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19 Jun 2018, 23:38
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (02:12) correct
33%
(01:59)
wrong
based on 158
sessions
History
Date
Time
Result
Not Attempted Yet
What is the units digit of the positive integer x?
(1) The units digit of x^2 is greater than the units digit of x^3
(2) The units digit of x is greater than the units digit of x^2
(1) The units digit of x^2 is greater than the units digit of x^3
(2) The units digit of x is greater than the units digit of x^2
Updated on: 20 Jun 2018, 06:01
Originally posted by DavidTutorexamPAL on 20 Jun 2018, 00:34.
Last edited by DavidTutorexamPAL on 20 Jun 2018, 06:01, edited 1 time in total.
Last edited by DavidTutorexamPAL on 20 Jun 2018, 06:01, edited 1 time in total.
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Bunuel
As it's unclear exactly where to start, we'll try a few examples.
This is an Alternative approach.
We can write things out:
Units of x, units of x^2, units of x^3
0, 0, 0
1, 1, 1
2, 4, 8
3, 9, 7
4, 6, 4
5, 5, 5
6, 6, 6
7, 9, 3
8, 4, 2
9, 1, 9
So, if (1) were true then the units digit of x could be 3,4,7 or 8. Insufficient.
If (2) were true, then the units digit of x could be 8 or 9. Insufficient.
Combined, the units digit of x must be 8. Sufficient.
(C) is our answer.
Updated on: 20 Jun 2018, 03:47
Originally posted by EgmatQuantExpert on 20 Jun 2018, 03:43.
Last edited by EgmatQuantExpert on 20 Jun 2018, 03:47, edited 2 times in total.
Last edited by EgmatQuantExpert on 20 Jun 2018, 03:47, edited 2 times in total.
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Solution
To find:
- • We need to find the units digit of the integer x.
Approach and Working:
Statement 1: The units digit of x^2 is greater than the units digit of x^3
Units digit of x^2 can be greater than x^3 if the units digit of x is either 3, 4, 7, or 8.
However, we do not have a unique value.
Hence, statement 1 is insufficient to find the answer.
Statement 2: The units digit of x is greater than the units digit of x^2 .
Units digit of x can be greater than the units digit of x^2 if units digit of x is either 8 or 9.
However, we do not have a unique value.
Hence, statement 2 is insufficient to find the answer.
Combining both the statements:
By combining both the statement, we get the units digits of x as 8.
Hence, option C is the correct answer.
Please Note: Do not make the mistake of considering Statement 1, while solving Statement 2, else you may end up marking option B as the answer.
Answer: C
