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D.
Possible values : 24, 36, 48
1) is sufficient : 48
2) is sufficient : 48
Difficulty Level : High
Time to Solve : <45 secs
Please discuss your approach and also provide time you took to solve the question. OA will be posted only when enough people have outlined their approach.
Q. k is a 2-digit positive integer, the value of k is 6 times the unit digit. What is the value of k?
1) The units’ digit is 4 greater than the tens’ digit.
2) The sum of the 2 digits is a 2-digit integer.
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100 sec.
D.
Possible values : 24, 36, 48
1) is sufficient : 48
2) is sufficient : 48
Originally Posted by Sohan
missed 12
let 2-digit integer be ab, where a - is ten digit integer and b - is unit integer
10*a + b = 6b,
2a = b, here you can see that a can vary from 1 to 4 (otherwise 2*a will be 2 digit number)
(thus you can see that ab can be 1 and 2 - 12, 2 and 4 - 24, 3 and 6 - 36, 4 and 8 - 48)
1) b = a + 4 (we already know that the only possible option is 4 and 8)
and 2a = b,
a = 4, b = 8 - sufficient
2) a + b >= 10 (the only possible option is 4 and 8)
and 2a = b,
3a >= 10, a>=3,3 - which means a starts from 4
as we already defined a, it varies from 1 to 4, therefor a is equal to 4, then b is equal to 8
which makes this answer also sufficient
D
Last edited by clerk; June 24th, 2009 at 11:44 PM.
Agreed wid Sohan.
D
Will be waiting for the answer, I kind of didn't get clerk explanation.
totally agree with answer above, set tenth digit = a, and the unit digit = b.
10a+b=6b => 2a=b
statement one: a+4=b with the equation above, two equations two variables, so solveable.
statement two: a + b > 10 lets, bring b=2a into the equation, we get a + 2a > 10
so, 3a > 10 which also is a > 3.33.... if both digit is interger, we will try 4 first, a=4, (no other numbers than 4 can be plugged in, since a=5, will be a two digit unit number, which the condition that a and b is both a single digit number is given out in the begining) which will be 48, and 6*unit digit 8 will be 48. answer is out, which is sufficient,
Rephrasing the question:
A 2 digit number is written in standard as 10x + y
Thus 6 times the units digit is 6y
Thus,
10x + y = 6y
10x = 5y
2x = y
Thus we have
k = 6y and
2x = y
Statement 1]
This can be rephrased to
y = x + 4
Combining this with 2x = y we have two equations and two unknowns. To make sure they are solveable...
2x = x + 4
x = 4
Since we have x we can find y
y = 2(4)
y = 8
k = 48
Statement 2]
This can be rephrased to x + y >= 10
Also, we know k is a 2 digit number and that when we multiply the units digit by 6 not only is k = 6y but also the units digit of k will still equal y. Not many two digit numbers qualify
Possible Units x 6
0 x 6 = 0
1 x 6 = 6
2 x 6 = 12
3 x 6 = 18
4 x 6 = 24
5 x 6 = 30
6 x 6 = 36
7 x 6 = 42
8 x 6 = 48
9 x 6 = 54
This
8 x 6 = 48
is the only number that satisfies the contraints thus statement 2 is sufficient
Ans D
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