It is currently 17 Oct 2017, 10:30

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is x<y?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 02 Jun 2017
Posts: 1

Kudos [?]: 1 [0], given: 3

Is x<y? [#permalink]

Show Tags

New post 01 Oct 2017, 13:13
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

17% (00:13) correct 83% (00:50) wrong based on 24 sessions

HideShow timer Statistics

Is x<y?

1 \(\sqrt{x} < y\)
2 \(x^2 < y\)
[Reveal] Spoiler: OA

Kudos [?]: 1 [0], given: 3

Expert Post
Manhattan Prep Instructor
User avatar
S
Joined: 04 Dec 2015
Posts: 402

Kudos [?]: 239 [0], given: 56

GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
Is x<y? [#permalink]

Show Tags

New post 01 Oct 2017, 13:42
sahil5695 wrote:
Is x<y?

1 \(\sqrt{x} < y\)
2 \(x^2 < y\)


Interesting problem! Since there are only two variables, and the math looks like it's simplified already, I'm going to start by testing cases.

Statement 1:
If \(\sqrt{x} < y\), we could have a very small x and a very large y: for instance, x = 1 and y = 100. In that case, x < y, so the answer to the question is yes.

On the other hand, we could have a situation where \(\sqrt{x}\) is smaller than y, but x itself is actually bigger than y. You could do this by picking an x that's only a little bit bigger than y. Then, when you take the square root, it gets much smaller. For instance, x = 4 and y = 3. In that case, x > y, so the answer to the question is no.

We got both 'yes' and 'no' answers to the question, so the statement is insufficient. Cross off A and D.

Statement 2:
Our first case will work here as well. x = 1 and y = 100. So, x < y, so the answer to the question is yes.

Now we need to think of a situation where \(x^2\) is smaller than y, but where x is actually bigger than y. That means x would have to be bigger than \(x^2\). That only happens when x is a fraction. Let's say that x = 1/2, so \(x^2\) = 1/4. Then we need to choose a value of y that's bigger than 1/4, but smaller than 1/2. Let's say x = 1/2 and y = 1/3. That fits the statement, and x > y, so the answer is no.

We got both 'yes' and 'no' answers to the question, so the statement is insufficient. Cross off B.

Both statements together:

The problem here is that you can't get a 'no' answer if both statements are true.

If statement 2 is true, the only way to get a 'no' answer is if x and y are fractions.

If statement 1 is true, the only way to get a 'no' answer is if x is bigger than \(\sqrt{x}\). That doesn't happen if x is a fraction.

So, there's no way to get a 'no' answer from both statements at the same time. The answer must be 'yes'. So, the right answer is C.
_________________

Image

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

Kudos [?]: 239 [0], given: 56

Is x<y?   [#permalink] 01 Oct 2017, 13:42
Display posts from previous: Sort by

Is x<y?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.