Official Guide Question 73

[KevinMoon]

Hi,

Can someone help me with this question:

Q: If X²+Y² = 29, what is the value of (X-Y)²?

(1) XY = 10
(2) X = 5

The solution states that (2) is not sufficient as you need the value of XY to solve the problem and X = 5 does not provide enough information to evaluate XY. However, if you know the value of X and you know that X²+Y² = 29, then surely this is sufficient?

What am I missing?

Thanks
Kevin

[Brent@GMATPrepNow]

If X² + Y² = 29, what is the value of (X - Y)²?

(1) XY = 10
(2) X = 5

Target question: What is the value of (X - Y)²?

Given: X² + Y² = 29

IMPORTANT: If we SCAN the answer choices, we can see that it may be useful to REPHRASE the target question.
If we EXPAND (X-Y)², we get X² + 2XY + Y²
Since we're told that X² + Y² = 29, we can replace X² + Y² with 29, to get...
(X - Y)² = X² + 2XY + Y² = 2XY + 29

So, to find the value of (X-Y)², we need only find the value of XY.
This means we can rephrase the target question as...

REPHRASED target question: What is the value of XY?

Statement 1: XY = 10
Perfect!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Aside: If we want to go back to the original target question, we can still see that statement 1 is sufficient. We get: (X - Y)² = X² + 2XY + Y² = 2(10) + 29 = 49. Done!


Statement 2: X = 5
This does not provide enough information to find the value of XY.
Here's why:
If X² + Y² = 29, we can replace X with 5 to get: 5² + Y² = 29
Simplify to get: 25 + Y² = 29, which means Y² = 4
Solve to get: Y = 2 OR Y = -2
If Y = 2, then XY = (5)(2) = 10
If Y = -2, then XY = (5)(-2) = -10
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Cheers,
Brent

[[email protected]]

Hi KevinMoon,

Brent has properly explained this DS questions, so I won't rehash that here.

What I can do is offer some advice about being thorough. The GMAT is a test of patterns (in all sections of the Test), so you have to learn and remember that patterns that will show up AND be prepared to have your knowledge/ability tested in a variety of ways.

Most people know that X^2 = 16 has two solutions (4 and -4), but can you see that EVERY TIME it appears. The GMAT tests certain concepts repeatedly as a way to gauge your ability and assign you a score that you deserve.

ANY time you see a squared-term, you should think "there's probably more than one answer" and then go about the necessary steps to PROVE the possibilities. This is one of the ways that the GMAT can determine your thoroughness.

GMAT assassins aren't born, they're made,
Rich

[rdds]

If X² + Y² = 29, what is the value of (X - Y)²?

(1) XY = 10
(2) X = 5

Target question: What is the value of (X - Y)²?

Given: X² + Y² = 29

IMPORTANT: If we SCAN the answer choices, we can see that it may be useful to REPHRASE the target question.
If we EXPAND (X-Y)², we get X² + 2XY + Y²
Since we're told that X² + Y² = 29, we can replace X² + Y² with 29, to get...
(X - Y)² = X² + 2XY + Y² = 2XY + 29

So, to find the value of (X-Y)², we need only find the value of XY.
This means we can rephrase the target question as...

REPHRASED target question: What is the value of XY?

Statement 1: XY = 10
Perfect!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Aside: If we want to go back to the original target question, we can still see that statement 1 is sufficient. We get: (X - Y)² = X² + 2XY + Y² = 2(10) + 29 = 49. Done!


Statement 2: X = 5
This does not provide enough information to find the value of XY.
Here's why:
If X² + Y² = 29, we can replace X with 5 to get: 5² + Y² = 29
Simplify to get: 25 + Y² = 29, which means Y² = 4
Solve to get: Y = 4 OR Y = -4
If Y = 4, then XY = (5)(4) = 20
If Y = -4, then XY = (5)(-4) = -20
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Cheers,
Brent

Pardon me if my question is very silly,
i did not understand why should we
Solve for: Y = 4 OR Y = -4
instead of y=2 or y=-2

[Brent@GMATPrepNow]

Pardon me if my question is very silly,
i did not understand why should we
Solve for: Y = 4 OR Y = -4
instead of y=2 or y=-2

You're absolutely correct. It should be y=2 or y=-2

I edited my response accordingly.

Cheers and thanks,
Brent

[Scott@TargetTestPrep]

Hi,

Can someone help me with this question:

Q: If X²+Y² = 29, what is the value of (X-Y)²?

(1) XY = 10
(2) X = 5

The solution states that (2) is not sufficient as you need the value of XY to solve the problem and X = 5 does not provide enough information to evaluate XY. However, if you know the value of X and you know that X²+Y² = 29, then surely this is sufficient?

What am I missing?

Thanks
Kevin

Solution:

We need to determine the total of games that Team A won given that they won 50% of their first 20 games and all the remaining games. Notice that they won 10 of their first 20 games.

Statement One Alone:

Since Team A played 25 games altogether, they won the last 5 games. Adding to this the 10 games they won in their first 20 games, they won 15 games altogether. Statement one alone is sufficient.

Statement Two Alone:

If we let x be the number of games remaining (after the first 20 games), we can create the equation:

10 + x = 0.6(20 + x)

10 + x = 12 + 0.6x

0.4x = 2

x = 2/0.4 = 20/4 = 5

Since they won all their remaining games, they won the last 5 games. Adding to thisPlus the 10 games they won in their first 20 games, they won 15 games altogether. Statement two alone is sufficient.

Answer: D

[gdumral]

How can we expand (X-Y)², as X² + 2XY + Y². Shouldn't it be X² - Y² ? What am I missing here?