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Manager  Joined: 05 Nov 2012
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Danny purchased a number of grease pumps of only two  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 65% (02:05) correct 35% (02:32) wrong based on 200 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 V Joined: 02 Sep 2009 Posts: 58453 Re: Danny purchased a number of grease pumps of only two [#permalink] Show Tags 3 4 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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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 20 Dec 2012, 00:44. Last edited by MacFauz on 20 Dec 2012, 00:48, edited 2 times in total. Director  Joined: 25 Apr 2012 Posts: 660 Location: India GPA: 3.21 WE: Business Development (Other) Re: Danny purchased a number of grease pumps of only two [#permalink] Show Tags 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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Re: Danny purchased a number of grease pumps of only two  [#permalink]

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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.

A is the answer.
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Re: Danny purchased a number of grease pumps of only two  [#permalink]

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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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_________________ Re: Danny purchased a number of grease pumps of only two   [#permalink] 25 Aug 2018, 09:53
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