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What is the tens digit of two-digit positive integer w?

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Joined: 04 Jul 2006
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What is the tens digit of two-digit positive integer w?  [#permalink]

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21 Feb 2019, 12:52
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Difficulty:

85% (hard)

Question Stats:

40% (02:33) correct 60% (02:44) wrong based on 40 sessions

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What is the tens digit of two-digit positive integer w?

(1) The tens digit of 2w is equal to the tens digit of w.
(2) The sum of the digits of w+5 is 5.
Manager
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)
Re: What is the tens digit of two-digit positive integer w?  [#permalink]

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21 Feb 2019, 13:26
kevincan wrote:
What is the tens digit of two-digit positive integer w?

(1) The tens digit of 2w is equal to the tens digit of w.
(2) The sum of the digits of w+5 is 5.

This took a while to solve!

from statement 1 we are told that 2*w and w share the same number in the tens digit.
now lets assume w is either from 10-20----90s or 19-29-39---99 series to test the extremes:
hence:
If w is:
10-20-30-40-50-60-70-80-90
2w will be:
20-40-60-80-100-120-140-160-180

or 2nd case:
w is
19-29-39-49-59-69-79-89-99
2w will be:
38-58-78-98-118-138-158-178-198

from the above we see only if w = 99 then 2w = 198 and satisfies the first statement. We also have other solutions such 95, 96, 97, 98, 99
Hence 1 is insufficient

Now in the second statement we are told: w+5 leads to a digit whose sum is 5.
Possible solutions are: 23, 32, 41, 50, 104
i.e. w = 18, 27, 36, 45, or 99
Again 2 is insufficient.

But if we combine 1 & 2 we get w=99

Hence both are required and C is the correct answer.
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Re: What is the tens digit of two-digit positive integer w?  [#permalink]

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21 Feb 2019, 19:04
eabhgoy wrote:
kevincan wrote:
What is the tens digit of two-digit positive integer w?

(1) The tens digit of 2w is equal to the tens digit of w.
(2) The sum of the digits of w+5 is 5.

This took a while to solve!

from statement 1 we are told that 2*w and w share the same number in the tens digit.
now lets assume w is either from 10-20----90s or 19-29-39---99 series to test the extremes:
hence:
If w is:
10-20-30-40-50-60-70-80-90
2w will be:
20-40-60-80-100-120-140-160-180

or 2nd case:
w is
19-29-39-49-59-69-79-89-99
2w will be:
38-58-78-98-118-138-158-178-198

from the above we see only if w = 99 then 2w = 198 and satisfies the first statement. We also have other solutions such 95, 96, 97, 98, 99
Hence 1 is insufficient

Now in the second statement we are told: w+5 leads to a digit whose sum is 5.
Possible solutions are: 23, 32, 41, 50, 104
i.e. w = 18, 27, 36, 45, or 99
Again 2 is insufficient.

But if we combine 1 & 2 we get w=99

Hence both are required and C is the correct answer.

The question is asking for only the tens digit, so therefore 1 is sufficient and two is insufficient since 27 and 99 can both be possible solutions.

Manager
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)
Re: What is the tens digit of two-digit positive integer w?  [#permalink]

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21 Feb 2019, 22:42
truplayer257 wrote:
eabhgoy wrote:
kevincan wrote:
What is the tens digit of two-digit positive integer w?

(1) The tens digit of 2w is equal to the tens digit of w.
(2) The sum of the digits of w+5 is 5.

This took a while to solve!

from statement 1 we are told that 2*w and w share the same number in the tens digit.
now lets assume w is either from 10-20----90s or 19-29-39---99 series to test the extremes:
hence:
If w is:
10-20-30-40-50-60-70-80-90
2w will be:
20-40-60-80-100-120-140-160-180

or 2nd case:
w is
19-29-39-49-59-69-79-89-99
2w will be:
38-58-78-98-118-138-158-178-198

from the above we see only if w = 99 then 2w = 198 and satisfies the first statement. We also have other solutions such 95, 96, 97, 98, 99
Hence 1 is insufficient

Now in the second statement we are told: w+5 leads to a digit whose sum is 5.
Possible solutions are: 23, 32, 41, 50, 104
i.e. w = 18, 27, 36, 45, or 99
Again 2 is insufficient.

But if we combine 1 & 2 we get w=99

Hence both are required and C is the correct answer.

The question is asking for only the tens digit, so therefore 1 is sufficient and two is insufficient since 27 and 99 can both be possible solutions.

I thout we had to solve for w

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Re: What is the tens digit of two-digit positive integer w?   [#permalink] 21 Feb 2019, 22:42
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