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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]

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19 Dec 2012, 23:36
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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 Math Expert Joined: 02 Sep 2009 Posts: 34449 Followers: 6273 Kudos [?]: 79598 [1] , given: 10022 Re: Danny purchased a number of grease pumps of only two [#permalink] ### Show Tags 20 Dec 2012, 03:00 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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]

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20 Dec 2012, 00:44
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. _________________ Did you find this post helpful?... Please let me know through the Kudos button. Thanks To The Almighty - My GMAT Debrief GMAT Reading Comprehension: 7 Most Common Passage Types Last edited by MacFauz on 20 Dec 2012, 00:48, edited 2 times in total. Moderator Joined: 25 Apr 2012 Posts: 728 Location: India GPA: 3.21 WE: Business Development (Other) Followers: 42 Kudos [?]: 615 [0], given: 723 Re: Danny purchased a number of grease pumps of only two [#permalink] ### Show Tags 20 Dec 2012, 00:46 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, 03:21, edited 1 time in total.
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Re: Danny purchased a number of grease pumps of only two [#permalink]

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04 Jul 2015, 01:08
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Re: Danny purchased a number of grease pumps of only two   [#permalink] 04 Jul 2015, 01:08
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# Danny purchased a number of grease pumps of only two

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