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# The tens digit of positive integer x is 3. Is the units digit of X

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Math Expert
Joined: 02 Sep 2009
Posts: 49496
The tens digit of positive integer x is 3. Is the units digit of X  [#permalink]

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02 Nov 2017, 01:57
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Difficulty:

45% (medium)

Question Stats:

68% (01:53) correct 32% (01:39) wrong based on 47 sessions

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The tens digit of positive integer x is 3. Is the units digit of X greater than 4?

(1) The units digit of 2x is less than the units digit of x.

(2) The tens digit of 2x is 7.

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Joined: 02 Jul 2017
Posts: 294
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
Re: The tens digit of positive integer x is 3. Is the units digit of X  [#permalink]

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02 Nov 2017, 02:24
The tens digit of positive integer x is 3. Is the units digit of X greater than 4?

Let x = 3a => (30+a)
Find if a > 4

(1) The units digit of 2x is less than the units digit of x.

a= 4 < 2x unit digit = 8
a= 5 > 2x unit digit = 0
a= 6 > 2x unit digit = 2
a= 7 > 2x unit digit = 4
a= 8 > 2x unit digit = 6
a= 9 > 2x unit digit = 8

=> this implies a >4
Sufficient

(2) The tens digit of 2x is 7.
As given tens digit of x is 3.. for ten digit of 2x = 7, 1 need to be carry forward from ones palce when multiples by 2

a= 4 => 2x unit digit = 8 => no carry forward
a= 5 => 2x unit digit = 10 => 1 carry forward to tens place
a= 6 => 2x unit digit = 12 => 1 carry forward to tens place
.. so on
=> this implies a >4
Sufficient

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Joined: 18 Aug 2016
Posts: 629
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
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Re: The tens digit of positive integer x is 3. Is the units digit of X  [#permalink]

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02 Nov 2017, 04:45
Bunuel wrote:
The tens digit of positive integer x is 3. Is the units digit of X greater than 4?

(1) The units digit of 2x is less than the units digit of x.

(2) The tens digit of 2x is 7.

(1) unit digit can take 5, 6, 7, 8,9....sufficient

(2) unit digit can take 5,6,7,8,9...sufficient

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Re: The tens digit of positive integer x is 3. Is the units digit of X &nbs [#permalink] 02 Nov 2017, 04:45
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# The tens digit of positive integer x is 3. Is the units digit of X

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