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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, 22:36
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5
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Difficulty:

45% (medium)

Question Stats:

65% (02:05) correct 35% (02:32) wrong based on 194 sessions

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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 ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 52285 Re: Danny purchased a number of grease pumps of only two [#permalink] ### Show Tags 20 Dec 2012, 02:00 2 3 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.

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Re: Danny purchased a number of grease pumps of only two  [#permalink]

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Updated on: 19 Dec 2012, 23:48
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 Originally posted by MacFauz on 19 Dec 2012, 23:44. Last edited by MacFauz on 19 Dec 2012, 23:48, edited 2 times in total. Director Joined: 25 Apr 2012 Posts: 683 Location: India GPA: 3.21 WE: Business Development (Other) Re: Danny purchased a number of grease pumps of only two [#permalink] ### Show Tags Updated on: 16 Jan 2014, 02:21 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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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Originally posted by WoundedTiger on 19 Dec 2012, 23:46.
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]

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06 Oct 2016, 05:50
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 $200. Source: HULT nice question! suppose we have x pumps that cost 5$ and y pumps that cost 25$. Danny then spent 5x+25y dollars on the pumps. we also know that the ratio of x to y is 13:7. minimum we can have is 13 x pumps and 7 y pumps. 13*5$ = 65$7*25 = 175$
so minimum spent 240$. 1. total purchase price is less than 400$. only 1 option works... B, C, and E are out.
2. we can have various options...we can have x=13, y=7, or x=26, y=14, etc. not sufficient. D is out.

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Joined: 25 Apr 2016
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Re: Danny purchased a number of grease pumps of only two  [#permalink]

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13 Jul 2017, 07:01
1
Took me a little bit long to solve this one. Actually there is an easier way to approach this question.

We already know the number ratio is 13:7. Therefore, $5 pump's minimum number should be 13, and$25 pump's minimum number should be 7. So the minimum total price is 5*13+25*7=240. And the next possible number of the pumps would be 26 and 14. So the next possible total price is 5*26 + 25*14 = 480. Therefore, as long as the total price less than $400, there is only one possibility: 13$5 pumps, and 7 \$25 pumps.
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Re: Danny purchased a number of grease pumps of only two  [#permalink]

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25 Aug 2018, 08:53
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Re: Danny purchased a number of grease pumps of only two &nbs [#permalink] 25 Aug 2018, 08:53
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