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15 Oct 2019, 23:42
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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.
(1) The units digit of 2x is less than the units digit of x.
(2) The tens digit of 2x is 7.
16 Oct 2019, 00:31
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Bunuel
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) The units digit of 2x is less than the units digit of x.
(2) The tens digit of 2x is 7.
(1) The units digit of 2x is less than the units digit of x.
--> Only possible when unit's digit of x = {5, 6, 7, 8, 9}
Unit's digit of x ------- Unit's digit of 2x
------ 5 --------------------- 0
------ 6 --------------------- 2
------ 7 --------------------- 4
------ 8 --------------------- 6
------ 9 --------------------- 8
--> Unit's digit is definitely greater than 4 --> Sufficient
(2) The tens digit of 2x is 7.
--> Only possible when last 2 digits of x are {35, 36, 37, 38, 39}
--> Unit's digit is definitely greater than 4 --> Sufficient
IMO Option D
gmatdordie
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16 Oct 2019, 11:23
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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.
tens digit of positive integer is 3 so we can have { 33, 34. 35, 36, 37} we need to find out if(unit digit of x >4?)
say we have X=3b
1) unit digit of 2x is less than unit digit of x
lets take corner values
if X=33, 2X=66, so unit digit of 2x will be greater than x which didnt fit the st1
if X =34, 2x=68 again unit digit of 2x is greater than x which is opposite to statement 1
if x=35, then 2x=70, so 0< 5 , means unit digit of 2x is less than x, which means unit digit of x is >4 so statement I is sufficient
2) tens digit of 2x=7, i.e 2x= 7b, we have x= 3b, only if b> 4, then it is possible so, statement II is sufficient
Ans:D
(1) The units digit of 2x is less than the units digit of x.
(2) The tens digit of 2x is 7.
tens digit of positive integer is 3 so we can have { 33, 34. 35, 36, 37} we need to find out if(unit digit of x >4?)
say we have X=3b
1) unit digit of 2x is less than unit digit of x
lets take corner values
if X=33, 2X=66, so unit digit of 2x will be greater than x which didnt fit the st1
if X =34, 2x=68 again unit digit of 2x is greater than x which is opposite to statement 1
if x=35, then 2x=70, so 0< 5 , means unit digit of 2x is less than x, which means unit digit of x is >4 so statement I is sufficient
2) tens digit of 2x=7, i.e 2x= 7b, we have x= 3b, only if b> 4, then it is possible so, statement II is sufficient
Ans:D
