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# m14, q16

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Manager
Joined: 10 Jul 2009
Posts: 129
Location: Ukraine, Kyiv
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Kudos [?]: 111 [0], given: 60

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20 Nov 2009, 09:26
This is from gmatclub test 14, question 16

A stationery store sells pens and pencils. If the price of each item is expressed as a non-zero whole number of cents, how much do 5 pencils cost?

1. 5 pencils and 3 pens cost 30 cents.
2. 4 pencils and 4 pens cost 32 cents.

# Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
# Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
# BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
# EACH statement ALONE is sufficient
# Statements (1) and (2) TOGETHER are NOT sufficient
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Never, never, never give up

Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
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Kudos [?]: 1121 [2] , given: 18

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20 Nov 2009, 14:26
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barakhaiev wrote:
This is from gmatclub test 14, question 16

A stationery store sells pens and pencils. If the price of each item is expressed as a non-zero whole number of cents, how much do 5 pencils cost?

1. 5 pencils and 3 pens cost 30 cents.
2. 4 pencils and 4 pens cost 32 cents.

# Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
# Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
# BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
# EACH statement ALONE is sufficient
# Statements (1) and (2) TOGETHER are NOT sufficient

Question Stem : What is the cost of 5 pencils?
Let p refer to price of one pencil and q refer to price of one pen.
We are given that both p and q must be non zero whole numbers (1,2,3,4,5.... and so on).

St. (1) : 5p + 3q = 30
This can be written as $$p = \frac{30-3q}{5} = 6 - \frac{3q}{5}$$
This implies that in order for p to be a whole number, q must be a multiple of 5. Also, we can see that if q = 10, then p will be equal to 0. Since this cant be possible, q must be less than 10. Also, since q itself cant be 0, it must be greater than 0. The only multiple of 5 that satisfies this condition is the number 5 itself.

Thus we get q = 5 and p = 3.

Statement is sufficient.

St. (2) : 4p + 4q = 32
This can be written as p + q = 8
Thus, since different sets of values of p and q can satisfy this condition, it cannot be sufficient.

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Re: m14, q16   [#permalink] 20 Nov 2009, 14:26
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# m14, q16

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