Lana bought two watches last year and sold both of them yest

Question

Lana bought two watches last year and sold both of them yesterday. If the selling price of watch B was twice that of watch A, did Lana make a profit on the purchase and sale of the two watches?

(1) Lana sold watch A for 20% more than what she paid for it.
(2) Lana sold watch B for more than 90% of what she paid for it.

paragw · Answer

Here's my solution:

Edskore · Answer

The constraint is that selling price of B = 2 * selling price of A. Let's call selling prices SA and SB = 2*SA, and cost prices a (for watch A) and b (for watch B).

Profit = (SA + SB) - (a + b) = SA + 2*SA - a - b = 3*SA - a - b

We need to know if 3*SA > a + b.

Statement 1: SA = 1.2a (sold A for 20% more than cost)
Substituting: 3*(1.2a) - a - b = 3.6a - a - b = 2.6a - b
For profit: need b < 2.6a

But Statement 1 tells us nothing about b. If b = 2a: profit = 0.6a > 0. If b = 10a: profit = -7.4a (loss). INSUFFICIENT.

Statement 2: SB > 0.9b, meaning she sold B for more than 90% of what she paid.
This tells us she didn't lose a lot on B, but says nothing about A or the overall picture. INSUFFICIENT.

Together: SA = 1.2a, SB = 2.4a
From Statement 2: SB > 0.9b, so 2.4a > 0.9b, which means b < 2.67a

Profit = 2.6a - b
We need b < 2.6a for a profit, but we only know b < 2.67a. Those aren't the same thing.

If b = 2.5a: profit = 2.6a - 2.5a = 0.1a > 0 (profit)
If b = 2.63a: profit = 2.6a - 2.63a = -0.03a < 0 (loss)

Both scenarios satisfy both statements, so we still can't determine the answer. INSUFFICIENT together.

Answer: E

This one trips people because Statement 1 sounds reassuring -- 20% gain on A is solid. And Statement 2 says she got at least 90% back on B, which also sounds decent. But B's selling price is tied to A's, so B could have a massive cost price, and "90% of a huge number" still leaves a big loss. That 2.6a vs 2.67a gap is very narrow, which is exactly why it's a hard DS question.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=88895 --- Harsha GMAT-Club-Forum-tjugb5d9.png

gullyboy09 · Answer

(2) Lana sold watch B for more than 90% of what she paid for it.

Here, we need to read this very carefully. Initially I took it as 90% more than CP, whereas it's saying more than 90% of CP, so SP can still be less than CP in this case.

basicboehly · Answer

Good question, I unfortunately translated the second statement as "greater than 1.9 times B's cost" for some reason

Lana bought two watches last year and sold both of them yest

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Lana bought two watches last year and sold both of them yest

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards