Maria can either buy a basket that contains p pounds of apples for $16

Question

Maria can either buy a basket that contains p pounds of apples for $16.50 or buy p pounds of apples at $0.95 per pound. Does it cost Maria more to buy the basket of apples than to buy p pounds of apples at $0.95 per pound?

(1) The basket contains less than 20 pounds of apples.

(2) It would cost Maria a total of $18.05 to buy p + 4 pounds of apples at $0.95 per pound.

ID 13137

VeritasPrepRon · Accepted Answer

This solution is absolutely true. Just to clarify on statement 1, the reason it's insufficient is that there are up to 20 pounds of apples, so there could be 0, 10, 15, 17 or 19 pounds of apples in the basket. Regardless, the basket costs 16.05$, but the price to get the same amount of apples per pound can be as low as 0$ or as high as 19 x 0.95 = 18.05$.

The only figure to be on the lookout for is when does the amount of apples purchased per pound hit 16.50$, which in this case is between 17 and 18 pounds. ( 16.15$ to 17.10$). If we know for sure which side of this line we lie on, then we have sufficient data. As an example, if the statement had read that the basket contains less than 15 pounds of apples, or if it indicated that the basket contains more than 20 pounds, then the answer would have been D.

Statement 2 as indicated gives a linear equation, so it will give one specific answer (the basket has 15 pounds of apples in it), and is therefore sufficient without requiring any math calculations.

Hope this helps!
-Ron

mau5 · Answer

F.S 1 clearly Insufficient. We don't know the value of p to compare the costs.

F.S 2 gives us a relationship as (p+4)*0.95 = 18.05. Hence, p*0.95 can be calculated. No need to calculate. The question stem can be answered. Sufficient.

B.

b2bt · Answer

P (pounds in baskets) and p are same here?

Bunuel · Answer

______________________
Yes.

sarahfiqbal · Answer

I got this question wrong only because I thought "P" and "p" mean two different values. I think it is unfair that the question is worded this way. I don't think it is right that "P" and "p" is written this way to mean the same thing in the context of this question-no clarity at all.

Manukaran · Answer

I am thinking would it really matter.

Statement 2 says that it would cost maria a total of $18.05 to buy p+4 pounds of apples at $0.95 per pound.

So, p + 4 costs 18.05
=> p would cost 18.05 - 0.95*4 = $14.25

So, now we know:

P pounds of apples cost $16.50 (given in the question)
p pounds of apples cost $14.25 (derived from Statement 2).

So, we know that p pounds of apples cost less.

Hence, statement 2 is sufficient and it doesn't matter whether P and p are different.

sanjna2023 · Answer

I got this question wrong because i thought P and p were 2 different values...strange wording for a GMAT ques

egmat · Answer

This is a classic "break-even" problem that tests your ability to set up inequalities and work with algebraic expressions systematically.

Let me walk you through the core logic you need to master here.

Understanding What We're Really Asking

You need to determine: Does $$16.50 > $0.95p$?

The basket has a fixed cost of $$16.50$, while buying individually costs $$0.95 \times p$. So we're looking for the "break-even" point where these costs are equal.

Analyzing Statement 1: $p < 20$

Here's where you need to test boundary values. Let's think about this systematically:

If $p = 10$: Individual cost = $10 \times $0.95 = $9.50$
Since $$9.50 < $16.50$, the basket costs MORE.

If $p = 19$: Individual cost = $19 \times $0.95 = $18.05$
Since $$18.05 > $16.50$, the basket costs LESS.

Notice how we get different answers depending on the value of p? This means Statement 1 is insufficient.

Analyzing Statement 2: $(p + 4)$ pounds costs $$18.05$

This is the key insight you need to see! If $(p + 4)$ pounds costs $$18.05$, then those extra 4 pounds cost $4 \times $0.95 = $3.80$.

Therefore: $p$ pounds costs $$18.05 - $3.80 = $14.25$

Now we can definitively compare:
- Basket: $$16.50$
- Individual: $$14.25$

Since $$16.50 > $14.25$, the answer is YES - the basket costs more.

Answer: B

The complete systematic approach for identifying break-even problems and the 3 alternative solution methods that save time on similar DS questions are covered in detail here on Neuron. You can also practice with comprehensive solutions for many other similar official questions to build your pattern recognition for Data Sufficiency problems.

Maria can either buy a basket that contains p pounds of apples for $16

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GMAT Data Sufficiency (DS) Questions

Maria can either buy a basket that contains p pounds of apples for $16

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