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# What is the value of x?

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Intern
Joined: 27 May 2013
Posts: 12
Concentration: Finance, Entrepreneurship
What is the value of x?  [#permalink]

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04 Sep 2015, 10:01
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65% (hard)

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51% (01:48) correct 49% (01:25) wrong based on 159 sessions

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What is the value of x?

(1) x:y = 3:11

(2) The least common multiple of x and y equals three times the value of y
EMPOWERgmat Instructor
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What is the value of x?  [#permalink]

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Updated on: 07 Apr 2019, 12:50
3
1
Hi rohankant12,

This question can be solved by TESTing VALUES.

We're asked for the value of X.

Fact 1: X:Y = 3:11

This ratio gives us a 'relationship' between X and Y, but does not tell us what either variable is. We know that X MUST be a multiple of 3 and Y MUST be an equivalent multiple of 11, but we don't have the actual numbers.

IF....X=3, Y=11, then the answer is 3
IF....X=6, Y=22, then the answer is 6
Fact 1 is INSUFFICIENT

Fact 2: The least common multiple of X and Y equals three times the value of Y

You might need to 'play around' with this Fact to figure out the pattern involved. From Fact 1, I'm thinking that we should look for X as a multiple of 3, so I'll start there...

IF...X = 3, then the LCM of X and Y has to be 3 TIMES the value of Y....

IF....X=3, Y=1, then the LCM is 3 (which is 3 times the value of Y) and the answer to the question is 3
IF....X=6, Y=2, then the LCM is 6 (which is 3 times the value of Y) and the answer to the question is 6
Fact 2 is INSUFFICIENT

Combined, we have evidence that X can likely be at least 2 different outcomes (3 or 6), but we have to incorporate all of the given information to prove it:

X = 3, Y = 11.... this fits the ratio 3:11 and the LCM is 33 (which is the value of 3Y).
X = 6, Y = 22.... this ratio (6:22) reduces to 3:11 and the LCM is 66 (which is the value of 3Y).
Combined, INSUFFICIENT

Final Asnwer:

As an aside, what is the source of this question?

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Originally posted by EMPOWERgmatRichC on 04 Sep 2015, 10:26. Last edited by EMPOWERgmatRichC on 07 Apr 2019, 12:50, edited 1 time in total. CEO Joined: 20 Mar 2014 Posts: 2624 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: What is the value of x? [#permalink] ### Show Tags 04 Sep 2015, 10:36 1 rohankant12 wrote: What is the value of X? 1) x:y = 3:11 2) the least common multiple of x and y equals three times the value of y Can someone help with this EMPOWERgmatRichC has presented a very good way of solving this question using values, but for algebraic way, look below: Per statement 1, x/y = 3/11 ---> x= 3k, y =11k, k $$\in$$integer. Thus this statement is not sufficient. Per statement 2, LCM (x,y) = 3y ---> different sets possible, (x,y)=(6,2), (3,1) etc. Thus this statement is not sufficient. Combining, you get, x=3k, y=11k and LCM (x,y)=3y Now, you need to consider 2 cases: Case 1: when k $$\neq$$3 or 11 ---> LCM (x,y) = LCM (3k, 11k) = 3*11*k = 33k =3y and this is true for ALL k. You will have many different values thus mkaing both statements NOT sufficient, but if you still want to proceed ahead, look below for the 2nd case. Case 2:when k = 3 or 11, LCM (x,y) = $$3^2$$*11 or 3*$$11^2$$ (in the simplest of terms). Thus you get 2 different possible values for different values of k, making E as the correct answer. Intern Joined: 16 Aug 2015 Posts: 18 Re: What is the value of x? [#permalink] ### Show Tags 04 Sep 2015, 13:18 Heey, this is how i solved the question. Statement(1) : x:y = 3:11 implies that x= 3k and y= 11k, hence x can be anything as it depends on the parameter k. So clearly statement 1 is insufficient. Statement (2) : the least common multiple of x and y equals three times the value of y We know that X*Y = LCM(x,y) * GCD(x,y) . by using this fact, we can interpret the S2 as follow: X*Y = 3*Y*GCD(X,Y), which after elimination becomes X= 3*GCD(X,Y). Here again we have no idea about the value of GCD(X,Y) so statement 2 is clearly insufficient. Now, if we take the two statements together, we can deduct that GCD(X,Y) = K, but does it add any valuable information or input? of course not ! the whole information embedded in one equation can be written as : X= 3 GCD(X,Y)= 3k... so the correct answer is (E). GL Director Joined: 05 Mar 2015 Posts: 999 What is the value of x? [#permalink] ### Show Tags 05 Oct 2015, 00:08 combining the two statements I got X=9 Y=33 isn't values were satisfied and we get answer choice as C Can anyone explain me please.... Math Expert Joined: 02 Sep 2009 Posts: 54369 Re: What is the value of x? [#permalink] ### Show Tags 05 Oct 2015, 02:02 rohit8865 wrote: combining the two statements I got X=9 Y=33 isn't values were satisfied and we get answer choice as C Can anyone explain me please.... What if x = 3 and y = 11? _________________ Current Student Joined: 20 Oct 2014 Posts: 37 GMAT 1: 740 Q49 V42 What is the value of x? [#permalink] ### Show Tags 05 Oct 2015, 11:21 Statement (1) is clearly insufficient. For statement (2), LCM of x and y is 3y. x=3 and x=3y both satisfy this constraint. Using both (1) and (2) also we don't get any more usable information. Hence, answer is 'E'. Board of Directors Joined: 17 Jul 2014 Posts: 2556 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: What is the value of x? [#permalink] ### Show Tags 29 Dec 2015, 19:37 we are given only absolute value. this is not sufficient to get a definite value for x. since multiple options are possible, the answer should be E. I tried to apply LCM/GCF formula, got to x=x. thus, can't do anything Intern Joined: 29 Aug 2018 Posts: 21 Re: What is the value of x? [#permalink] ### Show Tags 05 Apr 2019, 09:51 Hi guys , can anyone let me know where my mistake is : from the 2ed statement : we got , x=3 or x=3y now if we combine the two statements : x/y = 3/11 let's try x=3 , we got y=11 let's try x=3y , we got 3y/y =3/11 that means 3=3/11 which is not possible , so x=3 and y=11 so i picked c why am I getting this ? Bunuel please EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13950 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the value of x? [#permalink] ### Show Tags 05 Apr 2019, 12:57 Hi mike2100, If you consider Fact 2 by itself, then X COULD equal 3Y... meaning that X > Y. However, when you include the ratio in Fact 1, we know that X < Y... so X = 3Y is NOT a possibility. Consider these two options that fit BOTH facts: X = 3, Y = 11.... this fits the ratio 3:11 and the LCM is 33 (which is the value of 3Y). X = 6, Y = 22.... this ratio (6:22) reduces to 3:11 and the LCM is 66 (which is the value of 3Y). We now have two different possible values for X, so the final answer is INSUFFICIENT. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Intern
Joined: 29 Aug 2018
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Re: What is the value of x?  [#permalink]

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05 Apr 2019, 13:13
thanks for your reply , I understand that by testing values we get E , but I'm confused because my approach seems logical ,

EMPOWERgmatRichC wrote:
Hi mike2100,

If you consider Fact 2 by itself, then X COULD equal 3Y... meaning that X > Y. However, when you include the ratio in Fact 1, we know that X < Y... so X = 3Y is NOT a possibility.

ok so now since 3y is not a possibility , are we left with only x=3 ?
Manager
Joined: 25 Feb 2019
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Re: What is the value of x?  [#permalink]

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05 Apr 2019, 21:04
IMO E

from first we get

x = 3k
y = 11 k

from second statement we get ,

LCM = 3y

x*y*k = 3y

or xyk-3y = 0

y(xk-3) = 0

y=0 or xk-3 = 0

Y = 0 not possible

so xk-3=0

which is again the same equation as in statement 1

So IMO E

hope this helps

Posted from my mobile device
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Re: What is the value of x?  [#permalink]

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06 Apr 2019, 12:40
Hi mike2100,

I think that the general error in your thinking has to do with the information in Fact 2: "The least common multiple of X and Y equals three times the value of Y." This does NOT necessarily mean that X = 3Y. Since we're dealing with the LCM of a pair of integers, it's quite likely that the LCM is GREATER than both X and Y - but your work implies that the LCM is equal to X.

When dealing with Quant questions on the GMAT, if you're ever unsure about a math rule or whether you're properly interpreting a math pattern or not, the easiest way to prove if your thinking is correct is to come up with a couple of examples and see if they confirm that your idea is correct. In that way, TESTing VALUES can be useful on MOST Quant questions.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern Joined: 29 Aug 2018 Posts: 21 Re: What is the value of x? [#permalink] ### Show Tags 06 Apr 2019, 12:57 EMPOWERgmatRichC wrote: Hi mike2100, I think that the general error in your thinking has to do with the information in Fact 2: "The least common multiple of X and Y equals three times the value of Y." This does NOT necessarily mean that X = 3Y. Since we're dealing with the LCM of a pair of integers, it's quite likely that the LCM is GREATER than both X and Y - but your work implies that the LCM is equal to X. When dealing with Quant questions on the GMAT, if you're ever unsure about a math rule or whether you're properly interpreting a math pattern or not, the easiest way to prove if your thinking is correct is to come up with a couple of examples and see if they confirm that your idea is correct. In that way, TESTing VALUES can be useful on MOST Quant questions. GMAT assassins aren't born, they're made, Rich Dear Rich , thanks for your reply ,I think now I know exactly where my mistake was , I was thinking : LCM of x and y is 3y ok then the 3 must have come from x , so x have 2 options : 3y , 3 and that's correct in case y is a prime , but we don't know that, here's my mistake , right ? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13950 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the value of x? [#permalink] ### Show Tags 06 Apr 2019, 13:07 Hi mike2100, Yes - I think that properly explains the mistake. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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What is the value of x?  [#permalink]

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07 Apr 2019, 07:19
EMPOWERgmatRichC wrote:
Hi rohankant12,

This question can be solved by TESTing VALUES.

We're asked for the value of X.

Fact 1: X:Y = 3:11

This ratio gives us a 'relationship' between X and Y, but does not tell us what either variable is. We know that X MUST be a multiple of 3 and Y MUST be an equivalent multiple of 11, but we don't have the actual numbers.

IF....X=3, Y=11, then the answer is 3
IF....X=6, Y=22, then the answer is 6
Fact 1 is INSUFFICIENT

Fact 2: The least common multiple of X and Y equals three times the value of Y

You might need to 'play around' with this Fact to figure out the pattern involved. From Fact 1, I'm thinking that we should look for X as a multiple of 3, so I'll start there...

IF...X = 3, then the LCM of X and Y has to be 3 TIMES the value of Y....

IF....X=3, Y=1, then the LCM is 3 (which is 3 times the value of Y) and the answer to the question is 3
IF....X=6, Y=2, then the LCM is 6 (which is 3 times the value of Y) and the answer to the question is 6
Fact 2 is INSUFFICIENT

Combined, we have evidence that X can be at least 2 different outcomes (3 or 6).
Combined, INSUFFICIENT

Final Asnwer:

As an aside, what is the source of this question?

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

Hi Rich I do not know how the examples of statement 2 fulfill statement after you combine both statements. In both examples, the ration is NOT 3/11.
EMPOWERgmat Instructor
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Re: What is the value of x?  [#permalink]

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07 Apr 2019, 12:26
1
Hi Mo2men,

You're correct - the two pairs of values that you highlighted in Fact 2 do NOT fit the information in Fact 1 - so they don't "fit" all of the information that we're given. However, notice how X=3 and X=6 DO fit both Fact 1 and Fact 2. If you do the additional work (which I showed in a follow-up post), then you can prove the following:

X = 3, Y = 11.... this fits the ratio 3:11 and the LCM is 33 (which is the value of 3Y).
X = 6, Y = 22.... this ratio (6:22) reduces to 3:11 and the LCM is 66 (which is the value of 3Y).

Thus, X=3 and X=6 are both possible solutions and the final answer is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
SVP
Joined: 26 Mar 2013
Posts: 2133
Re: What is the value of x?  [#permalink]

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07 Apr 2019, 12:33
1
EMPOWERgmatRichC wrote:
Hi Mo2men,

You're correct - the two pairs of values that you highlighted in Fact 2 do NOT fit the information in Fact 1 - so they don't "fit" all of the information that we're given. However, notice how X=3 and X=6 DO fit both Fact 1 and Fact 2. If you do the additional work (which I showed in a follow-up post), then you can prove the following:

X = 3, Y = 11.... this fits the ratio 3:11 and the LCM is 33 (which is the value of 3Y).
X = 6, Y = 22.... this ratio (6:22) reduces to 3:11 and the LCM is 66 (which is the value of 3Y).

Thus, X=3 and X=6 are both possible solutions and the final answer is INSUFFICIENT.

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

Hi Rich,

Thanks a lot for you reply. Actually, I did the work as you suggest. Because you are neat and organized. I thought it might be helpful for other student to see the solution complete to avoid confusion for them.

Re: What is the value of x?   [#permalink] 07 Apr 2019, 12:33
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