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Math Expert V
Joined: 02 Sep 2009
Posts: 56303
What is the value of the two-digit number x?  [#permalink]

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10 00:00

Difficulty:   25% (medium)

Question Stats: 63% (00:54) correct 37% (00:58) wrong based on 445 sessions

### HideShow timer Statistics Project DS Butler: Day 23: Data Sufficiency (DS45)

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.

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

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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

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

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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

13
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Re: What is the value of the two-digit number x?  [#permalink]

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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

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

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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
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Math Expert V
Joined: 02 Sep 2009
Posts: 56303
Re: What is the value of the two-digit number x?  [#permalink]

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

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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 V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the value of the two-digit number x?  [#permalink]

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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.

-> 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.
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What is the value of the two digit number x ? (1) The sum of two digi  [#permalink]

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To the value of the two digit number x

Let x = ab where a represents the tens digit and b represents the units digit

x is a two digit number = > a $$\neq$$ 0

Statement 1

The sum of two digits is 4.

=> a + b = 4

'x' can be 13 or 22, 40 or 31

Statement 1 is not sufficient

Statement 2

The difference between the two digits is 2 => |a-b| = 2

=> 'x' can be 53 or 35 or 97 etc

Statement 2 is not sufficient

Combining statements 1 and 2

From statement 1 we have possible values of 'x' 13 or 22, 40 or 31

=> 'x' can be 13 or 31

Statement 1 and 2 together are insufficient

Hence option E
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Re: What is the value of the two digit number x ? (1) The sum of two digi  [#permalink]

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Bunuel wrote:
What is the value of the two digit number x ?

(1) The sum of two digits is 4.

(2) The difference between the two digits is 2.

Statement-1:-
Possible cased of two digits numbers x:- 13, 22, 31, and 40.
Insufficient.

Statement-2:-
Possible cased of two digits numbers x:- 13, 31,24,42,35,53 etc. (Tens digit-units digit=2 or Units digit-Tens digit=2)
Insufficient.

(1)+(2),
Possible cases: 13 & 31.
We have obtained more than one values of x.
Insufficient.

Ans. (E)
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Location: India
GPA: 3.64
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Re: What is the value of the two-digit number x?  [#permalink]

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

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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

Intern  B
Joined: 13 Nov 2018
Posts: 1
Re: What is the value of the two digit number x ? (1) The sum of two digi  [#permalink]

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Shouldn't we also consider the case where x = -13 or -31 as well as the positive counterparts?
In this case the answer would of course still be 'E', but thinking about other questions that might crop up where pos vs neg could make all the difference...

In the original statement I interpret the word 'value' to include positive or negative value. Can anyone comment?
Director  V
Joined: 27 May 2012
Posts: 814
Re: What is the value of the two-digit number x?  [#permalink]

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1
Bunuel wrote:

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

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.

Dear Moderator,
Found this question, this same question seems to have been duplicated in the link below, you may wish to merge the same. Thank you.

https://gmatclub.com/forum/what-is-the- ... l#p2095102
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- Stne
Math Expert V
Joined: 02 Sep 2009
Posts: 56303
Re: What is the value of the two-digit number x?  [#permalink]

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stne wrote:
Bunuel wrote:

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

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.

Dear Moderator,
Found this question, this same question seems to have been duplicated in the link below, you may wish to merge the same. Thank you.

https://gmatclub.com/forum/what-is-the- ... l#p2095102

_____________________
Topics Merged. Thank you.
_________________ Re: What is the value of the two-digit number x?   [#permalink] 21 Dec 2018, 07:16
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