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# Joan spent \$10 to buy at least one piece each of apples a

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e-GMAT Representative
Joined: 04 Jan 2015
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Joan spent \$10 to buy at least one piece each of apples a  [#permalink]

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23 May 2017, 07:07
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Difficulty:

25% (medium)

Question Stats:

78% (01:05) correct 22% (01:36) wrong based on 129 sessions

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Q.

Joan spent \$10 to buy at least one piece each of apples and oranges at a store where each apple cost \$2 and each orange cost \$1. How many apples did she buy?

(1) She spent more than \$6 on buying oranges

(2) She spent less than \$10 on buying oranges

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Thanks,
Saquib
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Joan spent \$10 to buy at least one piece each of apples a  [#permalink]

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Updated on: 31 May 2017, 04:53
The official solution has been posted. Looking forward to a healthy discussion..
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Originally posted by EgmatQuantExpert on 23 May 2017, 07:07.
Last edited by EgmatQuantExpert on 31 May 2017, 04:53, edited 1 time in total.
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Re: Joan spent \$10 to buy at least one piece each of apples a  [#permalink]

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23 May 2017, 08:50
2
Joan spent \$10 to buy at least one piece each of apples and oranges at a store where each apple cost \$2 and each orange cost \$1. How many apples did she buy?

(1) She spent more than \$6 on buying oranges
This statement tells us that Joan spent at least \$7 for buying oranges. If she spend \$7 on oranges, \$3 would remain with her. Since one apple costs \$2, she can buy one apple. Now she has \$1 remaining. From which she can buy one more orange. therefore Joan bought 1 apple. This statement is sufficient.

(2) She spent less than \$10 on buying oranges
Joan can spend either \$1 to \$8 on buying oranges. As this statement is not giving any more information, this statement is not sufficient.

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Re: Joan spent \$10 to buy at least one piece each of apples a  [#permalink]

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31 May 2017, 04:53

Official Solution

Steps 1 & 2: Understand Question and Draw Inferences

Let the number of apples bought be a and the number of oranges bought be r.

Given:

• a is an integer such that a ≥ 1

• r is an integer such that r ≥ 1

• And, 2a + r = 10

From the above equation and constraints the possible values of a and r are listed below:

(a,r) can be (1,8) (2,6) (3,4) and (4,2)

• We need to find the value of a.

Step 3: Analyze Statement 1 independently

• Statement 1 says that she spent more than \$6 on buying oranges

o r > 6

• From the possible cases listed above, the only possible value of r = 8

o So, a = 1

Sufficient to determine a unique value of a.

Step 4: Analyze Statement 2 independently

• Statement 2 says that she spent less than \$10 on buying oranges

o r < 10

• All the values of r, and hence of a, in the possible cases listed above, satisfy this statement.

Not Sufficient to determine a unique value of a.

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Joined: 12 Sep 2015
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Joan spent \$10 to buy at least one piece each of apples a  [#permalink]

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Updated on: 25 Sep 2017, 07:31
Top Contributor
EgmatQuantExpert wrote:
Joan spent \$10 to buy at least one piece each of apples and oranges at a store where each apple cost \$2 and each orange cost \$1. How many apples did she buy?

(1) She spent more than \$6 on buying oranges

(2) She spent less than \$10 on buying oranges

Target question: How many apples did Joan buy?

Given: Joan spent \$10 to buy at least one piece each of apples and oranges at a store where each apple cost \$2 and each orange cost \$1.
Since there are only a handful of possible outcomes, we might benefit from quickly listing them:
i) Joan buys 1 apple (for \$2) and 8 oranges (for \$8)
ii) Joan buys 2 apples (for \$4) and 6 oranges (for \$6)
iii) Joan buys 3 apples (for \$6) and 4 oranges (for \$4)
iv) Joan buys 4 apple (for \$8) and 2 oranges (for \$2)

Statement 1: She spent more than \$6 on buying oranges
When we check our list of possible outcomes, we see that only one outcome (case i) satisfies statement 1.
So, it MUST be the case that Joan bought 4 apples
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: She spent less than \$10 on buying oranges
When we check our list of possible outcomes, we see that ALL 4 outcomes satisfy statement 2.
So, it's possible that Joan bought 1 apple, 2 apples, 3 apples OR 4 apples
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

Originally posted by GMATPrepNow on 24 Sep 2017, 07:09.
Last edited by GMATPrepNow on 25 Sep 2017, 07:31, edited 1 time in total.
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Joan spent \$10 to buy at least one piece each of apples a  [#permalink]

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25 Sep 2017, 03:02
1
GMATPrepNow wrote:
EgmatQuantExpert wrote:
Joan spent \$10 to buy at least one piece each of apples and oranges at a store where each apple cost \$2 and each orange cost \$1. How many apples did she buy?

(1) She spent more than \$6 on buying oranges

(2) She spent less than \$10 on buying oranges

Target question: How many apples did Joan buy?

Given: Joan spent \$10 to buy at least one piece each of apples and oranges at a store where each apple cost \$2 and each orange cost \$1.
Since there are only a handful of possible outcomes, we might benefit from quickly listing them:
i) Joan buys 1 apple (for \$2) and 8 oranges (for \$8)
ii) Joan buys 2 apples (for \$4) and 6 oranges (for \$6)
iii) Joan buys 3 apples (for \$6) and 4 oranges (for \$4)
iv) Joan buys 4 apple (for \$8) and 2 oranges (for \$2)

Statement 1: She spent more than \$6 on buying oranges
When we check our list of possible outcomes, we see that only one outcome (case iv) satisfies statement 1.
So, it MUST be the case that Joan bought 4 apples
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Cheers,
Brent

Dear Brent,

Based on what you stated, it should be case i. It is the only case that orange greater than \$6 and be able to divide by \$2 and hence gives 1 apple.
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Joined: 12 Sep 2015
Posts: 2856
Re: Joan spent \$10 to buy at least one piece each of apples a  [#permalink]

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25 Sep 2017, 07:32
Top Contributor
Mo2men wrote:
Dear Brent,

Based on what you stated, it should be case i. It is the only case that orange greater than \$6 and be able to divide by \$2 and hence gives 1 apple.

Good catch - thanks!
I've edited my response accordingly.

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

Re: Joan spent \$10 to buy at least one piece each of apples a &nbs [#permalink] 25 Sep 2017, 07:32
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