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What is the value of x?
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06 Oct 2013, 09:01
Question Stats:
47% (00:54) correct 53% (00:41) wrong based on 390 sessions
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What is the value of x? (1) 4 < x < 6 (2) x = 4x − 15
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Re: What is the value of x? (1) 4 < x < 6 (2) x=4x−15
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06 Oct 2013, 09:05




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Re: Algebra
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22 Mar 2014, 13:48
derek123 wrote: According to me there are 2 solutions for x for option 2 and multiple solutions for option 1 as well (as x can be a noninteger ex. 4.5 or 5 or 5.5) So i think it should be E. But its not. Can someone please explain why?
Source: Babson Practise Test
Data Sufficiency 
What is the value of x?
(1) 4 < x < 6
(2) x=4x−15
A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked; B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked; C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked; D EACH statement ALONE is sufficient to answer the question asked; E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. you are confused for option 2: x=4x−15 X can be +ve / ve. for X = +ve x = 4x  15 , hence x = 5 For X = ve x =4x  15, hence x=3 , however this contradicts your assumption that x is ve. So this solution is ruled out, leaving x=5 as unique solution. Hence answer is B.
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Re: What is the value of x? (1) 4 < x < 6 (2) x=4x−15
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06 Oct 2013, 09:06



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Re: What is the value of x? (1) 4 < x < 6 (2) x=4x−15
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06 Oct 2013, 11:32
bunuel , m still confused that why B i got the point rhs and lhs being positive , but why 5 , there can be other possibilities as well such as 4(6)15=9 so won't the ans be "c" ??? plz correct me ,where i m wrong



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Re: What is the value of x? (1) 4 < x < 6 (2) x=4x−15
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06 Oct 2013, 11:35



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Re: What is the value of x? (1) 4 < x < 6 (2) x=4x−15
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06 Oct 2013, 11:43
thankz , bunuel it was a silly mistake



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According to me there are 2 solutions for x for option 2 and multiple solutions for option 1 as well (as x can be a noninteger ex. 4.5 or 5 or 5.5) So i think it should be E. But its not. Can someone please explain why?
Source: Babson Practise Test
Data Sufficiency 
What is the value of x?
(1) 4 < x < 6
(2) x=4x−15
A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked; B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked; C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked; D EACH statement ALONE is sufficient to answer the question asked; E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.



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Re: Algebra
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22 Mar 2014, 11:47
Hey to answer your question:
Regarding to option 2, how x can be 4.5 or 5.5 ? try to let x=4.5 or 5.5, do you think the equation will be correct? no i do not think so, the only answer is x=5



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What is the value of x?
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18 Sep 2014, 11:41
Bunuel wrote: Bunuel wrote: What is the value of x?
(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.
(2) x = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be nonnegative: \(4x15\geq{0}\) > \(x\geq{\frac{15}{4}}\) > \(x\) is positive, thus \(x=x\) > \(x=4x15\) > \(x=5\). Sufficient
Answer: B.
Hope it's clear. Similar questions to practice: whatisx126874.htmlHello Bunuel, I am confused that why B is answer. I still don't understand that why in this case we did not taken two cases for mod. I solved by taking two condition for LHS, one is positive and one is negative. x=4x−15 X can be +ve / ve. for X = +ve x = 4x  15 , hence x = 5 For X = ve x =4x  15, hence x=3 Why we rejected answer choice with ve X. Also can u please help me understand that in which cases we should take both +ve and ve values for MOD and in which cases should not. Absolute Value is a weak pint for me in DS Thanks
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Re: What is the value of x?
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18 Sep 2014, 12:18
him1985 wrote: Bunuel wrote: Bunuel wrote: What is the value of x?
(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.
(2) x = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be nonnegative: \(4x15\geq{0}\) > \(x\geq{\frac{15}{4}}\) > \(x\) is positive, thus \(x=x\) > \(x=4x15\) > \(x=5\). Sufficient
Answer: B.
Hope it's clear. Similar questions to practice: whatisx126874.htmlHello Bunuel, I am confused that why B is answer. I still don't understand that why in this case we did not taken two cases for mod. I solved by taking two condition for LHS, one is positive and one is negative. x=4x−15 X can be +ve / ve. for X = +ve x = 4x  15 , hence x = 5 For X = ve x =4x  15, hence x=3 Why we rejected answer choice with ve X. Also can u please help me understand that in which cases we should take both +ve and ve values for MOD and in which cases should not. Absolute Value is a weak pint for me in DS Thanks When you consider the case when x is negative and get x = 3 = positive, you should reject it, as x is not negative. Also, plug x = 3 into the equation, does it hold true? Below links might help. Theory on Abolute Values: mathabsolutevaluemodulus86462.htmlAbsolute value tips: absolutevaluetipsandhints175002.html
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Re: What is the value of x?
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10 Oct 2017, 08:12
nave wrote: What is the value of x?
(1) 4 < x < 6
(2) x = 4x − 15 Target question: What is the value of x? Statement 1: 4 < x < 6 ASIDE: Some students will assume that x is an integer and incorrectly conclude that x must equal 5. This is a common mistake on the GMAT. The truth of the matter is that there are infinitely many values of x that satisfy statement 1. For example x could equal 4.1, or x could equal 4.132 or 4.54 or 5 or 5.4211 etcSince we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x = 4x − 15There are 3 steps to solving equations involving ABSOLUTE VALUE: 1. Apply the rule that says: If x = k, then x = k and/or x = k2. Solve the resulting equations 3. Plug solutions into original equation to check for extraneous roots Given: x = 4x − 15 So, there are two possible cases to examine: Case a: x = 4x − 15. When we solve this equation, we get: x = 5Case b: x = (4x − 15). When we solve this equation, we get: x = 3 At this point, it LOOKS LIKE there are two possible values of x. However, we haven't performed step 3 yet: Plug solutions into original equation to check for extraneous roots Let's do that. Case a: Plug x = 5 into original equation to get:  5 = 4( 5) − 15 Simplify right side of equation to get:  5 = 5 This works, so x = 5 IS a possible value of x Case b: Plug x = 3 into original equation to get:  3 = 4( 3) − 15 Simplify right side of equation to get:  3 = 3 This DOES NOT work, so x = 3 is NOT a possible value of x Since there is only ONE possible value of x ( x = 5), statement 2 is SUFFICIENT Answer: Cheers, Brent
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Re: What is the value of x?
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06 Dec 2017, 05:15
Hi Bunuel,
I don't understand why ans should B?
Question does not say anything about 'X'. Therefore X can be integer or noninteger number. So if X =3.75 then X= 4X15 satisfies the condition. Further if I combine Condition 2 (i.e X= 4X15) with Condition 1 (i.e. 4<x<6) then also we will not get the exact value of X.
According to me Ans. should be E.



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Re: What is the value of x?
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06 Dec 2017, 05:23



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Re: What is the value of x?
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06 Dec 2017, 05:29
Yup Bunnel, You are right. Made the same mistake as done by Derek123. Thank you



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Re: What is the value of x?
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27 Dec 2018, 06:39
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Re: What is the value of x? &nbs
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