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If x is a two-digit number (so x = ba with b and a digits), what is th

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If x is a two-digit number (so x = ba with b and a digits), what is th  [#permalink]

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New post 22 Oct 2017, 05:37
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If x is a two-digit number (so x = ba with b and a digits), what is the last digit a of x?

(1) The number 3x is a three-digit number whose last digit is a.
(2) The digit a is less than 7.

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If x is a two-digit number (so x = ba with b and a digits), what is th  [#permalink]

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New post Updated on: 22 Oct 2017, 06:56
Bunuel wrote:
If x is a two-digit number (so x = ba with b and a digits), what is the last digit a of x?

(1) The number 3x is a three-digit number whose last digit is a.
(2) The digit a is less than 7.


We need unit's digit of \(x\)

Statement 1: implies that unit's digit of \(x\) is \(0\) or \(5\) because \(0\) multiplied by \(3\) unit's digit will be \(0\) and \(5\) multiplied by \(3\) unit's digit will be \(5\). Hence insufficient

Statement 2: \(a\) could be any number less than \(7\). Insufficient

Combining 1 & 2 again \(a\) can be \(0\) or \(5\). Insufficient

Option E

Originally posted by niks18 on 22 Oct 2017, 06:19.
Last edited by niks18 on 22 Oct 2017, 06:56, edited 2 times in total.
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If x is a two-digit number (so x = ba with b and a digits), what is th  [#permalink]

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New post 22 Oct 2017, 06:47
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S1- 3x is a three-digit number whose last digit is a.
For example, no. can be 35, 40, 45,... which when multiplied by 3, gives 105, 120, 135...and so on.
Not sufficient.

S2 - The digit a is less than 7. Many possibilities.
Not sufficient.

Combining, also not sufficient as both 0 and 5 are less than 7.
Answer E.

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Re: If x is a two-digit number (so x = ba with b and a digits), what is th  [#permalink]

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New post 23 Oct 2017, 02:00
While I agree with the answer, I do not think that the approach used here is correct.
The stem says x is a two-digit number, I am not getting why are you guys considering it to be a multiple of 5?
Stmt 1 says, X when multiplied with 3 will yield a 3 digit number. So X could be anything above 33.
Because 3 times 33 will give 99 and any 2 digit number above this will yield more than 2 digits when multiplied by 3.
So, from stmt 1, X has a lot of options. Hence insufficient.

Coming to stmt 2, it says a < 7 , meaning, the last digit of 3X is less than 7. Insuff.

1 + 2. take number 34, 3*34 = 102.
take number 35, 3*35 = 105.
take number 36, 3*36 = 108, last digit exceeds 7.
So, we are left out with 2 results 102 and 105 whose last digits are below 7. i.e., we have 2 options for X, 34 & 35.
Multiple answers, So both stmts are insuff.

Hence E.

Still, I would like to know how you guys considered X to be a multiple of 5. Please let me know if there is any logic that I might have missed while analyzing the stem.
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If x is a two-digit number (so x = ba with b and a digits), what is th  [#permalink]

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New post 23 Oct 2017, 03:01
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reachskishore wrote:
While I agree with the answer, I do not think that the approach used here is correct.
The stem says x is a two-digit number, I am not getting why are you guys considering it to be a multiple of 5?
Stmt 1 says, X when multiplied with 3 will yield a 3 digit number. So X could be anything above 33.
Because 3 times 33 will give 99 and any 2 digit number above this will yield more than 2 digits when multiplied by 3.
So, from stmt 1, X has a lot of options. Hence insufficient.

Coming to stmt 2, it says a < 7 , meaning, the last digit of 3X is less than 7. Insuff.

1 + 2. take number 34, 3*34 = 102.
take number 35, 3*35 = 105.
take number 36, 3*36 = 108, last digit exceeds 7.
So, we are left out with 2 results 102 and 105 whose last digits are below 7. i.e., we have 2 options for X, 34 & 35.
Multiple answers, So both stmts are insuff.

Hence E.

Still, I would like to know how you guys considered X to be a multiple of 5. Please let me know if there is any logic that I might have missed while analyzing the stem.


Since x=ba which when multiplied by 3 gives 3 digit number with last digit a, the only possibilities are a=0 or 5 . 0 and 5 are the only digits which when multiplied by 3 gives last digit 0 or 5.
Hope it is clear.
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Re: If x is a two-digit number (so x = ba with b and a digits), what is th  [#permalink]

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New post 23 Oct 2017, 23:03
souvonik2k wrote:
reachskishore wrote:
While I agree with the answer, I do not think that the approach used here is correct.
The stem says x is a two-digit number, I am not getting why are you guys considering it to be a multiple of 5?
Stmt 1 says, X when multiplied with 3 will yield a 3 digit number. So X could be anything above 33.
Because 3 times 33 will give 99 and any 2 digit number above this will yield more than 2 digits when multiplied by 3.
So, from stmt 1, X has a lot of options. Hence insufficient.

Coming to stmt 2, it says a < 7 , meaning, the last digit of 3X is less than 7. Insuff.

1 + 2. take number 34, 3*34 = 102.
take number 35, 3*35 = 105.
take number 36, 3*36 = 108, last digit exceeds 7.
So, we are left out with 2 results 102 and 105 whose last digits are below 7. i.e., we have 2 options for X, 34 & 35.
Multiple answers, So both stmts are insuff.

Hence E.

Still, I would like to know how you guys considered X to be a multiple of 5. Please let me know if there is any logic that I might have missed while analyzing the stem.


Since x=ba which when multiplied by 3 gives 3 digit number with last digit a, the only possibilities are a=0 or 5 . 0 and 5 are the only digits which when multiplied by 3 gives last digit 0 or 5.
Hope it is clear.


Oh yes !!! Had missed that detail. Sorry about that.
Thanks for clearing out my doubt.

+1Kudos to you
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Re: If x is a two-digit number (so x = ba with b and a digits), what is th &nbs [#permalink] 23 Oct 2017, 23:03
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