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

The equation is 10a+2g=12...
What is a?
1) g=2
Substitute in main equation...
One variable, one equation.. sufficient
10a+2*2=12...a=0.8
Sufficient
2) 2a<1g...
10a+2g=12..
You can have lot of solutions..
a=0.5..10*5+2g=12...g=3.5>2a or 2*0.5
a=0.8...g=2>2a
Insufficient

A
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Solution

Given:

• The cost of 10 pounds of apples and 2 pounds of grapes was $12

To find:

• The cost of per pound of apples

Analysing Statement 1

• As per the information given in statement 1, the cost per pound of grapes was $2

o So, the cost of 2 pounds of grapes = $4

As the cost of 10 pounds of apples and 2 pounds of grapes was $12, we can say:

• The cost of 10 pounds of apples = $12 - $4

From this, we can find out the cost of every pound of apples

Hence, statement 1 is sufficient to answer the question

Analysing Statement 2

• As per the information given in statement 2, the cost of 2 pounds of apples was less than the cost of 1 pound of grapes
• From this statement, we can’t find out the exact cost of one pound of apple

Hence, statement 2 is not sufficient to answer the question

Hence, the correct answer is option A.

Answer: A
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.

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

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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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