Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 29 Nov 2014
Posts: 1

What is the value of integer x?
[#permalink]
Show Tags
28 Feb 2015, 07:08
Question Stats:
62% (02:09) correct 38% (02:05) wrong based on 286 sessions
HideShow timer Statistics
What is the value of integer x? (1) 1  x  x + 1 = 0 (2) 7  x + 3 + x = 10
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: What is the value of integer x?
[#permalink]
Show Tags
28 Feb 2015, 07:33
What is the value of integer x?(1) 1  x  x + 1 = 0 1  x = x + 1 > square: 1  2x + x^2 = x^2 + 2x +1 > x = 0. Sufficient. (2) 7  x + 3 + x = 10. When both 7  x and 3 + x are positive (so when 3 <= x <= 7), then 7  x + 3 + x = 10 expands as 7  x + 3 + x = 10 > 10 = 10, which is true. This means that any x where 3 <= x <= 7 satisfies the equation. Not sufficient. Answer: A.
_________________




Math Expert
Joined: 02 Aug 2009
Posts: 7971

Re: What is the value of integer x?
[#permalink]
Show Tags
28 Feb 2015, 07:19
jashshah wrote: What is the value of integer x?
1. 1  x  x + 1 = 0
2. 7  x + 3 + x = 10 ans A.. 1) by looking at the statement 1 itself , one can find that x=0.. also by opening the mod, we can find that x gives only one value that is 0.. sufficient 2) 7 and 3 straight way gives one value of x as 0 and by opening mod, we have x can take multiple values 2 ,2,3,4etc ... so insufficient
_________________



Manager
Joined: 28 Jul 2011
Posts: 159

Re: What is the value of integer x?
[#permalink]
Show Tags
05 Oct 2015, 13:22
What is the value of integer x?
1. 1  x  x + 1 = 0 2. 7  x + 3 + x = 10
Can anyone help in how do we open the modules sign for 1 and 2?
this is how i solved it but its time consuming 1. x1  x+1 = 0 (x1)  (x+1) = 0 therefore x= 0 (x1) + (x+1) = 0 therefore x = 0
any alternate technique to solve this problem



CEO
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: What is the value of integer x?
[#permalink]
Show Tags
05 Oct 2015, 17:07
kuttingchai wrote: What is the value of integer x?
1. 1  x  x + 1 = 0 2. 7  x + 3 + x = 10
Can anyone help in how do we open the modules sign for 1 and 2?
this is how i solved it but its time consuming 1. x1  x+1 = 0 (x1)  (x+1) = 0 therefore x= 0 (x1) + (x+1) = 0 therefore x = 0
any alternate technique to solve this problem Make sure to format your question in such a way that puts your analysis under "spoiler". As for your question, Both statements can be solved in a similar way, Statement 1, 1xx+1=0 , now as ax=xa , you get x1x+1=0 > x1=x+1 > \(\pm (x1) = \pm (x+1)\) , you only get 2 possible cases giving you x=0 for both cases. Hence this statement is sufficient. Statement 2, 7  x + 3 + x = 10, using the same principle as shown in statement 1, you get the equation as \(\pm (x7) \pm (x+3) = 10\), giving you 2 possible cases again but giving you x=3 and x=7. Thus this statement is not sufficient. Hope this helps.



Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 599

Re: What is the value of integer x?
[#permalink]
Show Tags
06 Oct 2015, 00:18
kuttingchaiIn statement 2, you will notice that there is a 7 and 3 on the left side and 10 on the right. We also know 7+3=10, and if we choose x=0, we see the equation is indeed satisfied, and if we change x to 1, then also it is satisfied. So just by observation we can come up with two values for x, and say that statement 2 alone is not sufficient. For statement 1, one could quickly graph the functions 1x and x+1 and show that they only intersect at x=0. Actually, being able to graph these basic types of absolute value equations is important for the GMAT. And finally, the statement 1 is based on the following official GMAT question from official guide 10th edition, data sufficiency question#81. See the attached image. Cheers, Dabral
Attachments
OG10DS81.png [ 5.98 KiB  Viewed 8268 times ]



Board of Directors
Joined: 17 Jul 2014
Posts: 2510
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: What is the value of integer x?
[#permalink]
Show Tags
28 Nov 2015, 10:49
I didn't square, since I didn't know how to tackle this question rather than try the possible options, and although I selected A as the answer I later check and found something interesting: both positive both negative 1st positive second negative 1st negative second positive:
1. 1  x  x + 1 = 0 ++ 1xx+1=0=> 0=2x=>x=0  1+x+x+1=>2x=0 => x=0 + 1+xx+1 => 0=0  doesn't help us much, since there is no way to solve it. or x can take any value. + 1x+x+1 => 2=0  this is not a solution.
x 2. 7  x + 3 + x = 10
only 2 options tested, which yielded 2 different values for x, thus I dismissed B and D.



CEO
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: What is the value of integer x?
[#permalink]
Show Tags
08 Jan 2016, 09:57
shasadou wrote: What is the value of integer x?
(1) 1  x  x + 1 = 0 (2) 7  x + 3 + x = 10 For such questions the most straightforward method to solve is to realize that xa with a = constant is the distance of x from 'a' and ax = xa Thus 1x = x1 > distance of x from 1, Similarly for x+1, x7 and x+3. Do remember that x = integer (given information). Per statement 1, 1  x  x + 1 = 0 > x1  x + 1 = 0 > x1 = x + 1 > distance of integer x is same from 1 and 1 > x can only take 0 as the possible value. Unique value of x > sufficient statement. Per statement 2, 7  x + 3 + x = 10 > x7 + 3 + x = 10 > distance of x from 7 + distance of x from 3 = 10 units. This is satisfied by all integer values of x between 3 and 7. Consider x = 4 , distance from 7 = 3 , distance of x from 3 = 7 , total = 10. But if x = 0, distance from 7 = 7 and distance of x from 3 = 3 , total = 10 units. Thus this statement provides multiple values of x > not sufficient. A is thus the correct answer. Hope this helps.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8013
GPA: 3.82

Re: What is the value of integer x?
[#permalink]
Show Tags
10 Jan 2016, 19:10
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. What is the value of integer x? (1) 1  x  x + 1 = 0 (2) 7  x + 3 + x = 10 When it comes to absolute value, it indicates a distance between two dots. That is, it is a distance between xy=x and y in this question. In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. For 1), from 1x=x(1), since a distance from x to 1 is as same as a distance from x to 1, x=0 is derived, which is unique and sufficient. For 2), from 7x+x(3)=10, the sum of a distance between x and 7, and a distance between x and 3 is 10. That is, all values are possible in 3<=x<=7, which is not unique and not sufficient. Therefore, the answer is A. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Current Student
Joined: 28 Nov 2014
Posts: 818
Concentration: Strategy
GPA: 3.71

Re: What is the value of integer x?
[#permalink]
Show Tags
28 Sep 2016, 07:13
Bunuel: How do I deal with second case  7x + 3+x = 10 Now four possibilities can exist Case 1: 7x>0 and 3+x>0 3 < x < 7 On solving 10=10 Case 2: 7x<0 and 3+x<0 4=10 Dump this! Case 3: 7x>0 and 3+x<0 x<7 and x<3 or x<3 On solving we get ; x=3 Case 4: 7x<0 and 3+x>0 x > 3 and x >7 or x>7 On solving x = 7 Bunuel: Can you please suggest how do I conclude this.



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: What is the value of integer x?
[#permalink]
Show Tags
29 Sep 2016, 04:05
Keats wrote: Bunuel: How do I deal with second case  7x + 3+x = 10 Now four possibilities can exist Case 1: 7x>0 and 3+x>0 3 < x < 7 On solving 10=10 Case 2: 7x<0 and 3+x<0 4=10 Dump this! Case 3: 7x>0 and 3+x<0 x<7 and x<3 or x<3 On solving we get ; x=3 Case 4: 7x<0 and 3+x>0 x > 3 and x >7 or x>7 On solving x = 7 Bunuel: Can you please suggest how do I conclude this. \(3 + x + 7  x = 10\) 2 key points at 3 and 7. When \(x < 3\), then \(3 + x\) is negative and \(7  x\) is positive, thus \(3 + x + 7  x = 10\) becomes \((3 + x) + (7  x) = 10\) > \(x=3\). Discard since 3 is not in the range; When \(3 \leq x \leq 7\), then \(3 + x\) is positive and \(7  x\) is positive, thus \(3 + x + 7  x = 10\) becomes \((3 + x) + (7  x) = 10\) > \(10=10\). Since this is true, then this means that ANY x from the given range satisfies the equation; When \(x > 7\), then \(3 + x\) is positive and \(7  x\) is negative, thus \(3 + x + 7  x = 10\) becomes \((3 + x)  (7  x) = 10\) > \(x=3\). Discard since 7 is not in the range. Therefore, \(3 + x + 7  x = 10\) is true for any x where \(3 \leq x \leq 7\). Hope it's clear.
_________________



Director
Joined: 08 Jun 2013
Posts: 543
Location: France
GPA: 3.82
WE: Consulting (Other)

Re: What is the value of integer x?
[#permalink]
Show Tags
29 Sep 2018, 23:35
Statement 1 can be phrased as: 1−x=x+1. Trial and error shows that the two will only be equal if x=0. Accordingly, Statement 1 is sufficient. Statement 2, on the other hand, works for many integers. Simply trying and finding two integers that work is enough to know that multiple answers are possible: If x=3, then the statement holds: 7−3=4; 3+3=6; and 4+6=10. And if x=0, then the statement still holds: 7+3=10. Therefore, statement 2 is not sufficient, and again the correct answer is A.
_________________
Everything will fall into place…
There is perfect timing for everything and everyone. Never doubt, But Work on improving yourself, Keep the faith and Stay ready. When it’s finally your turn, It will all make sense.



Senior Manager
Joined: 10 Jan 2013
Posts: 295
Location: India
Concentration: General Management, Strategy
GPA: 3.95

Re: What is the value of integer x?
[#permalink]
Show Tags
07 Aug 2019, 23:53
jashshah wrote: What is the value of integer x?
(1) 1  x  x + 1 = 0
(2) 7  x + 3 + x = 10 Hi Bunuel and chetan2ui have a conceptual query on such questions.. whenever we have the question of the form in stmt 2; we usually open the mod by using a combination of ++, +, + right?




Re: What is the value of integer x?
[#permalink]
07 Aug 2019, 23:53






