The official solution has been posted. Looking forward to a healthy discussion..
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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.

Answer is A

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.


Answer: A


Thanks,
Saquib
Quant Expert
e-GMAT

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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

Answer:

Cheers,
Brent
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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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