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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # What is the value of the two-digit number x?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 51218 What is the value of the two-digit number x? [#permalink] ### Show Tags 07 Oct 2015, 05:31 00:00 Difficulty: 25% (medium) Question Stats: 66% (00:36) correct 34% (00:43) wrong based on 289 sessions ### HideShow timer Statistics Project DS Butler: Day 23: Data Sufficiency (DS45) For DS butler Questions Click Here What is the value of the two-digit number x? (1) The sum of the two digits is 4. (2) The difference between the two digits is 2. Kudos for a correct solution. _________________ CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2711 Location: India GMAT: INSIGHT WE: Education (Education) Re: What is the value of the two-digit number x? [#permalink] ### Show Tags 07 Oct 2015, 05:56 Bunuel wrote: What is the value of the two-digit number x? (1) The sum of the two digits is 4. (2) The difference between the two digits is 2. Kudos for a correct solution. Question : If x= ab where a and b are tens and units digit respectively then find x? Statement 1: a+b=4 x may be 13 or 22 or 31. Hence, NOT SUFFICIENT Statement 2: a-b = 2 or b-a=2 if a-b=2 then x = 31 if b-a=2 then x = 13. Hence, NOT SUFFICIENT Combining the two statements x may still be 13 or 31 Hence, NOT SUFFICIENT Answer: option E _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Intern Status: Focus - Determination - Domination Joined: 02 Mar 2015 Posts: 37 Location: India Re: What is the value of the two-digit number x? [#permalink] ### Show Tags 07 Oct 2015, 05:59 1 Bunuel wrote: What is the value of the two-digit number x? (1) The sum of the two digits is 4. (2) The difference between the two digits is 2. Kudos for a correct solution. statement 1: x can have following possible values 40 31 22 13 Insufficient statement 2: x can have following possible values 20 31 13 42 24 64 46 and so on Insufficient Combining statement 1 and statement 2 x can have values 31 and 13 Insufficient Answer :E 13 _________________ Let's Rock! Manager Joined: 21 Jun 2014 Posts: 131 Location: United States Concentration: General Management, Strategy GMAT 1: 630 Q45 V31 GPA: 3.4 WE: Engineering (Computer Software) Re: What is the value of the two-digit number x? [#permalink] ### Show Tags 07 Oct 2015, 09:46 Tens digit=x One's digit=y From A: $$x+y=4$$ so number can be 13,31,22 A is not sufficient From B: $$x-y=2$$ so number can be 31 or $$y-x=2$$ so number can be 13 B is not sufficient Combining both of them together , number can be 13 or 31 E is the right answer. _________________ Regards, Manish Khare "Every thing is fine at the end. If it is not fine ,then it is not the end " Manager Joined: 13 Mar 2013 Posts: 163 Location: United States Concentration: Leadership, Technology GPA: 3.5 WE: Engineering (Telecommunications) Re: What is the value of the two-digit number x? [#permalink] ### Show Tags 07 Oct 2015, 17:59 1 What is the value of the two-digit number x? (1) The sum of the two digits is 4. (2) The difference between the two digits is 2. St 1 -- 13,31 ,40 etc ... St 2 --- 13,31 , 42, 24 , etc together 13, 31 -- hence e ans _________________ Regards , Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: What is the value of the two-digit number x? [#permalink] ### Show Tags 11 Oct 2015, 06:16 Bunuel wrote: What is the value of the two-digit number x? (1) The sum of the two digits is 4. (2) The difference between the two digits is 2. Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION: Question Type: What Is the Value? This question asks for the value of the two-digit number x. Given information in the question stem or diagram: x is a two-digit number. Statement 1: The sum of the two digits is 4. There are only four two-digit numbers that have digits that total 4. They are 13, 22, 31, and 40. Since that allows for more than one value for x, this statement is not sufficient. Eliminate choices A and D. Statement 2: The difference between the two digits is 2. This means that for the tens digit (T) and the units digit (U), either: T – U = 2, or U – T = 2. Many people confuse this statement and think that the tens digit must be larger, such as 64, where T – U = 2. However, 46 would also be acceptable since the difference between the digits is 2. Clearly this statement is not sufficient alone as there are many two-digit numbers where T – U = 2 or U – T = 2. Eliminate choice B. Together: When taking the statements together it is best to start with the more limiting statement. Statement 1 only allows four values: 13, 22, 31, and 40. How many of these values are compatible with Statement 2? Two of them: 31 is T – U = 2; and 13 is U – T = 2. They each have a difference of 2. Since there are still two possible values for the two-digit number x, the correct answer is E. Note: This is a classic C vs. E problem. Almost everyone gets it down to choice C or E, but many people forget to differentiate between 13 and 31. (They either miss one in their list of possibilities for the first statement or assume that it must be 31 for the reasons discussed above.) Remember to do your best to exhaust all possibilities before picking answer C. _________________ Intern Joined: 24 May 2015 Posts: 1 Re: What is the value of the two-digit number x? [#permalink] ### Show Tags 05 Feb 2016, 15:51 1 I totally follow how you get to (e). but dsn't "1 minus 3" = -2??? If the test meant for us to consider 13, would it not have stated "the difference between the two digits is |2|"??? or am i overthinking. Thanks Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of the two-digit number x? [#permalink] ### Show Tags 06 Feb 2016, 18:36 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 the two-digit number x? (1) The sum of the two digits is 4. (2) The difference between the two digits is 2. In the original condition, it is two-digit integer, which makes 2 variables. You need 2 equations in order to match with the number of equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), 13 and 31 are derived, which is not unique and not sufficient. Therefore, the answer is E. -> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: What is the value of the two-digit number x?  [#permalink]

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28 Nov 2018, 07:12
Bumping for DS butler project:

Project DS Butler: Day 23: Data Sufficiency (DS45)

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Re: What is the value of the two-digit number x?  [#permalink]

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28 Nov 2018, 20:35
even i am confused. It says the difference is 2 and not -2. so 31 is the only number with +2 difference. where am i going wrong
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Re: What is the value of the two-digit number x?  [#permalink]

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28 Nov 2018, 21:04
1
Hi naned32 , gp27311
Difference between two numbers a and b is always non negative and is equal to| a-b|.
Difference between 6 and 4 = difference between 4 and 6 = |6-4| =2.
I hope it is clear now.
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Re: What is the value of the two-digit number x?  [#permalink]

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28 Nov 2018, 21:11
thanks gmatbuster i got it now
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Re: What is the value of the two-digit number x?  [#permalink]

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29 Nov 2018, 09:53
1) x+y =4
can be many options - 1+3 , 3+1 , 2+2
2) x-y = 2 again can be many options
Combining on and two also will give us two options 13 or 31

hence E
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Plz Kudos! if my post helps....

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Re: What is the value of the two-digit number x?  [#permalink]

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03 Dec 2018, 22:55
GMATinsight wrote:
Bunuel wrote:
What is the value of the two-digit number x?

(1) The sum of the two digits is 4.
(2) The difference between the two digits is 2.

Kudos for a correct solution.

Question : If x= ab where a and b are tens and units digit respectively then find x?

Statement 1: a+b=4
x may be 13 or 22 or 31. Hence,
NOT SUFFICIENT

Statement 2: a-b = 2 or b-a=2

Hi,

I choose C as I felt in 13, difference of the digits is -2. How to remove this ambiquity????
if a-b=2 then x = 31
if b-a=2 then x = 13. Hence,
NOT SUFFICIENT

Combining the two statements
x may still be 13 or 31
Hence,
NOT SUFFICIENT

Re: What is the value of the two-digit number x? &nbs [#permalink] 03 Dec 2018, 22:55
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