Problem Solving

Hey guys,

got 25 days left until test day. Hope you can help me out with this one:

PS Question 174 (OG for Quant. Review 2nd ed.)

" XY x YX
The product of the two-digit numbers above is the three-digit number XZX, where X,Y and Z, are three different nonzero digits. If X x Y < 10, what is the two-digit number XY?

Answer choices:

(A) 11
(B) 12
(C) 13
(D) 21
(E) 31

Correct Answer choice: D

Answer explanation:

Since it is given that XZX is a three-digit number, X <> 0 because "three-digit number" is used to characterize a number between 100 and 999, inclusive. Since X <> 0, X x Y < 10, and the units digit of the three-digit number XZX is X, then X x Y = X, which implies Y = 1. Then the problem simplifies to:

______________X1
____________x 1X
______________X²X
_____________X1
_____________XZX

Notice that the hundreds digit in the solution is the same as the hundreds digit of the second partial product, so there is no carrying over from the tens column. This means that Z < 10 and since Z = X² +1, then X² + 1 < 10, X² < 9, and X < 3. Since Y = 1 and X is different from Y, it follows that X = 2. Thus the value of XY is 21.[/b]

My Question:

How do you get to the second partial product and in particular to X²?
How do you know that the tens-digit of the solution (Z) is X² + 1 ?

The rest of the explanation sounds rather plausible to me.

It'd be great if you could clarify =).

Best regards,

Tobi

Hey There

I solved it this way and it was much simpler.

We are given that XY x YX = XZX ie if we multiply the unit digit of XY ie Y with YX ie X we should get X. Now, LOOK AT THE OPTIONS-

Only option which satisfies this condition is 21 ie (D)

Hope this answers your doubt.

Hi there,

Uhmm not quite sure if you mean this but if I understand your answer correctly, A and E would also work:

(A) Y x X = 1 * 1 = 1 = X
(E) Y x X = 1 * 3 = 3 = X

and of course D. How is this ?!

Please clarify !

Tobi

gander123 wrote:Hey guys,

got 25 days left until test day. Hope you can help me out with this one:

PS Question 174 (OG for Quant. Review 2nd ed.)

" XY x YX
The product of the two-digit numbers above is the three-digit number XZX, where X,Y and Z, are three different nonzero digits. If X x Y < 10, what is the two-digit number XY?

Answer choices:

(A) 11
(B) 12
(C) 13
(D) 21
(E) 31

Correct Answer choice: D

Much easier to plug in the answer choices.
Since X and Y must be different digits, eliminate A.

B: If XY=12, then XY*YX = 12*21 = 252.
D: If XY=21, then XY*YX = 21*12 = 252.
In each case, XZX = 252, implying that X=2 and that XY = 21.

The correct answer is D.

Hey Mitch,

Thanks for your simple approach. The thing is, if you are not a GMAT crack you dont recognize these high-level "easy-to-go" approaches.

But thanks anyway!

cheers ,

Tobi

Yes, gander123,

Sorry, I just looked at the question quickly and I don't know why I choose D... but you are right. My method has that fault in it.

gander123 wrote:Hi there,

Uhmm not quite sure if you mean this but if I understand your answer correctly, A and E would also work:

(A) Y x X = 1 * 1 = 1 = X
(E) Y x X = 1 * 3 = 3 = X

and of course D. How is this ?!

Please clarify !

Tobi

Hey Anurag,

lovely algebraic way to arrive at 0 < X² + 1 < 10. I've absorbed the content meanwhile.. Thanks alot !

However, I still wonder how you would rate the question difficulty ?! I know you cannot say this question is in the 400-500 range or 500-600 range or whatever. But would you consider this Quant. Problem a rather tough one ?

Keep busy !!

tobi