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The integer x has a tens digit of 6 and a units digit of 7. The units

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The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7
[Reveal] Spoiler: OA

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Re: The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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shasadou wrote:
The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7


You can solve it by the following method:

X : 67
Y : a8

So

67*a8 should give you the tens digit as 3+7a = 8 ---> 7a = 5 and the only multiple of 7 that has a 5 in the units place is when you have 5*7 , giving you a=5.

C is the correct answer.
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Re: The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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New post 17 Nov 2015, 04:58
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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7


Let x be 67 and y be a8. Then the product of x and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.
So the answer is (C).
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Re: The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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New post 03 Oct 2016, 23:04
MathRevolution wrote:
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7


Let x be 67 and y be a8. Then the product of x and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.
So the answer is (C).


Hello,

Can you please elaborate how you arrived to below conclusion :-
"So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5"
Thanks.

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Re: The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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New post 23 Nov 2016, 09:33
I did it by Hit and trail.
Anyway here is my solution =>
x=67
y=p8
=> multiplying them => (10p+8)*67 => 670p+536 =>


Checking values
p=3 => Tens digit of the result =4
p=4 => Tens digit of the result =1
p=5 => Tens digit of the result =8
BINGO
Hence C
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Re: The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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New post 25 Nov 2016, 20:36
There hasn't been a lot of posting for quite some time.
However, could some please explain how we get to "3+7a" in the first place? How does this equation represent the tens digit?

Thanks in advance.

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Re: The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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New post 17 Aug 2017, 19:32
I think I get where the confusion is. Admittedly I kind of stared at these solutions for a moment before understanding.

I did it a little differently (after getting it wrong the first time, naturally):

67 * (10a + 8)
670 * (a) + 536

Ok now we have some digit 'a' that has some bearing on what the 10's digit is going to be. What does 'a' interact with in that expression? The '0' on 670? yes, but it will be 0.

The '7' in 670? Yes --> ok then 7*a + 3 because the 3 comes from the 536 we need to add to our result in order to get a 10's digit of 8 for the product of x and y.

Therefore we have:

7a + 3 = 8
7a = 5
a = 5/7

In order for 'a' to be an integer, it needs to be a multiple of 7 and there's only one multiple of 7 in the answer choices.

Hope that helps!

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Re: The integer x has a tens digit of 6 and a units digit of 7. The units [#permalink]

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New post 17 Aug 2017, 20:04
Answer is 5
67 * a8=
536
+ X 0=
Z86
7a=35 then x=5 will satisfy




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Re: The integer x has a tens digit of 6 and a units digit of 7. The units   [#permalink] 17 Aug 2017, 20:04
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