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15 Jun 2018, 23:33
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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:
65%
(hard)
Question Stats:
59% (02:29) correct
41%
(02:29)
wrong
based on 243
sessions
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The 2-digit positive integer x has the property that it is divisible by its units digit. What is x?
(1) x^3 has a units digit of 7
(2) x + 1 is also divisible by its units digit.
(1) x^3 has a units digit of 7
(2) x + 1 is also divisible by its units digit.
16 Jun 2018, 02:14
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Bunuel
The 2-digit positive integer x has the property that it is divisible by its units digit. What is x?
(1) x^3 has a units digit of 7
(2) x + 1 is also divisible by its units digit.
(1) x^3 has a units digit of 7
(2) x + 1 is also divisible by its units digit.
Stat 1) Cyclic power of 3 and 7 will have 7 as a unit digit
Any two digit number of the form \(A3^3\) has unit digit 7 and \(A7^1\) will have unit digit 7
Now for the given condition that The 2-digit positive integer x has the property that it is divisible by its units digit we can multiple values of X satisfying statement 1
for eg 33 , 63, 93, 77 ; Multiple values of X hence Not suff
Stat 2) X+1 is also divisible by its unit digit
here we can also have multiple values of X for eg
X = 32 , 63
X+1 = 33, 64
hence NOt Suff
Together
We can have only one value ie 63 that satisfies both condition hence Suff Ans C
16 Jun 2018, 08:31
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Bunuel
The 2-digit positive integer x has the property that it is divisible by its units digit. What is x?
(1) x^3 has a units digit of 7
(2) x + 1 is also divisible by its units digit.
(1) x^3 has a units digit of 7
(2) x + 1 is also divisible by its units digit.
From 1: Since X^3 has a unit digit 7, therefore, unit digit of x must be 3.
Now two digit numbers, which are divisible to its own unit digit are 33,63 & 93 - Since Multiple answer, therefore not sufficient
From 2: if x=11 then x+1=12, all of these are divisible by it's unit digit. Similarly, (21,22), (31,32)......- Multiple answer- Not Sufficient
Combining 1 & 2, we have only 63, which satisfy both.
Hence, C is the answer.
