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Danny purchased a number of grease pumps of only two

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Danny purchased a number of grease pumps of only two [#permalink] New post 19 Dec 2012, 22:36
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Danny purchased a number of grease pumps of only two possible variants: $5 pumps and $25 pumps. If the ratio between the number of $5 pumps purchased and the number of $25 pumps purchased is 13:7, How many $5 grease pumps did Danny buy?

(1) The total purchase price of the grease pumps Danny bought was less than $400 .
(2) The total purchase price of the grease pumps Danny bought was greater than $200.

Source: HULT
[Reveal] Spoiler: OA
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Re: Danny purchased a number of grease pumps of only two [#permalink] New post 19 Dec 2012, 23:44
Amateur wrote:
Danny purchased a number of grease pumps of only two possible variants: $5 pumps and $25 pumps. If the ratio between the number of $5 pumps purchased and the number of $25 pumps purchased is 13:7, How many $5 grease pumps did Danny buy?
(1) The total purchase price of the grease pumps Danny bought was less than $400 .

(2) The total purchase price of the grease pumps Danny bought was greater than $200.

Source: HULT


Let no. of $25 pumps be T. Then no. of $5 pumps should be \(\frac{13T}{7}\)

\(25*T + 5*\frac{13T}{7} = P\) where T is an positive integer divisible by 7.

=> \(25*T + \frac{65T}{7} = P\)

T = 7, P = 240
T=14, P = 480 and so on.

1) T = 7. Sufficient.

2)T can be 7,14,21 and so on.. Insufficient.

Answer is hence A.
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Last edited by MacFauz on 19 Dec 2012, 23:48, edited 2 times in total.
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Re: Danny purchased a number of grease pumps of only two [#permalink] New post 19 Dec 2012, 23:46
Amateur wrote:
Danny purchased a number of grease pumps of only two possible variants: $5 pumps and $25 pumps. If the ratio between the number of $5 pumps purchased and the number of $25 pumps purchased is 13:7, How many $5 grease pumps did Danny buy?
(1) The total purchase price of the grease pumps Danny bought was less than $400 .

(2) The total purchase price of the grease pumps Danny bought was greater than $200.

Source: HULT



Hi,

Let ' a ' be the no of 5$ pumps and 'b' be the no of 25$ pump. We need to find a

Given a: b :: 13: 7

From St 1, 5a +25b < 400

Since a and b are in the ratio of 13:7, there is only one possible value of a and b i.e 13 and 7 only

So St1 is sufficient

From St 2, 5a +25 b>200. There can be many values of a and b in the ratio of 13:7 ie. 13 and 7 or 26 and 14 etc

Hence ans should be B
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Last edited by WoundedTiger on 16 Jan 2014, 02:21, edited 1 time in total.
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Re: Danny purchased a number of grease pumps of only two [#permalink] New post 20 Dec 2012, 02:00
Expert's post
Danny purchased a number of grease pumps of only two possible variants: $5 pumps and $25 pumps. If the ratio between the number of $5 pumps purchased and the number of $25 pumps purchased is 13:7, How many $5 grease pumps did Danny buy?

Given that \(\frac{({$}5 \ pumps)}{({$}25 \ pumps)}=\frac{13x}{7x}\), for some positive integer \(x\).

(1) The total purchase price of the grease pumps Danny bought was less than $400 --> \(5*13x+25*7x<400\) --> \(x<\frac{5}{3}\). Since \(x\) is an integer then \(x=1\) --> \(({$}5 \ pumps)=13x=13\). Sufficient.

(2) The total purchase price of the grease pumps Danny bought was greater than $200 --> \(5*13x+25*7x>200\) --> \(x>\frac{5}{6}\) --> \(x\) can be any integer more than or equal to 1. Not sufficient.

Answer: A.
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Re: Danny purchased a number of grease pumps of only two [#permalink] New post 04 Jul 2015, 00:08
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Re: Danny purchased a number of grease pumps of only two   [#permalink] 04 Jul 2015, 00:08
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