What is the units digit of 435^x + 1932^

Question

What is the units digit of  435^x + 1932^{(x + 3y)}

1)  x + 3y = 21

2)  2y - 6 = |y|

nasgmatbag · Answer

At the time of solving this problem, there was no answer available. So I'm showing my steps in the hope that someone can confirm if I got this correct.

1) x + 3y = 21 -> tells that the second value (1932) = 1932^21, we could find the unit digit. The other value (435) will always have an unit digit of 5 no matter the exponent, so I saw this as sufficient since we could solve to find the unit digit

2) 2y - 6 = |y| -> in this case y could only be 6, since 12-6 = |6|. With this information we do not know the value of x in the prompt for 1932, hence insufficient

My answer: A

gmatophobia · Answer

You're almost there nasgmatbag

In your solution, you've assumed x as a positive integer. However, nothing on the question restricts us to use positive integers. Hint: What if x = 0 (or negative), can we still conclude 435^x will end in 5?

nasgmatbag · Answer

Hi  gmatophobia ,

You're absolutely correct. I don't know why I've assumed that.. but with this information is the following correct?

1) x + 3y = 21 -> gives only the value of the second digit (1932), we cannot conclude anything from x and therefore the first digit, hence insufficient

2) 2y - 6 = |y| -> in this case y could only be 6, since 12-6 = |6|. With this information we do not know the value of x in the prompt for 1932, hence insufficient

1 & 2) -> since y = 6, we can conclude that x must be 3. Therefore when both statements are combined we can find the unit digit

Answer: C

pudu · Answer

|y|=+/- Y. then we get two different values for y. Naturally that gives two different values for x. Even if we combine 1 & 2 , then too we don't get unique value. Then how it is C?

someone please explain this to me

Bunuel · Answer

Let me ask you, what tow values are you getting when solving 2y - 6 = |y|?

pudu · Answer

That is immaterial because whatever it is, the value remains 5. I need to think only about whether it is a non zero integer or zero. Thank you. i got it

Bunuel · Answer

2y - 6 = |y| has only one root: y = 6.

2y - 6 = |y|;

2y = |y| + 6.

The right hand side is the sum of the absolute value and a positive number, hence it's positive. Consequently, the left hand side must be positive, making y positive. If y is positive, then |y| = y and we can rewrite the equation as:

2y = y + 6

y = 6.

Hope it helps.

What is the units digit of 435^x + 1932^

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What is the units digit of 435^x + 1932^

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