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A certain fruit stand sold apples for $0.70 each and bananas

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Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] New post 25 May 2011, 01:55
mrsmarthi wrote:
A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?

a) 10
b) 11
c) 12
d) 13
e) 14.


63:

Just recall table of 7 and stop where units digit is either 3 or 8.

7,14,21,28(We got it). Four 7's. Rest 5's.

Another answer could be 9.
7*9=63 but buyer purchased both. Ignore this.
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Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] New post 03 Dec 2011, 10:07
Here's a quick way to do this one.

7a + 5b=63

You basically subtract 7 from 63 which leads us to

7 + 56 = 63. Is 56 a multiple of 5? No. Then move on to
2 (7 ) + 49 = 63. Is 49 a multiple of 5? No. Then move on to
3 (7 ) + 42 = 63. Is 42 a multiple of 5? No. Then move on to
4 (7 ) + 35 = 63. Is 35 a multiple of 5? Yes. Save this answer
5 (7) + 28 = 63. Is 28 is a multiple of 5? No. Then move on to
6 (7) + 21 = 63. Is 21 a multiple of 5? No. Then move on to
7 (7) + 14 = 63. Is 14 a multiple of 5? No. Then move on to
8 (7) + 7 = 63. Is 7 a multiple of 5? No. Then move on to
9 (7) + 0. 63. Does not work because he/she bought both Apples and Bananas.

So the answer is 4 + 7 = 11.
The reason you start with 7 in your assessment is that it's the bigger number and 63 is a multiple of 7. This is my opinion, I hope it helps.
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Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] New post 22 Aug 2014, 09:39
VeritasPrepKarishma wrote:
n2739178 wrote:

this is really doing my head in!



I have put up this theory on this link:
http://gmatquant.blogspot.com/2010/11/integral-solutions-of-ax-by-c.html

See if it makes sense now.
If there are doubts, get back to me on my blog itself or here...


Hi Karishma,

Interesting post -- makes complete sense. A question though: In your hypothetical question about "- And, a trickier thing to think about - how many integral solutions would 3x - 5y = 42 have?" -- both have to go up, right? So x would have to go up from 14, to 19, to 24 etc. Conversely, y would also go up from 0 to 3, to 6 etc. Neither of those values can be negative since we have the positive integer constraint. Am I correct?

Can you recommend other questions similar to this? Thanks!
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Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] New post 22 Aug 2014, 09:44
Expert's post
mrsmarthi wrote:
A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14


Given: 0.7b+0.5a=6.3 Question: a+b=?

0.7a+0.5b=6.3 --> 7a+5b=63 --> 5b=63-7a --> 5b=7(9-a) --> 5b must be multiple of 7 --> b must be multiple of 7 --> b can not be 0 (as "a customer purchased both apples and bananas") or >13 (as 5b in this case would be more than $6.30), so b=7 --> a=4 --> a+b=4+7=11.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-140732.html
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Re: A certain fruit stand sold apples for $0.70 each and bananas [#permalink] New post 24 Aug 2014, 21:50
Expert's post
russ9 wrote:
VeritasPrepKarishma wrote:
n2739178 wrote:

this is really doing my head in!



I have put up this theory on this link:
http://gmatquant.blogspot.com/2010/11/integral-solutions-of-ax-by-c.html

See if it makes sense now.
If there are doubts, get back to me on my blog itself or here...


Hi Karishma,

Interesting post -- makes complete sense. A question though: In your hypothetical question about "- And, a trickier thing to think about - how many integral solutions would 3x - 5y = 42 have?" -- both have to go up, right? So x would have to go up from 14, to 19, to 24 etc. Conversely, y would also go up from 0 to 3, to 6 etc. Neither of those values can be negative since we have the positive integer constraint. Am I correct?

Can you recommend other questions similar to this? Thanks!


Yes, the first easy solution would be 14, 0. Both x and y will move in same direction. Since neither can be negative, they must move up only.
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Re: A certain fruit stand sold apples for $0.70 each and bananas   [#permalink] 24 Aug 2014, 21:50
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