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26 Oct 2010, 02:40
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (01:36) correct
23%
(02:35)
wrong
based on 183
sessions
History
Date
Time
Result
Not Attempted Yet
Two positive integers differ by 4, and sum of their reciprocals is 10/21. Then one of the numbers is
a) 3
b) 1
c) 5
d) 21
e) 28
a) 3
b) 1
c) 5
d) 21
e) 28
26 Oct 2010, 03:53
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There are several ways to solve this question:
Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 10/21
Solve for n => n=3. Hence, answer b) is correct.
Picking numbers:
Start with middle choice, i.e. 5
5 obviously cannot be the larger of the two integers as this would mean that the smaller integer would equal 1 (hence reciprocal also 1) and the sum of the reciprocals would exceed 10/21.
If 5 is the smaller of the two integers => 1/5 + 1/9 = 14/45. This is smaller than 10/21.
Next, choose 3 and 7 (because 12 and 28 would obviously make sum of the reciprocals too small) => 1/3 + 1/7 = 10/21. Hence, answer b) is correct.
Considering Least common multiple:
For the sum of the reciprocals of the integers to have the denominator 21 both numbers must be divisors of 21. This only holds true for answer choice b).
Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 10/21
Solve for n => n=3. Hence, answer b) is correct.
Picking numbers:
Start with middle choice, i.e. 5
5 obviously cannot be the larger of the two integers as this would mean that the smaller integer would equal 1 (hence reciprocal also 1) and the sum of the reciprocals would exceed 10/21.
If 5 is the smaller of the two integers => 1/5 + 1/9 = 14/45. This is smaller than 10/21.
Next, choose 3 and 7 (because 12 and 28 would obviously make sum of the reciprocals too small) => 1/3 + 1/7 = 10/21. Hence, answer b) is correct.
Considering Least common multiple:
For the sum of the reciprocals of the integers to have the denominator 21 both numbers must be divisors of 21. This only holds true for answer choice b).
26 Oct 2010, 04:23
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My take on this question - to solve it in the least time - is to make algebraic equation and then pick numbers.
If one number is n, the other is (n + 4).
Given 1/n + 1/(n+4) = 10/21
I look at the options and say that I need 21 as the denominator. 3 is given as an option. If 3 is one number, the other will be 7. Quickly substitute the values and confirm.
1/3 + 1/7 = 10/21
Note: In GMAT it is advisable to confirm your answer even if it seems pretty obvious. They like to put small little tricks to waylay you!
If one number is n, the other is (n + 4).
Given 1/n + 1/(n+4) = 10/21
I look at the options and say that I need 21 as the denominator. 3 is given as an option. If 3 is one number, the other will be 7. Quickly substitute the values and confirm.
1/3 + 1/7 = 10/21
Note: In GMAT it is advisable to confirm your answer even if it seems pretty obvious. They like to put small little tricks to waylay you!
