What is the value of x?

Question

(1) x:y = 3:11

(2) The least common multiple of x and y equals three times the value of y

EMPOWERgmatRichC · Answer

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:  E

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

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

ENGRTOMBA2018 · Answer

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  
eq 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.

issamL · Answer

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

rohit8865 · Answer

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.... :oops:

Bunuel · Answer

What if x = 3 and y = 11?

korrag · Answer

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'.

mvictor · Answer

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

mike2100 · Answer

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

EMPOWERgmatRichC · Answer

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

mike2100 · Answer

thanks for your reply , I understand that by testing values we get E , but I'm confused because my approach seems logical , ok so now since 3y is not a possibility , are we left with only x=3 ?

m1033512 · Answer

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

award kudos if helpful

Posted from my mobile device

EMPOWERgmatRichC · Answer

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

mike2100 · Answer

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 ?

EMPOWERgmatRichC · Answer

Hi mike2100,

Yes - I think that properly explains the mistake.

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

Mo2men · Answer

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.

EMPOWERgmatRichC · Answer

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

Mo2men · Answer

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. Again thank for your effort.

What is the value of x?

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What is the value of x?

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