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Total number of stamps bought

This topic has 4 expert replies and 2 member replies

Total number of stamps bought

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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

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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
Let x = # of 2-cent stamps purchased
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:
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
Let x = # of 2-cent stamps purchased
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:
http://www.beatthegmat.com/to-find-the-ratio-of-adults-to-children-t273004.html#706713

Thanks - Sri

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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.

Hi Sri,

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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gmattesttaker2 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?
Let the number of stamps of each type bought be N

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.

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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?
This isn't correct, at least in this context. (It may be in other ones, but not when dealing with equations in two variables.)

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 Very Happy

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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

ng x = the number of stamps of each denomination that he bought, we can create the equation:

2x + 3x = 100

5x = 100

x = 20

So x + x = 20 + 20 = 40 stamps were purchased.

Answer: C

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