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If x is a positive integer, is y^2(x^3-x+1)>75?1. y>12. (x-1)^2=16Source: GMAT Club Tests - hardest GMAT questions Hi, I think the answer/ explanation of this question is wrong. Here is the official explanation: --------------------------------------------- We need to know two things here The value of x Whether y is greater than 1 From S1, we only know that y>1 From S2, we only have the value of x. we also know that x is positive. So, we have to only consider the positive root. Combining the two statements, we have the required information. The correct answer is C. ------------------------------------------------ However, i think the answer is E, since we dont have any information on whether y is an integer or not. It can be possible that y is a fraction. Am i missing something guys????
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When you consider the statements together, you must use Statement 1 which tells you that 1 is greater than 1. It could be a fraction, but it will be a fraction greater than 1, thus making the statements together, still sufficient. jimmiejaz wrote: Hi,
I think the answer/ explanation of this question is wrong.
If x is a positive integer, is y^2(x^3-x+1)>75?
1. y>1
2. (x-1)^2=16
Here is the official explanation:
---------------------------------------------
We need to know two things here
The value of y
Whether y is greater than 1
From S1, we only know that y>1
From S2, we only have the value of x. we also know that x is positive. So, we have to only consider the positive root.
Combining the two statements, we have the required information.
The correct answer is C.
------------------------------------------------
However, i think the answer is E, since we dont have any information on whether y is an integer or not. It can be possible that y is a fraction.
Am i missing something guys????
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Hi. From S2 we know that x=5. If x=5 we know that (x^3-x+1)=125-5+1=121. As long as y>1, we are sure that y^2(x^3-x+1)>75. Hope this makes sense. jimmiejaz wrote: Hi,
I think the answer/ explanation of this question is wrong.
If x is a positive integer, is y^2(x^3-x+1)>75?
1. y>1
2. (x-1)^2=16
Here is the official explanation:
---------------------------------------------
We need to know two things here
The value of x
Whether y is greater than 1
From S1, we only know that y>1
From S2, we only have the value of x. we also know that x is positive. So, we have to only consider the positive root.
Combining the two statements, we have the required information.
The correct answer is C.
------------------------------------------------
However, i think the answer is E, since we dont have any information on whether y is an integer or not. It can be possible that y is a fraction.
Am i missing something guys????
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jimmiejaz wrote: Hi,
I think the answer/ explanation of this question is wrong.
If x is a positive integer, is y^2(x^3-x+1)>75?
1. y>1
2. (x-1)^2=16
Here is the official explanation:
---------------------------------------------
We need to know two things here
The value of x
Whether y is greater than 1
From S1, we only know that y>1
From S2, we only have the value of x. we also know that x is positive. So, we have to only consider the positive root.
Combining the two statements, we have the required information.
The correct answer is C.
------------------------------------------------
However, i think the answer is E, since we dont have any information on whether y is an integer or not. It can be possible that y is a fraction.
Am i missing something guys???? Both statement togather are suff. we need two things i.e. values of x and y. Statement 1 tells us the range of y. Statement 2 tells us the value of x. so togather the value of y^2 (x^3 - x + 1) is at least > 121. suff. C.
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In statement 2 why don't we account for:
x-1 = -4 ==> x = -3
and x-1 = 4 ==> x = 5
This would yield E as the answer. Am I missing something?
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CIO
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We know from the question stem that x is a positive integer. x-ALI-x wrote: In statement 2 why don't we account for:
x-1 = -4 ==> x = -3
and x-1 = 4 ==> x = 5
This would yield E as the answer. Am I missing something?
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ooops, didn't catch that part. Thanks! dzyubam wrote: We know from the question stem that x is a positive integer. x-ALI-x wrote: In statement 2 why don't we account for:
x-1 = -4 ==> x = -3
and x-1 = 4 ==> x = 5
This would yield E as the answer. Am I missing something? |
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Thanks dzyubam for the explanation.
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Just a useful reminder - you can write mathematical expressions in the posts by enclosing them in the [m] math [/m] tags. If you don't want to write those out, just select the line or part of the text that you want to be converted into math, and hit the "m" button in the menu (the one directly below the big "B") and the software will automatically insert the tags. You can also include a reference to the test question by hitting the "t" button.
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by expanding (x-1)^2=16 using foil, I created a quadratic equation x^2-2x-15=0 This produced the expression (x-5)*(x+3)=0 .... Plugging the solutions x=5 and x=-3 into the question stem I produced a "maybe" or "yes and no" answer to the question stem and rendered an answer of E! Please help!
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You forget that x is a positive integer, as stated in the question stem. jbark55 wrote: by expanding (x-1)^2=16 using foil, I created a quadratic equation x^2-2x-15=0 This produced the expression (x-5)*(x+3)=0 .... Plugging the solutions x=5 and x=-3 into the question stem I produced a "maybe" or "yes and no" answer to the question stem and rendered an answer of E! Please help!
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My answer is C.
This probem is similar to one given in the OG.
If x is a positive integer, is y^2(x^3-x+1)>75?
1. y>1
2. (x-1)^2=16
1. Insufficient. Y can be any number >1 and no X value is given.
2. Insufficient however statement 2 does give good information
(x-1)^2=16 can be simplified to read:
take the sqrt of both sides. x-1 = 4
x = 5... however we dont know what x is.
so we take statement 1 and combine with statement 2 and we can solve the equation.
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(x-1)^2 = 16shall be simplified as x-1=+-4or x=+5, x=-3if we consider (x-1)^2=4^2 and consider x-1 = 4We miss the second root ie x =-3<quadratic equation must have 2 roots>. In this question we are spared even if we consider x-1=4 , However if question had not specified x as positive integer, answer would have been E. y^2(x^3-x+1) +ve in case x=+5 and -ve in case x=-3. Good question...
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S1 is not sufficient as no info about x
S2 is not sufficient as no info about y
S2implies x=5, so as long as S1 is true (i.e. y>1) the inequality in the stem is holds good.
So Answer C
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we already know statement (1) or (2) proved insufficient when considered individually. When Combined, we get y^2(121) since y>1, the expression becomes (1 + k)(121)....k is some positive value being part of y. That is: 121 + 121k > 75 correct response is C
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If x is a positive integer, is y^2(x^3-x+1)>75
1. y>1
2. (x-1)^2=16
St 1 alone is not suff(B & D elimitated)
St2:
=>x=5,-3 (Since x is +ve , x=5)
St 2 alone is not suff(A & D eliminated)
Now, Combining both
y>1 & x=5
y^2(x^3-x+1)>75
=> OA is C.
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again i make careless mistake not read Q properly. Ans: C
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First I took statement 2 , We get x = 5 since x =-3 is ruled out. Applying x = 5 in the eqn we get y (121) > 75.For this expr to be true I want atleast y > 1 which is in statment 1. So each statement alone is insuff whereas both the statements combined can yield a result..
I will go with option C
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So immediately we are told more about x than y. We know that x is a positive integer. This being so, the whole blob of Xcubed whatever can be nothing less than 1. X cannot be less than 1 and so xcubed minus x plus 1 can be nothing less than 1. Now we need to know more about y.
Statement 1. tells us that y is greater than 1. This coupled with what we know about x is insufficient to tell us if the whole thing is greater than 75. Statement 1 did not tell us anything more than what we knew about x (that it is equal to or greater than 1), and not enough about y. Not sufficient.
Statement 2. (x-1)squared =16. This still tells us nothing about y and thus will likely be insufficient by itself.
But lets look further. FOILing out the (X-1)(x-1) = x^2 -2x+1=16 --->X^2 -2x-15=0. Now factoring this we get (x+3)(x-5)=0. So x could be either -3 or 5. We know that x cannot be negative from the initial statement. So x must be 5. Then plugging 5 back into the x cubed thing we get 125-5+1=121. So (y^2)121. Y is greater than 1 so the product must be greater than 75. If we put statements 1 and 2 together we get C. 1 and 2 are sufficient together.
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