What is X? : GMAT Data Sufficiency (DS)
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# What is X?

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23 Dec 2013, 18:59
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Difficulty:

25% (medium)

Question Stats:

68% (01:52) correct 32% (00:39) wrong based on 116 sessions

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What is x?

(1) x= 4y-4
(2) xy = 8
[Reveal] Spoiler: OA

Last edited by uwengdori on 23 Dec 2013, 19:00, edited 1 time in total.
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23 Dec 2013, 18:59
uwengdori wrote:
Hi, I'm working on MGMAT algebra, and one question is

what is x?
1) x= 4y-4
2) xy = 8

Easy stuff obviously. we substitute and we get y = 2, and y = -1, which gives us x = 4, and x = -8

My question is I thought the answer would be 'C', but the answer says E. yes there are two x solutions, but from a quadratic equation pt of view, we did find definite solid answers for x, which are the two values we found above. So the way my brain thinks is we did answer the question of 'what the x is'. It is a singular 'is' in the question but still.

Of course, there are many scenarios of DS, but when solving DS questions, should I assume that there is absolutely and should only be one single answer in such cases as this?
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24 Dec 2013, 01:15
uwengdori wrote:
uwengdori wrote:
Hi, I'm working on MGMAT algebra, and one question is

what is x?
1) x= 4y-4
2) xy = 8

Easy stuff obviously. we substitute and we get y = 2, and y = -1, which gives us x = 4, and x = -8

My question is I thought the answer would be 'C', but the answer says E. yes there are two x solutions, but from a quadratic equation pt of view, we did find definite solid answers for x, which are the two values we found above. So the way my brain thinks is we did answer the question of 'what the x is'. It is a singular 'is' in the question but still.

Of course, there are many scenarios of DS, but when solving DS questions, should I assume that there is absolutely and should only be one single answer in such cases as this?

When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can get the single numerical value of this variable.

Since you get TWO possible values of x, the statements are not sufficient.

Hope it's clear.
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24 Dec 2013, 02:26
uwengdori wrote:
uwengdori wrote:
Hi, I'm working on MGMAT algebra, and one question is

what is x?
1) x= 4y-4
2) xy = 8

Easy stuff obviously. we substitute and we get y = 2, and y = -1, which gives us x = 4, and x = -8

My question is I thought the answer would be 'C', but the answer says E. yes there are two x solutions, but from a quadratic equation pt of view, we did find definite solid answers for x, which are the two values we found above. So the way my brain thinks is we did answer the question of 'what the x is'. It is a singular 'is' in the question but still.

Of course, there are many scenarios of DS, but when solving DS questions, should I assume that there is absolutely and should only be one single answer in such cases as this?

even without substitution or solving the two statements combined you get E: becasue you still do not the value of Y, via the other way around.

regards
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The value of x: 2 roots problem [#permalink]

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05 Jan 2014, 01:24
Hello there =)

I'm using the Manhattan GMAT Strategy Guides set for preparation and I've come across several obvious mistakes in the answers/explanations that follow the problem sets. This time, however, I cannot decide whether the "official" answer is a mistake or is it just that my understanding of the question mismatches the one of the GMAT tests / guides compilers.

So, without further ado, here it goes. In the problem set concluding the Quadratic Expressions chapter of the Algebra guide there is an extremely easy task for Data Sufficiency, namely:

DS: What is x?

(1) x = 4y - 4
(2) xy = 8

It is not too hard to see that the possible x's values are -8 and 4, and we can only come to that conclusion by using both statements simultaneously. Hence, my answer choice is C. The Manhattan people, however, quite disagree, and I quote:

"10. (E): Each statement alone is not enough information to solve for x. Using statements 1 and 2 combined,
if you substitute the expression for x in the first equation, into the second, you get two different answers:

/here goes the detailed solving process/

(E) Statements 1 and 2 TOGETHER are NOT SUFFICIENT".

I'm begging you, explain this to me I could've understood it if the question was formulated as "what is the VALUE of x", but in its current wording I can only answer that, using both statements provided, we can derive that x assumes values of -8 and 4. Is existence of several clearly defined roots considered as absence of a value of a variable in English-speaking world, is this simply a typo or am I completely dumb?

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Re: The value of x: 2 roots problem [#permalink]

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05 Jan 2014, 02:59
Hi,

i have not even checked my calculation but took me 20 seconds to find out it was E.

This is a typical GMAT DS problem: in theory you end up with to answers since you have (with both) 8=4y² - 4y

You end up with your two possibilities and you will have two value of X. Since you are asked only one, the answer is E.

Hope it helps
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Re: The value of x: 2 roots problem [#permalink]

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05 Jan 2014, 04:28
Paris75

Thanks for answering =) However, I still don't get it: the "E" option implies that the information given in the two statements is not enough to provide an answer to the question stated as follows: "What is x?", which means, to my mind, the same as "What is the solution for these equations in terms of x?", which, in turn, equals the task of solving the equation / the system of two equations. And that's the answer: x takes values of -8 and 4, it is the solution, it's just that in the hard and tangled real life variables may assume more than just one value. Or shall I always understand such questions as those requiring one and only possible value as an answer?
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Re: The value of x: 2 roots problem [#permalink]

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05 Jan 2014, 04:38
By the way, I'm not completely sure I posted this in the right thread, it seems that this subforum is dedicated to posting the tasks rather than asking how to solve them. Strictly speaking, I did post a task here, but it still doesn't feel right =) Would you kindly redirect me to the right subforum -- I already have found another task seemingly wrongly solved by the much respected Manhattans, but I don't want to risk posting my second plea for help not in the right place, too =)
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Re: The value of x: 2 roots problem [#permalink]

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05 Jan 2014, 05:06
werbliben wrote:
Hello there =)

I'm using the Manhattan GMAT Strategy Guides set for preparation and I've come across several obvious mistakes in the answers/explanations that follow the problem sets. This time, however, I cannot decide whether the "official" answer is a mistake or is it just that my understanding of the question mismatches the one of the GMAT tests / guides compilers.

So, without further ado, here it goes. In the problem set concluding the Quadratic Expressions chapter of the Algebra guide there is an extremely easy task for Data Sufficiency, namely:

DS: What is x?

(1) x = 4y - 4
(2) xy = 8

It is not too hard to see that the possible x's values are -8 and 4, and we can only come to that conclusion by using both statements simultaneously. Hence, my answer choice is C. The Manhattan people, however, quite disagree, and I quote:

"10. (E): Each statement alone is not enough information to solve for x. Using statements 1 and 2 combined,
if you substitute the expression for x in the first equation, into the second, you get two different answers:

/here goes the detailed solving process/

(E) Statements 1 and 2 TOGETHER are NOT SUFFICIENT".

I'm begging you, explain this to me I could've understood it if the question was formulated as "what is the VALUE of x", but in its current wording I can only answer that, using both statements provided, we can derive that x assumes values of -8 and 4. Is existence of several clearly defined roots considered as absence of a value of a variable in English-speaking world, is this simply a typo or am I completely dumb?

Merging similar topics.

For answer check this post: what-is-x-164957.html#p1309657

Hope this helps.
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05 Jan 2014, 05:28
Bunuel

Thanks =) And my apologies for double-posting this task.
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31 Mar 2015, 23:19
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What is x?
(1) x = 4y - 4
(2) x y = 8

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31 Mar 2015, 23:21
x = 4y — 4
xy — (4y - 4)y = 8
4y2-4 y = 8
y2 - y - 2 = 0
0 + D 0/ - 2) = 0
y = { - l ,2 }
X = { - 8, 4}

As we are able to get the value of X, shouldn't the answer be C.
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01 Apr 2015, 00:40
From St1, its pretty evident Not sufficient.
From St2, y=8/x.

Combining we get, x=32/x -1
Solving we get x=-8 or 4.
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01 Apr 2015, 02:38
ashuaggi wrote:
x = 4y — 4
xy — (4y - 4)y = 8
4y2-4 y = 8
y2 - y - 2 = 0
0 + D 0/ - 2) = 0
y = { - l ,2 }
X = { - 8, 4}

As we are able to get the value of X, shouldn't the answer be C.

Merging similar topics.

For answer check this post: what-is-x-164957.html#p1309657

Hope this helps.
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01 Apr 2015, 02:52
uwengdori wrote:
What is x?

(1) x= 4y-4
(2) xy = 8

(1) x= 4y-4
X=4(Y-1)
Not sufficient.
(2) xy = 8
Not sufficient.

combined together :
Y(Y-1)=2
Y=-1,2 and so X=-8,4
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05 Apr 2015, 19:49
If we add eqns from statement 1 & 2, we have:

x + xy = 4y+ 4
x(1 + y) = 4(y+1)
Divide both sides by (y+1), we get x = 4.
Hence C

Can someone tell plz me, what did I miss here ?

Thanks!
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06 Apr 2015, 11:05
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Hi sytabish,

When you divided both sides by (Y+1), you 'removed' a potential solution. Here's a slightly different way to look at the algebra involved:

X = 4Y - 4
XY = 8

We can substitute in the value for X, giving us....

(4Y-4)(Y) = 8
4Y^2 - 4Y - 8 = 0

This is a Quadratic that can be factored into 2 pieces:

4Y^2 - 4Y - 8 = 0
(Y + 1)(4Y - 8) = 0

Y = -1 or +2

Since Y has 2 different solutions, you can plug those options into the second equation to prove that X has 2 different solutions:

IF...
Y = -1
XY = 8
X = -8

IF...
Y = 2
XY = 8
X = 4
Combined, INSUFFICIENT

[Reveal] Spoiler:
E

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Re: What is X?   [#permalink] 06 Apr 2015, 11:05
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