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If the tens digit of positive integers x, y are 6, how many values of

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If the tens digit of positive integers x, y are 6, how many values of [#permalink]

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If the tens digit of positive integers x, y are 6, how many values of the tens digit of 2(x+y) can be there?

A. 2
B. 3
C. 4
D. 5
E. 6


* A solution will be posted in two days.

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Re: If the tens digit of positive integers x, y are 6, how many values of [#permalink]

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If the tens digit of positive integers x, y are 6, how many values of the tens digit of 2(x+y) can be there?

A. 2
B. 3
C. 4
D. 5
E. 6


-> If X=y=60, 2(x+y)=240 is derived. If x=y=69, 2(x+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
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Re: If the tens digit of positive integers x, y are 6, how many values of [#permalink]

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New post 17 Jul 2016, 05:16
Hi!
did used a small layman method.. correct my approach (though crack down the answer correctly)
lets fix 6 for x
for y we have 1 .....9 = means 9 numbers
1+6 =7
2+6= 8
3+6= 9
4+6= 1 (10 but took 1 as for tens digit)
5+6 =1 (11... took 1 for tens digit)
...
..
.
so all 1 for tens digit hence same.

7,8,9,1 means 4 ...
correct me .
really interesting question.
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Re: If the tens digit of positive integers x, y are 6, how many values of [#permalink]

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New post 22 Aug 2016, 02:22
I get 2 as ans.

If the sum of the units digits of X and Y is less than 9, then the tens digits of x+y is 2. When this sum is multiplied by the 2, the tens digit will become 4.

If the sum of the units digit of X and Y is more than 9, then the tens digit of x+y is 3, because maximum 1 can be carried over from units place and thus 6+1+6 will leave 3 in the tens place. 3*2 will leave 6 for 2(x+y).

Thus total 2 numbers in tens place for the operation 2(x+y)!!

please tell me where am i going wrong?
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Re: If the tens digit of positive integers x, y are 6, how many values of [#permalink]

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New post 22 Aug 2016, 09:11
deeksha6 wrote:
I get 2 as ans.

If the sum of the units digits of X and Y is less than 9, then the tens digits of x+y is 2. When this sum is multiplied by the 2, the tens digit will become 4.

If the sum of the units digit of X and Y is more than 9, then the tens digit of x+y is 3, because maximum 1 can be carried over from units place and thus 6+1+6 will leave 3 in the tens place. 3*2 will leave 6 for 2(x+y).

Thus total 2 numbers in tens place for the operation 2(x+y)!!

please tell me where am i going wrong?


Hey you are missing something after multiplication that can be carry over.
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Re: If the tens digit of positive integers x, y are 6, how many values of [#permalink]

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New post 23 Aug 2016, 01:54
sahil7389 wrote:
deeksha6 wrote:
I get 2 as ans.

If the sum of the units digits of X and Y is less than 9, then the tens digits of x+y is 2. When this sum is multiplied by the 2, the tens digit will become 4.

If the sum of the units digit of X and Y is more than 9, then the tens digit of x+y is 3, because maximum 1 can be carried over from units place and thus 6+1+6 will leave 3 in the tens place. 3*2 will leave 6 for 2(x+y).

Thus total 2 numbers in tens place for the operation 2(x+y)!!

please tell me where am i going wrong?


Hey you are missing something after multiplication that can be carry over.


Yes! Thank you for pointing that out :)
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Re: If the tens digit of positive integers x, y are 6, how many values of [#permalink]

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New post 12 Feb 2018, 09:12
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MathRevolution wrote:
If the tens digit of positive integers x, y are 6, how many values of the tens digit of 2(x+y) can be there?

A. 2
B. 3
C. 4
D. 5
E. 6


* A solution will be posted in two days.


Minimum value possible = 60+60=120*2=240
Maximum value possible = 69+69=138*2=276
Thus, all values between 4 and 7 inclusive - 4,5,6 and 7 - can be present as tense digit.

Answer should be C
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Re: If the tens digit of positive integers x, y are 6, how many values of   [#permalink] 12 Feb 2018, 09:12
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