Ines has $15 to purchase fruit. All apples are priced equally and all

Question

Ines has $15 to purchase fruit. All apples are priced equally and all bananas are priced equally. If 5 apples and 5 bananas cost exactly $15, could she afford 4 apples and 6 bananas with the money she has?

(1) The cost of one apple exceeds the cost of one banana by more than $0.20.

(2) Ines cannot afford 6 apples and 4 bananas with the money she has.

deplehehe · Accepted Answer

Say the price of apple is a, the price of banana is b the question is: 5a+5b>4a+6b or not => a>b or not 1) clearly sufficient 2 => 5a+5b<6a+4b => b sufficient OA: D

IanStewart · Answer

She can buy precisely 5 apples and 5 bananas with her $15. The question is, if she replaces one apple with a banana, can she still afford it? The answer will be "yes" if bananas are cheaper than apples (because then the total cost will go down if we replace an apple with a banana). Each statement tells us bananas are cheaper than apples, so the answer is D.

aniket16c · Answer

Official explanation

For an Algebraic Translations question, take what’s given and convert it into equations. Because the question talks about apples and bananas, use a to represent the cost of an apple and b to represent the cost of a banana. Given that Ines has exactly $15, the question is asking whether 4 apples and 6 bananas have a combined cost of less than or equal to $15.

Translate the fact from the question stem, simplifying and isolating one variable:

5a + 5b = 15

a + b = 3

a = 3 – b

Translate the question: Is 4a + 6b ≤ $15?

At this point, you can either continue to the statements or you can further simplify to Rephrase the question. In general, if you can rephrase further, you should, as it will save you time and effort on the statements. Both a and b are in the question as it is written; eliminate one of those variables using the given fact you have already simplified.

Is 4a + 6b ≤ $15? Substitute a = 3 – b into the inequality and simplify

Is 4(3 – b) + 6b ≤ 15?

Is 12 – 4b + 6b ≤ 15?

Is 12 + 2b ≤ 15?

Is 2b ≤ 3?

Is b ≤ 1.5?

The question can be rephrased back into words: Is the cost of a banana less than or equal to $1.50?

Equivalently, the question is also: Is the cost of an apple greater than or equal to $1.50?

Because one apple and one banana cost a total of $3, the question can also be phrased as a comparison between the two fruits: Does an apple cost the same as or more than a banana? Does an apple cost at least as much as a banana?

(1) SUFFICIENT: This statement says the cost of one apple exceeds the cost of one banana, so the answer to the rephrased question Does an apple cost the same as or more than a banana? is a definite Yes. Since there is only one answer, this statement is sufficient. Eliminate choices (B), (C), and (E).

(2) SUFFICIENT: Keep the various rephrases of the question in mind as you evaluate this statement. There is more than one approach you could take.

Logical Reasoning

According to the question stem, 5 apples and 5 bananas cost exactly $15. According to this statement, 6 apples and 4 bananas cost more than $15. In practical terms, removing a banana and replacing it with an apple increases the total cost, so an apple must cost more than a banana. The answer to the rephrased question Does an apple cost the same as or more than a banana? is a definite Yes.

Algebra – option 1

6a + 4b > 15 Substitute the equation a = 3 – b into the inequality

6(3 – b) + 4b > 15

18 – 6b + 4b > 15

– 2b > –3

2b < 3

b < 1.5

The answer to the rephrased question Is the cost of a banana less than or equal to $1.50? is a definite Yes.

Algebra – option 2

6a + 4b > 15 from Statement (2)

5a + 5b = 15 from the question stem

a – b > 0 subtract the equation from the inequality

Thus, a > b. The answer to the rephrased question Does an apple cost the same as or more than a banana? is a definite Yes.

Since there is only one answer, Yes, this statement is sufficient.

The correct answer is (D).

bumpbot · Answer

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Ines has $15 to purchase fruit. All apples are priced equally and all

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