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What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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Updated on: 26 Jan 2016, 14:15
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What is the value of x? (1) \(x^2 + x + 10 = 16\) (2) \(x = 4y^4+2y^2+2\)
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Originally posted by GMAT4937 on 26 Jan 2016, 13:54.
Last edited by GMAT4937 on 26 Jan 2016, 14:15, edited 1 time in total.



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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26 Jan 2016, 14:09
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Quote: What is the value of x ?
(1) x² + x + 10 = 16
(2) x = 4y⁴ + 2y² +2 Target question: What is the value of x? Statement 1: x² + x + 10 = 16 Rewrite as: x² + x  6 = 0 Factor: (x + 3)(x  2) = 0 So, x = 3 OR x = 2Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x = 4y⁴ + 2y² + 2 As you can see, the value of x depends on the value of y. Consider these two cases: Case a: y = 0, in which case x = 4( 0⁴) + 2( 0²) + 2. Evaluate to see that x = 2Case b: y = 1, in which case x = 4( 1⁴) + 2( 1²) + 2. Evaluate to see that x = 8Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that x = 3 OR x = 2Statement 2: Since y⁴ and 2y² are greater than or equal to zero FOR ANY value of y, we can see that 4y⁴ + 2y² + 2 MUST BE POSITIVE. In other words, x must be POSITIVE. If x must be POSITIVE, then x MUST equal 2Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent
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What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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26 Jan 2016, 14:31
Thanks for your explanation! I was thrown off by the extra variable "y" in the second statement, but when I got a positive and negative solution for x in statement one, that should've helped me figure out how to make use of the second.



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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15 May 2016, 09:34
Hi,
Can anyone clarify my query here?
Nothing is stated about 'y' rite...?? So y can be irrational, rational, integer, etc.
If i assume an extreme case: y an irrational number, then the answer is E rite?
Please clarify? Should i not take this case into consideration?



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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15 May 2016, 09:40
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HARRY113 wrote: Hi,
Can anyone clarify my query here?
Nothing is stated about 'y' rite...?? So y can be irrational, rational, integer, etc.
If i assume an extreme case: y an irrational number, then the answer is E rite?
Please clarify? Should i not take this case into consideration? For (2): regardless what real number y is (rational, irrational, ...), y in even power would be nonnegative. Thus, \(x = 4y^4+2y^2+2=nonnegative+nonnegative+positive=positive\). From (1) x = 3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient. Answer: C.
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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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21 May 2016, 14:03
This is good question to help you make start thinking on a higher level for the GMAT and start for DS questions start asking the question "Why are they giving me this information?"
The question is x = ?
Statement 1:
When factored works out to be x = 2 or x = 3. This is clearly insufficient as we have two answers for x, one positive and one negative. When I solve and quadratic and I get one positive and one negative answer its usually a good idea to double check the question to make it doesn't provide a small bit of info that could eliminate one of the answer choices. In this case, there's no additional info so we'll carry on.
Statement 2:
Just by looking at the question we can see it's insufficient. Plug in 1 for y and we get one answer and plug in 2 and we get a different answer.
Statements 1 & 2:
This is where it might look insufficient. But if we look back at statement 2 and ask ourselves why did the test makers give us this info? We have one negative answer for x and one positive answer. Is there any value for y we can plug in that will give us an negative answer for x? No, all of the powers of Y are even so the answer will always be positive. Therefore, X = 2 and we pick answer C.



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Re: What is the value of x? [#permalink]
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28 Feb 2017, 15:04
souvonik2k wrote: What is the value of x?
(1) x² + x + 10 = 16 (2) x = 4y⁴ + 2y² +2
Target question: What is the value of x? Statement 1: x² + x + 10 = 16 Given: x² + x + 10 = 16 Subtract 16 from both sides: x² + x  6 = 0 Factor: (x + 3)(x  2) = 0 So, EITHER x = 3 OR x = 2Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x = 4y⁴ + 2y² +2 Since we don't know anything about the value of y, there are many possible values of x. Here are two: Case a: if y = 0, then x = 4(0)⁴ + 2(0)² +2 = 2 Case b: if y = 1, then x = 4(1)⁴ + 2(1)² +2 = 8 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that x = 3 OR x = 2 Statement 2 tells us that x is POSITIVE. How do we know that x is POSITIVE? Well, 4y⁴ ≥ 0 and 2y² ≥ 0 for all values of y. So, the SUM 4y⁴ + 2y² +2 MUST BE POSITIVE. Since x = 4y⁴ + 2y² +2, we know that x is POSITIVE. If x is positive, then x cannot equal 3, which means x must equal 2Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent
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What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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27 Jul 2017, 18:50
GMAT4937 wrote: What is the value of x?
(1) \(x^2 + x + 10 = 16\) (2) \(x = 4y^4+2y^2+2\) (1) \(x^2 + x + 10 = 16\) \(x^2 + x + 10  16 = 0\) \(x^2 + x + 6 = 0\) \(x^2 + 3x  2x + 6 = 0\) \(x(x + 3)  2 (x + 3) = 0\) \((x2)(x + 3) =0\) Therefore \(x\) could be \((2)\) or \((3)\) I is Not sufficient. (2) \(x = 4y^4+2y^2+2\) Value of \(x\) depends on value of \(y\). We do not know value of \(y\), hence we cannot find value of \(x\) from the equation alone. II is Not Sufficient. Combining (1) and (2) From (1) we get \(x\) could be \((2)\) or \((3)\) From (2) we get \(x\) should be positive. Hence \(x\) should be \(2\) Answer (C)...



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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08 Oct 2017, 13:23
Solve that in a similar way. In condition 2 x must be even since all numbers on the right side are even. So, only possible answer is x = 2 considering condition 1.



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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08 Oct 2017, 13:51
GC2808 wrote: Solve that in a similar way. In condition 2 x must be even since all numbers on the right side are even. So, only possible answer is x = 2 considering condition 1. You can only make that assumption if you know the numbers are integers. For instance, here's a much simpler problem: x = 2y + 4 If you know that x and y are both integers, x definitely has to be even. But if they don't have to be integers, you could say that y = 0.5. In that case, x = 1 + 4 = 5, which is odd.
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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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10 Dec 2017, 10:43
Can someone please tell me if my approach is correct or incorrect:
If we plug in x as 3 into the second statement, we get 4y^4 + 2y^2 + 5 = 0  but if we try to solve for a value of y, we are unable to because we cannot factor.
If we plug in x as 2 into the second statement, we get 4y^4 + 2y^2 = 0, we get either 2y^2 = 0, which means y must be 0, or we get 2y^2 = 1 which, when we simplify, get a negative root  y = root(1/2). So only one case will work where y is equal to 0  so x must be 2? Is there anything wrong with this approach?
Thank you!



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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11 Dec 2017, 03:00
Bunuel wrote: HARRY113 wrote: Hi,
Can anyone clarify my query here?
Nothing is stated about 'y' rite...?? So y can be irrational, rational, integer, etc.
If i assume an extreme case: y an irrational number, then the answer is E rite?
Please clarify? Should i not take this case into consideration? For (2): regardless what real number y is (rational, irrational, ...), y in even power would be nonnegative. Thus, \(x = 4y^4+2y^2+2=nonnegative+nonnegative+positive=positive\). From (1) x = 3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient. Answer: C. Hi Bunuel, If you substitute X=3 back into the equation, it does not satisfy L.H.S=R.H.S Can you help me understand, when should we substitute back and when not? I am told that always to substitute back in such equations and in case of MODS. ?



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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11 Dec 2017, 05:54
GMP12 wrote: Bunuel wrote: HARRY113 wrote: Hi,
Can anyone clarify my query here?
Nothing is stated about 'y' rite...?? So y can be irrational, rational, integer, etc.
If i assume an extreme case: y an irrational number, then the answer is E rite?
Please clarify? Should i not take this case into consideration? For (2): regardless what real number y is (rational, irrational, ...), y in even power would be nonnegative. Thus, \(x = 4y^4+2y^2+2=nonnegative+nonnegative+positive=positive\). From (1) x = 3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient. Answer: C. Hi Bunuel, If you substitute X=3 back into the equation, it does not satisfy L.H.S=R.H.S Can you help me understand, when should we substitute back and when not? I am told that always to substitute back in such equations and in case of MODS. ? I assume you are talking about the equation x^2 + x + 10 = 16 . If you substitute x=3 in this, then LHS = (3)^2 + (3) + 10 = 93+10 = 16, which is same as RHS But this same value of x=3 cannot be substituted in second statement's equation (it wont make sense) x = 4y^4 + 2y^2 + 2 because RHS can never be negative, as other people (including Bunuel) have already explained in this thread.



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Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 [#permalink]
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11 Dec 2017, 22:51
From (1) x = 3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient.
Answer: C.[/quote]
Hi Bunuel,
If you substitute X=3 back into the equation, it does not satisfy L.H.S=R.H.S
Can you help me understand, when should we substitute back and when not? I am told that always to substitute back in such equations and in case of MODS.
?[/quote]
I assume you are talking about the equation x^2 + x + 10 = 16 . If you substitute x=3 in this, then LHS = (3)^2 + (3) + 10 = 93+10 = 16, which is same as RHS
But this same value of x=3 cannot be substituted in second statement's equation (it wont make sense) x = 4y^4 + 2y^2 + 2 because RHS can never be negative, as other people (including Bunuel) have already explained in this thread.[/quote]
Apologies.. I made a stupid calculation mistake!!




Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2
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