If the digits of a two-digit number are interchanged, the resulting in

Question

If the digits of a two-digit number are interchanged, the resulting integer is 18 more than the original number. What is the difference between the tens digit and the units digit of the original number?

(A) -2
(B) -1
(C) 1
(D) 2
(E) 3

(A) -2
(B) -1
(C) 1
(D) 2
(E) 3

D3N0 · Answer

Ans: A

lets say origional number is 10a+b and reverse number is 10b+a.
As given 9b-9a=18 so b-a= 2 but question is asking for (a-b) so the ans is -2.

EgmatQuantExpert · Answer

:Answer Updated:

The difference of two any numbers can be either a - b or b -a. However, we usually take the positive value of the difference.

In this case, the question specifically asks us to find the difference between the "tens" digit and "units" digit of the "original number".

Hence, the correct answer will be -2

Had the question been find the difference between the two digits, the answer would have been "2" only.

D3N0 · Answer

OK... got it .. because question did not assign any variables for the unit and ten digit and did not ask us for specific (b-a) or (a-b) we just need to ans the distance. not the value of specific a-b or b-a..

Thanks for this.. such a big point in miss while understanding what the question is asking...

RohitGoyal1123 · Answer

Let XY be the two digit number in question which can be written as 10X + y
so X = ten's digit and Y = unit's digit

Required : X-Y

As per the question 10Y+X = 10X+Y +18
or 9(X-Y) = -18
or X-Y = -2

Hence Option  A

RohitGoyal1123 · Answer

I don't think this is correct. I think you have mixed distance and difference.
Please recheck and confirm, as per me Answer will be OptionA

panthu110 · Answer

To clear the confusion, let orginal number be 02, reversing it, we get 20(02+18=20)
So 0-2=-2.
0(tens place)- 2(units place) gives -2.

-2 is the answer

Sent from my Mi A1 using  GMAT Club Forum mobile app

EgmatQuantExpert · Answer

We have updated our solution. Please check.

EgmatQuantExpert · Answer

Your explanation is technically correct.

However, there is just one problem with it. The question clearly states, that the number is a two digit number, thus 02 is not a really good example.

You could have taken 13 and 31 to explain it to avoid any confusion.

D3N0 · Answer

OK So my answer was correct..

I am not that bad in quant afterall but i think i need to be more confident because i believed you without questioning..

EgmatQuantExpert · Answer

You need to have more confidence in yourself.

And yes, you are more than welcome to question us! Even we experts are humans, we can make mistakes. All the best for your prep!

ScottTargetTestPrep · Answer

We can let the original number = 10A + B, in which A = tens digit and B = units digit, and the interchanged number as 10B + A, in which B = tens digit and A = units digit.

Since the resulting integer is 18 more than the original number:

10A + B + 18 = 10B + A

9A + 18 = 9B

A + 2 = B

A - B = -2

Answer: A

72pala · Answer

I may have done this wrong but I thought of integers that are 18 apart and came up with 13 & 31. They, interchanged would be 18 apart and then did subtraction of the ten spot and got -2.

1 (ten spot) -  3 (ten spot) =  -2

gracie · Answer

difference between any reversed two-digit numbers is a multiple of 9
difference between reversed numbers/9=difference between reversed digits
18/9 normally gives us +2, but, as specified here, correct answer is -2
A

CrackverbalGMAT · Answer

This is probably one of the easiest questions that you can see on the concept of numbers and digits. If this is one of your strong areas, solving this question should not take you more than 1 minute. 
However, there is a trap answer involved, so beware!

A two digit number can be expressed as xy or also as 10x + y.

When this number is interchanged, it becomes yx or 10y + x.

It’s given that, on interchanging the original number xy, the number obtained yx is 18 more. This means,

10y + x = 10x + y + 18.

Simplifying the above equation, we get,

9y – 9x = 18 or

y – x = 2.

Does this mean the answer is option D? Of course not!

Observe how the question is worded. It does not ask you the difference between the digits of the number xy. Had it asked this, the answer would have been option D.

The question specifically asks the difference between the ten’s digit and the unit’s digit of the original number xy. Therefore, the only plausible conclusion that we can make, is that the question is asking us to find out x – y and not just x~y.

Note: ~ represents difference.

If y-x = 2, x-y has to be -2. Therefore, the correct answer option is A.

This question could have been made less ambiguous if the question has been worded like this “ What is the value when the units digit of the original number is subtracted from the tens digit of the original number?”.

If you marked the answer as D, do not feel bad, because, although your answer is officially wrong, it still means that you understood the concept and solved the question right; it’s just that the language is a bit ambiguous and therefore, you need to take the end result with a pinch of salt!

Hope this helps!

CrackverbalGMAT · Answer

This is probably one of the easiest questions that you can see on the concept of numbers and digits. If this is one of your strong areas, solving this question should not take you more than 1 minute. 
However, there is a trap answer involved, so beware!

A two digit number can be expressed as xy or also as 10x + y.

When this number is interchanged, it becomes yx or 10y + x.

It’s given that, on interchanging the original number xy, the number obtained yx is 18 more. This means,

10y + x = 10x + y + 18.

Simplifying the above equation, we get,

9y – 9x = 18 or

y – x = 2.

Does this mean the answer is option D? Of course not!

Observe how the question is worded. It does not ask you the difference between the digits of the number xy. Had it asked this, the answer would have been option D.

The question specifically asks the difference between the ten’s digit and the unit’s digit of the original number xy. Therefore, the only plausible conclusion that we can make, is that the question is asking us to find out x – y and not just x~y.

Note: ~ represents difference.

If y-x = 2, x-y has to be -2. Therefore, the correct answer option is A.

This question could have been made less ambiguous if the question has been worded like this “ What is the value when the units digit of the original number is subtracted from the tens digit of the original number?”.

If you marked the answer as D, do not feel bad, because, although your answer is officially wrong, it still means that you understood the concept and solved the question right; it’s just that the language is a bit ambiguous and therefore, you need to take the end result with a pinch of salt!

Hope this helps!

If the digits of a two-digit number are interchanged, the resulting in

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