GMAT Weekly Math Quest - June 21, 2009

Hagrid · #1 (**permalink**) June 22nd, 2009, 02:03 AM

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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Sohan · #2 (**permalink**) June 22nd, 2009, 04:41 AM

100 sec.

D.
Possible values : 24, 36, 48

1) is sufficient : 48
2) is sufficient : 48

clerk · #3 (**permalink**) June 23rd, 2009, 03:28 AM

Quote:

Originally Posted by Sohan

100 sec.

D.
Possible values : 24, 36, 48

1) is sufficient : 48
2) is sufficient : 48

missed 12

clerk · #4 (**permalink**) June 23rd, 2009, 03:35 AM

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

docaseem · #5 (**permalink**) June 23rd, 2009, 03:36 AM

Agreed wid Sohan.
D

m-alum11 · #6 (**permalink**) June 26th, 2009, 04:40 PM

Will be waiting for the answer, I kind of didn't get clerk explanation.

robbie523 · #7 (**permalink**) August 11th, 2009, 10:39 AM

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,