Pedro weighs less than 90 pounds but x percent more than Pablo.

Question

Pedro weighs less than 90 pounds but x percent more than Pablo. Is x>20?

(1) Pedro weighs 16 pounds more than Pablo.

(2) If Pedro’s weight decreased by 18% and Pablo’s weight remained the same, Pedro would still weigh more than Pablo.

Edskore · Answer

The concept being tested here is Data Sufficiency with percent increase and an inequality — a combination that trips up a lot of people because they instinctively try to solve for exact weights instead of just checking whether the condition x > 20 can be confirmed or ruled out.

Quick setup: If Pedro weighs x% more than Pablo, then Pedro = Pablo × (1 + x/100). The question asks: is x > 20?

Step 1 — Translate the question into algebra.
Let Pablo's weight = P. Then Pedro's weight = P(1 + x/100).
We're also told Pedro < 90. The question is just: is x > 20?

Step 2 — Test Statement (1): Pedro weighs 16 pounds more than Pablo.
This tells us Pedro − Pablo = 16, so x/100 = 16/P, meaning x = 1600/P.
For x > 20, we'd need P < 80.
But we only know Pedro < 90 — Pedro could be 88 (so Pablo = 72, x ≈ 22) OR Pedro could be 17 (so Pablo = 1, x = 1600). Both satisfy Pedro < 90 and the 16-pound difference.
The trap here is assuming that "16 pounds more" uniquely pins down x. It doesn't — x depends entirely on Pablo's actual weight, which we don't know.
Statement (1) alone is Not Sufficient.

Step 3 — Test Statement (2): If Pedro's weight decreased by 18%, he'd still weigh more than Pablo.
This means 0.82 × Pedro > Pablo.
Since Pedro = Pablo(1 + x/100), substituting:
0.82 × Pablo(1 + x/100) > Pablo
→ 0.82(1 + x/100) > 1
→ 1 + x/100 > 1/0.82 ≈ 1.2195
→ x/100 > 0.2195
→ x > 21.95

So x is definitely greater than 20. Statement (2) alone is Sufficient.

Answer: B

The common trap: Students spend time trying to find Pablo's exact weight using Statement (1) instead of recognizing it's a relationship question. In DS, always ask "can I answer yes/no?" before solving for values.

Takeaway: When DS asks about a percent relationship, set up the inequality first — if one statement resolves it completely without needing a specific value, that's your answer.

— Kavya | 725 (Q90, V85, DI79) | GMAT Focus Edition

kevincan · Answer

I love your use of P in your commentary about statement 1, but then you abandoned it and momentarily lost sight of the question as a result

GMATcracker101 · Answer

Let's first understand the equations provided in the question before moving to the statements.

Pedro = a 
Pable = b

a<90, ------ (i)

b(1 + x/100) = a, ------ (ii)

x>20?

This is what is given in the question.

Now, let us take statement (1) -

(1) Pedro weighs 16 pounds more than Pablo.

a = b + 16 ------- (iii)

We will observe and use (i), (ii) and (iii) to solve this. I am not sure if this method is 100% accurate but the way I have solved this is - 
assume that the max value of a = 90 (as it is weight and it could be 89.99 as close to 90 as possible)

=> b = 74 and x = 21.62%, by solving (ii) and (iii).

The lesser the value of a the higher x will be hence I have assumed the max value of a.

ex. if we assume a = 80 then x = 25%

Hence, we get that x>20, so this is sufficient.

(2) If Pedro’s weight decreased by 18% and Pablo’s weight remained the same, Pedro would still weigh more than Pablo. 
 
82/100 a > b or 0.82a > b ---- (iv)

Same as above we will use (i), (ii) and (iv) to solve this.

Again assume max value of a = 90 hence b = 73.8 and x = 21.95%

if we assume a lower value of a, for ex. 80 then b = 65.6 and x = 21.95%.

Hence, we get that x>20, so this is also sufficient.

Therefore, the answer is (D).

Appreciate a confirmation if this method is accurate.

kevincan · Answer

This is correct !

I would have reasoned that , according to statement 1 , Pablo weighs less than 74, and that 16 pound difference is more than 1/5 of 74. I’m a big fan of fractions!

As for (2) , if 0.82a > b, a > 100b/82 > 1.2b
1

crimson_noise · Answer

You correctly wrote: Pedro = p(1+x/100) And from Statement (1): x = 1600/p Also correct. You concluded: For x > 20, we’d need P < 80 Correct so far. But you then said: We only know Pedro < 90 — Pedro could be 88 or 17 — so x is not fixed. This misses a critical constraint. We know: Pedro = P + 16 And we are told: Pedro < 90 So: P + 16 < 90 P < 74 Not 80. It must be less than 74, not less than 90 independently. That restriction changes everything. Now check x with the correct bound x =1600/P The smallest possible x happens when P is largest. Largest allowed P is just under 74. x > 1600/74 = approx. 21.62 That is always greater than 20 . There is no possible value where x <= 20 . So: Statement (1) is Sufficient.

egmat · Answer

Pedro weighs x% more than Pablo, so:
Pedro = Pablo × (1 + x/100)

Rearranging: x = 100 × (Pedro - Pablo) / Pablo

We need to determine: Is x > 20?

---
Statement 1: Pedro weighs 16 pounds more than Pablo.

So x = 1600 / Pablo

Is x > 20? This requires: Pablo < 80

From the question stem: Pedro < 90, and Pedro = Pablo + 16
So: Pablo + 16 < 90 → Pablo < 74

Since Pablo < 74, which is definitely less than 80:
x = 1600/Pablo > 1600/74 > 21.6

x is always greater than 20. → SUFFICIENT

--
Statement 2: If Pedro's weight decreased by 18%, Pedro would still weigh more than Pablo.

This means: Pedro × 0.82 > Pablo
So: Pedro/Pablo > 1/0.82 ≈ 1.2195

This tells us Pedro is more than ~22% greater than Pablo.

Since x represents how much percent more Pedro weighs than Pablo:
x > 21.95%

x is always greater than 20. → SUFFICIENT

---

Answer: D

kevincan · Answer

Wonderfully explained, though your dividing 1600 by 74 was needless, as you had already established that the answer is yes if Pablo weighs less than 80

Pedro weighs less than 90 pounds but x percent more than Pablo.

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GMAT Data Sufficiency (DS) Questions

Pedro weighs less than 90 pounds but x percent more than Pablo.

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