What is the value of the two-digit number x?

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.

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

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.

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

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.

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

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)

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

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.

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

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?

ST 1. it can be 2+2 or 3+1, 1+3 or 4+0 St 1 alone is not sufficient

ST 2. it can 4-2 or 3-1 or any other combination. St 2 alone is not sufficient

ST1 +St2

if sum is 4 and difference of digits is 2 then it still could be 31 or 13

E

VeritasKarishma

Well, since we are talking about a two digit "number," why can't we take the values such as 1.3 or 3.1? The question doesn't say it has to be an integer. 1.3 is as much a two digit number as 13.

I did this with algebra by substituting (1) and (2), and arrived at 31. But how come algebra is not showing the other result when we have solved the single values of values?

"Two digit number" implies units and tens digits - no decimal.

"Two digit number" implies units and tens digits - no decimal. [/quote]

That's new! Interesting. So what would we call 1.3? Two digit decimal? VeritasKarishma