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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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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.
[Reveal] Spoiler: OA

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Kudos [?]: 135364 [0], given: 12691

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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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22 Oct 2017, 06:19
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

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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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.

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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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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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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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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.

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   [#permalink] 23 Oct 2017, 23:03
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