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# Each gift certificate sold yesterday by a certain bookstore

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Each gift certificate sold yesterday by a certain bookstore [#permalink]  08 Oct 2012, 01:49
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Difficulty:

55% (hard)

Question Stats:

65% (02:49) correct 35% (01:38) wrong based on 495 sessions
Each gift certificate sold yesterday by a certain bookstore cost either $10 or$50. If yesterday the bookstore sold more than 5 gift certificates that cost $50 each, what was the total number of gift certificates sold yesterday by the bookstore? (1) Yesterday the bookstore sold fewer than 10 gift certificates that cost$10 each.
(2) The total cost of gift certificates sold yesterday by the bookstore was $460. Practice Questions Question: 57 Page: 279 Difficulty: 600 [Reveal] Spoiler: OA _________________ Math Expert Joined: 02 Sep 2009 Posts: 29172 Followers: 4735 Kudos [?]: 50006 [4] , given: 7518 Re: Each gift certificate sold yesterday by a certain bookstore [#permalink] 08 Oct 2012, 01:50 4 This post received KUDOS Expert's post 3 This post was BOOKMARKED SOLUTION Each gift certificate sold yesterday by a certain bookstore cost either$10 or $50. If yesterday the bookstore sold more than 5 gift certificates that cost$50 each, what was the total number of gift certificates sold yesterday by the bookstore?

Let x be the number of $10 gift certificates and y be the number of$50 gift certificates.
Given: y > 5.
Question: x + y = ?.

(1) Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each. x<10. clearly insufficient. (2) The total cost of gift certificates sold yesterday by the bookstore was$460. 10x+50y=460. Several pairs are possible: for example x=1 and y=9 as well as x=6 and y=8. Not sufficient.

(1)+(2) x=1 and y=9 as well as x=6 and y=8 satisfy both statements. Not sufficient.

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Re: Each gift certificate sold yesterday by a certain bookstore [#permalink]  08 Oct 2012, 02:15
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Let x be $10 Certificate & y be$50 Certificate, We need to find value of x+y=?
ST1: Insufficient: SInce x<10, x can take any value from 0 to 9 & Since y >5, y can take any value greater than 5. So x+y will have multiple values.
ST2: Insufficient: Given: 10x+50y =460, x>5, So multiple combination can satisfy this equation, for example (x,y) = (9,1), (8,6),.....
1+2: Still insufficient for above reason in ST2.
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Re: Each gift certificate sold yesterday by a certain bookstore [#permalink]  08 Oct 2012, 02:26
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Let the no of $10 &$50 certificates is x & y respectively
Question is x+y=?
Given y>5
Note:- x & y can only take positive integer values
1) x<10 ---> Not sufficient
2) 10x + 50y = 460 ----> x + 5y = 46
Possible values of (x & y) are (16,6), (11,7), (6,8) ,(1,9) --->Insufficient
1+2) Given x<10 & y>5 , possible pairs are (6,8) ,(1,9) ----> No unique value -->Insufficient
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Re: Each gift certificate sold yesterday by a certain bookstore [#permalink]  08 Oct 2012, 04:13
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Let Y = # of gift certificates sold with a value of 50.
Let X = # of gift certificates sold with a value of 10.
Y > 5
Find X + Y

1) X < 10
The solution could be 16X + 6Y = 460 or it could be 6X + 9Y = 390 Insufficient

2) 10X + 50Y = 460
The solution could be 16X + 6Y = 460 or it could be 1X + 9Y = 460 Insufficient

Combining 1 + 2 X < 10, 10X + 50Y = 460
The solution could be 1X + 9Y = 460 (Total of 10) or it could be 16X + 6Y = 460 (Total of 22) Insufficient

[Reveal] Spoiler:

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Re: Each gift certificate sold yesterday by a certain bookstore [#permalink]  09 Oct 2012, 06:14
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each gift certificate sold yesterday by a certain bookstore cost either $10 or$50. If yesterday the bookstore sold more than 5 gift certificates that cost $50 each, what was the total number of gift certificates sold yesterday by the bookstore? (1) Yesterday the bookstore sold fewer than 10 gift certificates that cost$10 each.
(2) The total cost of gift certificates sold yesterday by the bookstore was $460. let x be the nos of 10$ copies and y be nos of 50$copies so x10 + y50 = some value stem also says y>5 Question x+y = ? Statement 1/ x<10 (from stem y>5) many combinations are possible for x+y so NS Statment 2/ x10 + y50 = 460 As y> 5 then we can find out the possible values for x x10 + 300 = 460 ............ when y = 6 then x=16 x10 + 350 = 460 ................. y=7 then x=11 x10 + 400 = 460..................y=8 then x=6 x10 + 450 = 460 .............y=9 then x=1 on solving above we can get x = 16,11,6,1 Nt sufficient to calcuate value of x+y Combined we know y>5 and x <10 even then we have 2 value pairs for (x,y) = (6,8) (1,9) so E Senior Manager Joined: 16 Feb 2012 Posts: 255 Concentration: Finance, Economics Followers: 5 Kudos [?]: 136 [1] , given: 121 Re: Each gift certificate sold yesterday by a certain bookstore [#permalink] 09 Oct 2012, 08:30 1 This post received KUDOS Each gift certificate sold yesterday by a certain bookstore cost either$10 or $50. If yesterday the bookstore sold more than 5 gift certificates that cost$50 each, what was the total number of gift certificates sold yesterday by the bookstore?

(1) Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each. (2) The total cost of gift certificates sold yesterday by the bookstore was$460.

Statement 1: Insufficient
We don't know the exact number of gift certificates sold, there could be more than one solution.
Statement 2: Insufficient
Same as in the statement 1, there could be one 10$gift certificate and nine 50$ gift certificates...or sixteen 10$gift certificates and six 50$ gift certificates.

Together statements don't provide the solution, so the answer is E.
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Re: Each gift certificate sold yesterday by a certain bookstore [#permalink]  11 Oct 2012, 13:04
Expert's post
SOLUTION

Each gift certificate sold yesterday by a certain bookstore cost either $10 or$50. If yesterday the bookstore sold more than 5 gift certificates that cost $50 each, what was the total number of gift certificates sold yesterday by the bookstore? Let x be the number of$10 gift certificates and y be the number of $50 gift certificates. Given: y > 5. Question: x + y = ?. (1) Yesterday the bookstore sold fewer than 10 gift certificates that cost$10 each. x<10. clearly insufficient.

(2) The total cost of gift certificates sold yesterday by the bookstore was $460. 10x+50y=460. Several pairs are possible: for example x=1 and y=9 as well as x=6 and y=8. Not sufficient. (1)+(2) x=1 and y=9 as well as x=6 and y=8 satisfy both statements. Not sufficient. Answer: E. Kudos points given to everyone with correct solution. Let me know if I missed someone. _________________ Director Joined: 08 Jun 2010 Posts: 769 Followers: 0 Kudos [?]: 53 [0], given: 181 Re: Each gift certificate sold yesterday by a certain bookstore [#permalink] 26 Feb 2013, 03:40 not easy at all. I pick many numbers. Manager Joined: 12 Jan 2013 Posts: 249 Followers: 3 Kudos [?]: 39 [0], given: 47 Re: Each gift certificate sold yesterday by a certain bookstore [#permalink] 10 Jan 2014, 07:36 Bunuel wrote: Each gift certificate sold yesterday by a certain bookstore cost either$10 or $50. If yesterday the bookstore sold more than 5 gift certificates that cost$50 each, what was the total number of gift certificates sold yesterday by the bookstore?

(1) Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each. (2) The total cost of gift certificates sold yesterday by the bookstore was$460.

Practice Questions
Question: 57
Page: 279
Difficulty: 600

We are given the equation: 10*x + 50*y = Total Sales, by the stem. Also, we're given the restriction y > 5.

1) Gives us the restriction x < 10, but as we have absolutely no idea what total sales are, theoretically we have almost infinite possibilities (and even with TS it would be insufficient). Insufficient.
2) Solves one of our three unknowns, so clearly insufficient..

If we combine the two, the only thing we know is that 10*10 + 5*50 is not a possible value (neither are certain other combinations of x and y), and that the total sales = 460.. So, 10*x + 5*y = 460..
This means that the difference could be more/less than 110 (because of 10*10 + 5*50 = 110 not being a possible combination) .. And we could combine x and y in many different ways to arrive at 110, for instance 11x's and no y's, or 2y's and 1 x... And even at that, we still only have a vague, non-definite relation between X and Y, even though we have solved for Total Sales.

So all in all, the stem + the two statements really only give us a weak restriction for X and Y, and solve for total sales.. So we still have 2 unknowns that we need to solve for, and thus the info is insufficient..

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Re: Each gift certificate sold yesterday by a certain bookstore [#permalink]  22 Feb 2015, 10:43
Hi BB. You are doing great job. Salute.
Is this question really 700 level? OG is said to be in increasing difficulty order so how can Q.57 be level 700 question?

Respectfully,
Verve42
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Re: Each gift certificate sold yesterday by a certain bookstore [#permalink]  22 Feb 2015, 10:51
Expert's post
Verve42 wrote:
Hi BB. You are doing great job. Salute.
Is this question really 700 level? OG is said to be in increasing difficulty order so how can Q.57 be level 700 question?

Respectfully,
Verve42

Thank you! But I'm not BB. BB is completely different person: members/member-3.html

As for the difficulty level of this question: it's calculated based on the Timer (check the original post) and according to sessions of 356 users, it is a 700 question.
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Re: Each gift certificate sold yesterday by a certain bookstore   [#permalink] 22 Feb 2015, 10:51
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