Number Problems

[rosyneha]

Problem Definition: A two-digit even number is such that reversing its digits creates an odd number greater than the original number. which one of the following cannot be the first digit of the original number?
(A)1 (B)3 (C)5 (D)7 (E)9.

My question is first digit of the number is the digit in the unit's place or ten's place?

[Atekihcan]

My question is first digit of the number is the digit in the unit's place or ten's place?

I think first digit means first from the left, i.e. in this case the digit in ten's place.
And the answer choices confirms what I think as all of them are odd.


Let us assume the number is XY, where X and Y are ten's and unit's digit respectively.

As the original number is even, Y must be even.
The reversed number YX is odd, so the X must be odd.

Now, YX > XY
So, X must be less than Y.
Now, Y cannot be greater than 8.
So, X must be less than 8.

Answer : E

[Jim@StratusPrep]

It has to be the tens digit as the ones digit must be even... E is the answer.

[TG_GMAT]

Now, YX > XY
So, X must be less than Y.
Now, Y cannot be greater than 8.
So, X must be less than 8.

[/quote]Now, YX > XY
So, X must be less than Y.
Now, Y cannot be greater than 8.
So, X must be less than 8.

Hi,

I figured the answer out but while looking at the explanation, I dont understand why X must be less than Y.

Can you please explain?

Thanks

[TG_GMAT]

Hi,

I figured the answer out but while looking at the explanation, I dont understand why X must be less than Y.

Now, YX > XY
So, X must be less than Y.
Now, Y cannot be greater than 8.
So, X must be less than 8.

Can you please explain?

Thanks

[Atekihcan]

...but while looking at the explanation, I dont understand why X must be less than Y.

If a 2-digit integer (Say, M) is less than another 2-digit integer (Say, N), then the ten's digit of M cannot be greater than the ten's digit of N. For example, 12 is less than 21, 1 < 2 or 34 is less than 43, 3 < 4 or 24 < 28 and 2 is not greater than 2.

So, in general if XY < YX, then X cannot be greater than Y, i.e. X ≤ Y
As in this case X is an odd integer and Y is an even integer, X cannot be equal to Y.
So, X < Y

Hope that helps.

[TG_GMAT]

Great, that helps. Thanks.

[freyesinsb]

pick some numbers using the answer choices and eliminate those that violate the definition.

Even < odd
(A)1-12 or 21 eliminate
(B)3-38 or 83 eliminate
(C)5-58 or 85 eliminate
(D)7-78 or 87 eliminate
(E)9. correct answer.