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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]  19 Dec 2012, 22:36
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Difficulty:

5% (low)

Question Stats:

44% (02:44) correct 55% (01:26) wrong based on 9 sessions
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 Moderator Joined: 02 Jul 2012 Posts: 1119 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Followers: 48 Kudos [?]: 496 [0], given: 90 Re: Danny purchased a number of grease pumps of only two [#permalink] 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.

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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]  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 _________________ “Many of life's failures are people who did not realize how close they were to success when they gave up.” “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.” “Renew, release, let go. Yesterday’s gone. There’s nothing you can do to bring it back. You can’t “should’ve” done something. You can only DO something. Renew yourself. Release that attachment. Today is a new day!” Last edited by WoundedTiger on 16 Jan 2014, 02:21, edited 1 time in total. Math Expert Joined: 02 Sep 2009 Posts: 16790 Followers: 2770 Kudos [?]: 17572 [0], given: 2184 Re: Danny purchased a number of grease pumps of only two [#permalink] 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.

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Re: Danny purchased a number of grease pumps of only two   [#permalink] 20 Dec 2012, 02:00
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