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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.

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

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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.

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.

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]

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06 Oct 2016, 06:50

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.

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

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13 Jul 2017, 08:01

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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