Hello,
Can you please tell me if my answer is correct here:
Mario bought equal numbers of 2 cent and 3 cent stamps. If the total cost of the stamps was $1.00, what was the total number of stamps bought?
A) 25
B) 34
C) 40
D) 46
E) 50
I am getting 46
Thanks,
Sri
Total number of stamps bought
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Let x = # of 2-cent stamps purchasedgmattesttaker2 wrote:Hello,
Can you please tell me if my answer is correct here:
Mario bought equal numbers of 2 cent and 3 cent stamps. If the total cost of the stamps was $1.00, what was the total number of stamps bought?
A) 25
B) 34
C) 40
D) 46
E) 50
Since Mario bought equal numbers of 2 cent and 3 cent stamps, we can let x = # of 3-cent stamps purchased
So, VALUE (in cents) of the 2-cent stamps purchased = 2x
And VALUE (in cents) of the 3-cent stamps purchased = 3x
The total cost of the stamps was $1.00
In other words, the total cost was 100 cents
So, we can write 2x + 3x = 100
simplify: 5x = 100
solve: x = 20
So, Mario purchased 20 2-cent stamps and 20 3-cent stamps, for a total of 40 stamps.
Answer: C
Cheers,
Brent
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Brent@GMATPrepNow wrote:Let x = # of 2-cent stamps purchasedgmattesttaker2 wrote:Hello,
Can you please tell me if my answer is correct here:
Mario bought equal numbers of 2 cent and 3 cent stamps. If the total cost of the stamps was $1.00, what was the total number of stamps bought?
A) 25
B) 34
C) 40
D) 46
E) 50
Since Mario bought equal numbers of 2 cent and 3 cent stamps, we can let x = # of 3-cent stamps purchased
So, VALUE (in cents) of the 2-cent stamps purchased = 2x
And VALUE (in cents) of the 3-cent stamps purchased = 3x
The total cost of the stamps was $1.00
In other words, the total cost was 100 cents
So, we can write 2x + 3x = 100
simplify: 5x = 100
solve: x = 20
So, Mario purchased 20 2-cent stamps and 20 3-cent stamps, for a total of 40 stamps.
Answer: C
Cheers,
Brent
Hello Brent,
Thank you very much for your excellent explanation. I think I overlooked the equal part in the question. Now if this was a data sufficiency question and the question does not mention equal number of 2 cent and 3 cent stamps but asks us to find the total number of stamps, will 41 2-cent stamps and 6 3-cent stamps also be correct since they both add in value to 100 cents? I think I read in one of the postings that if the 2 numbers don't have a common (factor?) then they can have only 1 value. Is this correct? Thanks a lot for your help.
Best Regards,
Sri
Update:
Hello Brent, this was the type of question that I was thinking:
Joanna bought only $0.15 and $0.29 stamps. How many $0.15 stamps did she buy?
(1) She bought $4.40 worth of stamps.
This is the post:
https://www.beatthegmat.com/to-find-the- ... tml#706713
Thanks - Sri
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Hi Sri,gmattesttaker2 wrote: Hello Brent,
Now if this was a data sufficiency question and the question does not mention equal number of 2 cent and 3 cent stamps but asks us to find the total number of stamps, will 41 2-cent stamps and 6 3-cent stamps also be correct since they both add in value to 100 cents? I think I read in one of the postings that if the 2 numbers don't have a common (factor?) then they can have only 1 value. Is this correct? Thanks a lot for your help.
I'm not aware of any such rule.
Notice that 2 and 3 don't have any common factors, but there are many possible scenarios for the number of stamps that add to $1.00 if we buy 2- and 3-cent stamps only. Here are 3:
20 2-cent stamps and 20 3-cent stamps for a total of 40 stamps
41 2-cent stamps and 6 3-cent stamps for a total of 47 stamps
47 2-cent stamps and 2 3-cent stamps for a total of 49 stamps
.
.
.
(there are more)
Cheers,
Brent
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Let the number of stamps of each type bought be Ngmattesttaker2 wrote:Mario bought equal numbers of 2 cent and 3 cent stamps. If the total cost of the stamps was $1.00, what was the total number of stamps bought?
Thus N stamps were of 2 cents and N stamps were of 3 cents , making a total of 2N stamps.
So , 2N + 3N = 100
Or, 5N = 100
Or, N = 20
We have taken N as 20 and we know two types of stamps were bought both " N " Numbers .
Thus 20 stamps were of 2 cents and 20 stamps were of 3 cents , making a total of 40 stamps...
hence answer is 40.
Abhishek
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This isn't correct, at least in this context. (It may be in other ones, but not when dealing with equations in two variables.)gmattesttaker2 wrote: I think I read in one of the postings that if the 2 numbers don't have a common (factor?) then they can have only 1 value. Is this correct?
Generally speaking, an equation like
2x + 3y = 100
has an infinite number of solutions for x and y.
If you put some restrictions on x and y (such as x and y must both be positive integers), however, you can have a finite number of solutions - sometimes only one (very common in GMAT DS!) But finding that single solution can be a real pain
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ng x = the number of stamps of each denomination that he bought, we can create the equation:gmattesttaker2 wrote:Hello,
Can you please tell me if my answer is correct here:
Mario bought equal numbers of 2 cent and 3 cent stamps. If the total cost of the stamps was $1.00, what was the total number of stamps bought?
A) 25
B) 34
C) 40
D) 46
E) 50
2x + 3x = 100
5x = 100
x = 20
So x + x = 20 + 20 = 40 stamps were purchased.
Answer: C
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