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If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought

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If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought

by BTGModeratorVI » Fri May 29, 2020 6:25 am

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If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought at least one of each denomination, what is the number of 25-cent stamps that she bought?

(1) She spent a total of $1.45 for stamps.
(2) She bought exactly 6 stamps.

Answer: E
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Source: — Data Sufficiency |
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Re: If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought

by deloitte247 » Sun May 31, 2020 4:52 am

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Each stamp cost 20, 25 or 30 cents
Total money spent on stamps = 20x + 25y + 30z

Target question => What is the number of 25 cent stamps? i.e find y
Given that she bought at least one of each denomination
Total money is at least 20 + 25 + 30 = 75 cents

Statement 1 => She spent a total of $1.45 for stamps i.e 145 cents
Possible variation in money spent are:
- (20*2) + (25*3 ) + (30*1) = 145 and y = 3
- (20*3) + (25*1) + (30*2) = 145 and y = 1
These 2 possible scenario yield two different value of y. Hence, statement 1 is NOT SUFFICIENT

Statement 2 => She bought exactly 6 stamps
This statement does not give any information about the quality of each stamp because lots of possible variations and ways of arranging 3 different stamps into 6 places i.e 2,2,2; 2,1,3; 1,2,3; so the exact value of y cannot be determined. Statement 2 is NOT SUFFICIENT

Combining both statements together =>
According to the information available in the two statements, the possible scenarios are (20*2) + (25*3) + (30*1) = 145 and (20*3) + (25*1) + (30*2) = 145 and y = 1
The possible scenarios yield different value of y. Hence, both statements together ARE NOT SUFFICIENT

Answer = E
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Re: If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought

by Brent@GMATPrepNow » Mon Jun 01, 2020 8:48 am

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BTGModeratorVI wrote: ↑
Fri May 29, 2020 6:25 am
 If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought at least one of each denomination, what is the number of 25-cent stamps that she bought?

(1) She spent a total of $1.45 for stamps.
(2) She bought exactly 6 stamps.

Answer: E
Source: GMAT prep
Target question: What is the number of 25-cent stamps that she bought?

Tricky question!!
We can quickly see that statements 1 and 2 alone are not sufficient.
The hard part comes when we COMBINE the statements.

Statements 1 and 2 combined
After examining some possible scenarios, we get these two conflicting cases:
Case a: Carla bought 2 20-cent stamps, 3 25-cent stamps, and 1 30-cent stamp (6 stamps for a total of 145 cents). In this case, the answer to the target question is Carla bought 3 25-cent stamps
Case b: Carla bought 3 20-cent stamps, 1 25-cent stamp, and 2 30-cent stamps (6 stamps for a total of 145 cents). In this case, the answer to the target question is Carla bought 1 25-cent stamp
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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