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gander123
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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
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
