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gmatophobia
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What is the units digit of 435^x + 1932^ 25 Apr 2023, 13:10
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C
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Difficulty:

85% (hard)

Question Stats:

38% (02:13) correct 63% (01:39) wrong based on 40 sessions

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

1) \(x + 3y = 21\)

2) \(2y - 6 = |y|\)
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C
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What is the units digit of 435^x + 1932^ 26 Apr 2023, 04:41
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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
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What is the units digit of 435^x + 1932^ 26 Apr 2023, 05:38
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nasgmatbag
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
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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?
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What is the units digit of 435^x + 1932^ 26 Apr 2023, 06:39
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nasgmatbag
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

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?
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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
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What is the units digit of 435^x + 1932^ 06 May 2023, 17:24
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What is the units digit of \(435^x + 1932^{(x + 3y)}\)

1) \(x + 3y = 21\)

2) \(2y - 6 = |y|\)
Show more

|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
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What is the units digit of 435^x + 1932^ 07 May 2023, 01:45
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pudu
gmatophobia
What is the units digit of \(435^x + 1932^{(x + 3y)}\)

1) \(x + 3y = 21\)

2) \(2y - 6 = |y|\)

|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
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Let me ask you, what tow values are you getting when solving 2y - 6 = |y|?
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What is the units digit of 435^x + 1932^ 07 May 2023, 23:55
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gmatophobia
What is the units digit of \(435^x + 1932^{(x + 3y)}\)

1) \(x + 3y = 21\)

2) \(2y - 6 = |y|\)

|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

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

:angel: 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 :)
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What is the units digit of 435^x + 1932^ 08 May 2023, 00:02
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What is the units digit of \(435^x + 1932^{(x + 3y)}\)

1) \(x + 3y = 21\)

2) \(2y - 6 = |y|\)


|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

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

:angel: 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 :)
Show more

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.
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