Each gift certificate sold yesterday by a certain bookstore

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.
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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.
Hence answer E.

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
Answer E

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

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

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.

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..

Our answer is E.

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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Statement 1: It doesn't provide any useful information on its own to solve the problem. Knowing fewer than 10 certificates of cost $10 is not enough to answer the problem.
Statement 2: We can have 8 number of $50 and 6 number of $10 or we can have 9 number of $50 and 1 number of $10.

Combining both, we don't get a unique solution,we still have 2 valid choices. So the answer is E

We can let x = the number of $10 gift certificates and y = the number of $50 gift certificates.

Thus, we know that y > 5.

We need to determine the value of x + y.

Statement One Alone:

Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each.

Using the information in statement one, we know that x < 10.

Without knowing the exact values of x and y, statement one alone is not sufficient to answer the question.

Statement Two Alone:

The total cost of gift certificates sold yesterday by the bookstore was $460.

We can create the following equation:

10x + 50y = 460

x + 5y = 46

We see that y could be 8 and x could be 6, or y could be 9 and x could be 1. In one case, x + y is 14, and in the other, x + y is 10. Therefore, we do not have a definitive value for x + y. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the given information, we see that:

y > 5

x < 10

x + 5y = 46

Furthermore, x and y are integers. We can substitute integer values for y (as long as it satisfies the first inequality) and check whether these values will also satisfy the other inequality and equation. For example:

If y = 6, then x = 16 (using the equation x + 5y = 46). But, then x is not less than 10, so y can’t be 6.

If y = 7, then x = 11. Again, x is not less than 10, so y can’t be 7.

If y = 8, then x = 6. We see that x is less than 10. So y can be 8 and x will be 6.

If y = 9, then x = 1. We see that x is less than 10, so y can be 9 and x will be 1.

However, we have two different values each for x and y, adding up to different values. Both statements together still are not sufficient to answer the question.

Answer: E
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Hi All,

We're told that Each gift certificate sold yesterday cost either $10 or $50 and that the bookstore sold MORE than 5 gift certificates that cost $50 each. We're asked for the total number of gift certificates sold yesterday by the bookstore. This question can be solved by TESTing VALUES.

1) Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each.

Fact 1 tells us that there could be from 0-10 $10 certificates and 6 or more $50 certificates, but we don't know the TOTAL certificates sold.
Fact 1 is INSUFFICIENT

2) The total cost of gift certificates sold yesterday by the bookstore was $460.

IF...
8 $50 certificates and 6 $10 certificates were sold, then the answer to the question is 14.
9 $50 certificates and 1 $10 certificates were sold, then the answer to the question is 10.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that 'fit' both Facts and provide different results:
8 $50 certificates and 6 $10 certificates were sold, then the answer to the question is 14.
9 $50 certificates and 1 $10 certificates were sold, then the answer to the question is 10.
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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