What is the price of an orange?(1) The price ...

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What is the price of an orange?
(1) The price of 3 oranges and 2 apples is \$7.
(2) The price of an orange and the price of an apple are both integers.
• 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;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Statement 1:
We are given that the combined price of 3 oranges and 2 apples is \$7:
3(Price of 1 orange)+2(Price of 1 apple)=7
This is a linear equation with two variables. From it alone, we cannot get the unique value of the price of an orange.
Let's take two cases.
1. Say the price of an apple = \$1, then the price of an orange is
2. Say the price of an apple = \$2, then the price of an orange is
No unique value of the price of an orange. Insufficient!
Statement 2:
Merely knowing that the price of an orange and the price of an apple are integers is not sufficient.
Statement 1 & 2 together:
Say the price of an orange = x and the price of an apple = y;
Thus, from Statement 1, we get,
3x + 2y = 7
From Statement 2, we know that the price of an orange and the price of an apple are integers, thus they must be positive. That is,
x ≥ 1
y ≥ 1
Let's assume a few possible integer values of the price of an apple (y) and see whether it results in a unique positive integer value of the price of an orange (x).
We get only one valid value of x, i.e. the price of an orange = \$1, a unique value.
So, our analysis has yielded a unique value of x (=1). Sufficient!

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Statement 1:We are given that the combined price of 3 oranges and 2 apples is \$7:3(Price of 1 orange)+2(Price of 1 apple)=7This is a linear equation with two variables. From it alone, we cannot get the unique value of the price of an orange.Lets take two cases.1. Say the price of an apple = \$1, then the price of an orange is2.Say the price of an apple = \$2, then the price of an orange isNo unique value of the price of an orange. Insufficient!Statement 2:Merely knowing that the price of an orange and the price of an apple are integers is not sufficient.Statement 1 & 2 together:Say the price of an orange = x and the price of an apple = y;Thus, from Statement 1, we get,3x + 2y = 7From Statement 2, we know that the price of an orange and the price of an apple are integers, thus they must be positive. That is,x ≥ 1y ≥ 1Lets assume a few possible integer values of the price of an apple (y) and see whether it results in a unique positive integer value of the price of an orange (x).We get only one valid value of x, i.e. the price of an orange = \$1, a unique value.So, our analysis has yielded a unique value of x (=1). Sufficient!