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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

ans is b...... since x and y are both +ive int, x*y>1... only exception being x=y=1 as it is not given they are different integers... however it is given1/x +1/y<2.. this cannot be true if x=y=1.... so one or both have to be > 1
_________________

X and Y are positive integers. If 1/X + 1/Y < 2, which of the following must be true?

(A) X+Y>4 (B) X*Y>1 (C) X/Y+Y/X<1 (D) (X-Y)^2>0 (E) None of the above

Let X=1, 1+1/Y<2 1/Y<1 1<Y

Y>1 when X=1, A --> yes and no B --> yes C--> yes and no D--> yes and no

Answer: B
_________________

"The best day of your life is the one on which you decide your life is your own. No apologies or excuses. No one to lean on, rely on, or blame. The gift is yours - it is an amazing journey - and you alone are responsible for the quality of it. This is the day your life really begins." - Bob Moawab

X and Y are positive integers. If 1/X + 1/Y < 2, which of the following must be true?

(A) X+Y>4 (B) X*Y>1 (C) X/Y+Y/X<1 (D) (X-Y)^2>0 (E) None of the above

Trying a few values makes us realize that the only relation that holds is (B). But how can we be sure that (B) holds for all acceptable values of X and Y.

1/X + 1/Y < 2 implies (1/X + 1/Y)/2 < 1 A useful property of positive numbers is AM >= GM Arithmetic Mean >= Geometric Mean

Say, the numbers are 1/X and 1/Y AM = (1/X + 1/Y)/2 It is given that (1/X + 1/Y)/2 < 1 so we know that AM < 1

GM = \(\sqrt{\frac{1}{X}*\frac{1}{Y}}\)

Since GM <= AM,

\(\sqrt{\frac{1}{X}*\frac{1}{Y}}\) < 1

\(\frac{1}{XY} < 1\) (Squaring the inequality)

\(XY > 1\) (X and Y are positive so the inequality doesn't change)
_________________

Guys, can you guide me how D is not true? coz last time i checked, square of any number is greater than 0. Even if x is less than y, still, it's square would me more than 0..unless, x = y...
_________________

Appreciation in KUDOS please! Knewton Free Test 10/03 - 710 (49/37) Princeton Free Test 10/08 - 610 (44/31) Kaplan Test 1- 10/10 - 630 Veritas Prep- 10/11 - 630 (42/37) MGMAT 1 - 10/12 - 680 (45/34)

Guys, can you guide me how D is not true? coz last time i checked, square of any number is greater than 0. Even if x is less than y, still, it's square would me more than 0..unless, x = y...

Given: 1/X + 1/Y < 2 Say X = 2, Y = 2 These values satisfy the inequality: 1/2 + 1/2 < 2

But they do not satisfy (D) (X-Y)^2>0 (2-2)^2 = 0, not greater than 0 Hence (D) must not be true for all values. There are values that satisfy the inequality but does not satisfy (D)
_________________

Karishma, now i need a confirmation on GMAT questions... lets say that if two unknowns are given (like X and Y ), can we assume that these two are equals? I thought if we say x and y, they are implicitly different numbers..

VeritasPrepKarishma wrote:

krishnasty wrote:

Guys, can you guide me how D is not true? coz last time i checked, square of any number is greater than 0. Even if x is less than y, still, it's square would me more than 0..unless, x = y...

Given: 1/X + 1/Y < 2 Say X = 2, Y = 2 These values satisfy the inequality: 1/2 + 1/2 < 2

But they do not satisfy (D) (X-Y)^2>0 (2-2)^2 = 0, not greater than 0 Hence (D) must not be true for all values. There are values that satisfy the inequality but does not satisfy (D)

_________________

Appreciation in KUDOS please! Knewton Free Test 10/03 - 710 (49/37) Princeton Free Test 10/08 - 610 (44/31) Kaplan Test 1- 10/10 - 630 Veritas Prep- 10/11 - 630 (42/37) MGMAT 1 - 10/12 - 680 (45/34)

Karishma, now i need a confirmation on GMAT questions... lets say that if two unknowns are given (like X and Y ), can we assume that these two are equals? I thought if we say x and y, they are implicitly different numbers..

VeritasPrepKarishma wrote:

krishnasty wrote:

Guys, can you guide me how D is not true? coz last time i checked, square of any number is greater than 0. Even if x is less than y, still, it's square would me more than 0..unless, x = y...

Given: 1/X + 1/Y < 2 Say X = 2, Y = 2 These values satisfy the inequality: 1/2 + 1/2 < 2

But they do not satisfy (D) (X-Y)^2>0 (2-2)^2 = 0, not greater than 0 Hence (D) must not be true for all values. There are values that satisfy the inequality but does not satisfy (D)

Until and unless they mention 'distinct numbers' or 'X not equal to Y', X and Y can be equal. The equality can be a deal breaker/maker sometimes so you have to make sure that you have analyzed its effects too.
_________________

Until and unless they mention 'distinct numbers' or 'X not equal to Y', X and Y can be equal. The equality can be a deal breaker/maker sometimes so you have to make sure that you have analyzed its effects too.

_________________

Appreciation in KUDOS please! Knewton Free Test 10/03 - 710 (49/37) Princeton Free Test 10/08 - 610 (44/31) Kaplan Test 1- 10/10 - 630 Veritas Prep- 10/11 - 630 (42/37) MGMAT 1 - 10/12 - 680 (45/34)

Re: x and y are positive integers. If 1/x + 1/y < 2, which of [#permalink]

Show Tags

20 Apr 2014, 00:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: x and y are positive integers. If 1/x + 1/y < 2, which of [#permalink]

Show Tags

16 Aug 2015, 17:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: x and y are positive integers. If 1/x + 1/y < 2, which of [#permalink]

Show Tags

12 Feb 2016, 19:06

barakhaiev wrote:

x and y are positive integers. If 1/x + 1/y < 2, which of the following must be true?

(A) x + y > 4 (B) xy>1 (C) x/y + y/x < 1 (D) (x - y)^2 > 0 (E) None of the above

I thought it is some kind of trap here.. we can rewrite the original as: x+y<2xy

A - x=2, y=2 -> x+y is not greater than 4, yet 1/2 + 1/2 < 2. so A is out. B - if x and y are both positive integers, xy>1 all the times - looks good. C - x/y +y/x <1 or x^2 + y^2 < xy - which will never be true, if x and y are positive integers. D - x^2 + y^2 > 2xy - suppose x=2 and y=2. 4+4 = 8. 2*2*2=8. 8=8, it's not an inequality. E - since B works, e is out.

Re: x and y are positive integers. If 1/x + 1/y < 2, which of [#permalink]

Show Tags

26 May 2017, 07:54

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________