The cost of 10 pounds of apples and 2 pounds of grapes was $1

.

Let the cost of 1 pound of apple be Rs. x

And cost of 1 pound of grapes be y.

10 pounds of apple + 2 pounds of grapes: \(10x + 2y = 12\) ---------------------------1

We have to find value of x ( cost of per pound apple)

Statement 1 : The cost per pound of grapes was $2

\(y = 2\) is given. Clearly if we substitute in equation 1, we would get the value of x.

Hence Sufficient.

Statement 1 : The cost of 2 pounds of apples was less than the cost of 1 pound of grapes.

It is given that \(2x < y\). using this in Equation 1, will only give us range.
Let's try for practice : -
\(2x < y\)
\(4x < 2y\). Using this in 1.

\(10x + 4x < 12\)
\(x < \frac{12}{14}\)

no definite value of x.
Not Sufficient.

Ans - A.

Need to find out the cost of per pounds Apples .

Suppose ,

the cost of per pounds apples is x
the cost of per pounds grapes is y

10 x + 2 y = 12

Statement 1:
y = $ 2

10 x + 2 y = 12
10 x + 2 * 2 = 12
10 x = 8

x = 8/10
x = 4/5.

Sufficient

Statement 2:

2x< y

both x and y are unknown. Insufficient.

Thus A is the best answer.

Dear Experts,

Instead of pound, if pieces were UOM then D would have been the answer, with a definite no?

Answer: Option A

Video solution by GMATinsight

Solution:


Question Stem Analysis:

We need to determine the per-pound cost of apples. If we let a be the per-pound cost of apples and g be the per-pound cost of grapes per pound, we can create the equation:

10a + 2g = 12

We need to determine the value of a. As we can see, if we know the value of g, then we can determine the value of a.

Statement One Alone:

Statement one tells us that the value of g is 2. Since we know the value of g, we can determine the value of a, the per-pound cost of apples. Statement one alone is sufficient.

Statement Two Alone:

Although statement two tells us that the cost of 2 pounds of apples was less than the cost of 1 pound of grapes (i.e., 2a < g), without knowing the value of g, we can’t determine the value of a. Statement two alone is not sufficient.

Answer: A

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