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

(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

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

HI, thank you for the explanation. One quick question, but what if the unit is 0? Then you wouldn't be able to find it out.
Thank you

The units digit of x cannot be 0 because this violates both statements.

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

Now, if the units digit of x were 0, then the units digit of 2*x would also be 0. So, in this case the units digit of 2*x would NOT be less than the units digit of x.

(2) says: The tens digit of 2*x is 7.

If the units digit of x were 0, then the last two digits of 2*x would be 2*...30 = ...60. So, in this case the tens digit of 2*x would NOT be 7.

Hope it's clear.
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