and 4 packets of pencils => $4(3) + $3(4) = $24 and the ratio of pens to pencils is 3:4
Statement 2 [INSUFFICIENT] - This just means that half of the total amount spent is a multiple of 3 and 4. This still leaves many possible totals ($24, $48, $96) so there are still many possible combinations.
The correct answer is A.
