GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 26 Sep 2018, 05:51

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

If x/y >1and x and y are integers, is x>1?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6815
If x/y >1and x and y are integers, is x>1?  [#permalink]

Show Tags

New post 26 Jun 2018, 09:26
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (02:35) correct 53% (02:13) wrong based on 43 sessions

HideShow timer Statistics

If \(\frac{x}{y}>1\) and x and y are integers, is x>1?
1) \(y^2+5y=6\)
2) \(x^2+x=6\)


New tricky question

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1343
Location: India
Premium Member
If x/y >1and x and y are integers, is x>1?  [#permalink]

Show Tags

New post 26 Jun 2018, 11:19
chetan2u wrote:
If \(\frac{x}{y}>1\) and x and y are integers, is x>1?
1) \(y^2+5y=6\)
2) \(x^2+x=6\)


New tricky question


x/y > 1 and x, y are both integers. Now both x & y have to have the same sign (both positive or both negative) for x/y to be > 1.
If x & y are both positive, then x has to be > y (then only x/y will be > 1, eg, x= 3, y= 2)
If x & y are both negative, then x has to be < y (then only x/y will be > 1, eg, x= -3, y= -2)
Basically for x/y > 1, x & y must have same signs and magnitude of x has to be greater than magnitude of y, i.e., |x| > |y|.

(1) y*(y+5) = 6.
Here y can be either 1 or -6. If y=1, then x > 1. But if y= -6, then x is negative.
So this statement is not sufficient.

(2) x*(x+1) = 6.
Here x can be either 2 or -3. So x can be > 1 or < 1.
This statement is also not sufficient.

Combining the two statements, we know that y can take only two values: 1 or -6. And x can also take only two values: 2 or -3.
Now if y= 1, then x can only be = 2 (because x/y has to be > 1).
If y= -6, then neither value of x will be ok here. Because if x= 2, then x/y will become negative; and if x= -3, then x/y will become < 1.
This means the only acceptable value of y is = 1, and thus the only acceptable value of x is = 2, which is > 1.
Thus sufficient.

Hence C answer.
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 596
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: If x/y >1and x and y are integers, is x>1?  [#permalink]

Show Tags

New post 26 Jun 2018, 11:41
chetan2u wrote:
If \(\frac{x}{y}>1\) and x and y are integers, is x>1?
1) \(y^2+5y=6\)
2) \(x^2+x=6\)


New tricky question


Interesting question! What makes this one tricky is the extra information in the question. My first thought on seeing it: I really need to remember that x/y is bigger than 1! I'm not trying to figure out whether x/y is bigger or smaller than 1. Instead, that's a fact I already know, and I'll need to combine it with the facts in the statements.

I don't know whether y is positive or negative, so I can't simplify the question by multiplying by y. So, I'll leave it how it is for now.

Statement 1: This simplifies, using quadratic rules, to 'y = -6 or y = 1'. At this point, I know two facts: I know that y is one of those two numbers, -6 or 1, although I don't know which one it is. I also know that x/y > 1, but I don't know what x is.

Given those two facts, is it possible for x to be greater than 1? Is it possible for x to be less than 1? If both of those are possible, then this statement is insufficient.

Well, since y might be 1, we could say that x = 100. That follows all of the rules (y is one of those two values, and x/y > 1), and x is greater than 1.

And since y might be -6, we could say that x = -600. That follows all of the rules (y is one of those two values, and x/y > 1), and x is less than 1.

Since x could be either bigger or smaller than 1, the statement is insufficient. Eliminate A and D.

Statement 2: This simplifies using quadratic rules to 'x = -3 or x = 2'. Again, I know two facts: I know that x is one of those two numbers (although I don't know which one). I also know that x/y > 1. That's not a very interesting fact, since I have no way of figuring out what y is.

It's possible for x to be less than 1, since x could equal -3.

It's also possible for x to be greater than 1, since x could equal 2.

So, the statement doesn't tell us whether x is less than or greater than 1. Insufficient. Eliminate B.

Both statements: Now, we know three facts! Here they are:

x = -3 or 2
y = 1 or -6
x/y > 1

And we're trying to figure out:

is x > 1?

The first thing to figure out is whether x and y could be any of those numbers, or whether we can eliminate some possibilities because they break the rules. It's not possible for x to be -3 and y to be 1, since if that's true, we'd be breaking the third rule, that says x/y > 1. Similarly, it's not possible for x to be -3 and y to be -6. It's also not possible for x to be 2 and y to be -6. The only set of numbers that follows all three of our rules is x = 2 and y = 1.

So basically, we can translate the two statements plus the question as giving us this information:

x = 2 and y = 1.

If we know that, do we know the answer to the question ('is x > 1?')? Yes, we do, since x is definitely 2 and 2 is definitely bigger than 1.
_________________

Image

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

Intern
Intern
avatar
B
Joined: 15 May 2017
Posts: 25
GMAT ToolKit User CAT Tests
If x/y >1and x and y are integers, is x>1?  [#permalink]

Show Tags

New post 26 Jun 2018, 15:39
x and y are integers.
1. We get y is 1 or -6
X can take any value +ve or -ve and accordingly be greater or smaller than y
Not Suff

2. we get x is 2 or -3
Y can take any value +ve or -ve and accordingly be greater or smaller than X
Not suff

Both together
we know \(\frac{X}{Y}\) >1
So X=2 and Y=1

Correct Answer C
GMAT Club Bot
If x/y >1and x and y are integers, is x>1? &nbs [#permalink] 26 Jun 2018, 15:39
Display posts from previous: Sort by

If x/y >1and x and y are integers, is x>1?

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

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.