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Alice bought a certain number of 30 cent stamps, 35 cent stamps, and 40 cent stamps. She spent a total of $4.20 buying

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by M7MBA » Sat Nov 28, 2020 11:42 pm

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B

C

D

E

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Difficulty—

Alice bought a certain number of 30 cent stamps, 35 cent stamps, and 40 cent stamps. She spent a total of $4.20 buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.

(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.

Answer: B

Source: Princeton Review
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Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps, and 40 cent stamps. She spent a total of $4.20 buyi

by deloitte247 » Thu Dec 10, 2020 8:04 pm
Let 30 cent stamps = a; 35 cent stamps = b; and 40 cent stamps = c
30a + 35b + 40c = $4.20 = 420 cents
Target question: Did she buy more than 5 stamps of any of the three values?

Statement 1: The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
i.e b=c
30a + 35b + 40c = 420 and 30a + 75b = 420
The value of 'a' and 'b' could be a=4 and b=4; or a=9 and b=2
One has the value of a >5 and for the other a<5. So, the answer is not definite, hence, statement 1 is NOT SUFFICIENT.

Statement 2: The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.
$$i.e\ a=b\ and\ b\le c;\ hence,\ 30a+35b+40c=420$$
65a + 40c = 420
$$Since\ b<c,\ and\ a=b,\ automatically,\ a\le c.$$
The case value that fits is when a=b=4 and c=4, so that a=4, b=4, and c=4.
In conclusion, none of the stamp value is more than 5, therefore, statement 2 alone is SUFFICIENT.

Answer = option B
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