If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is
A) 3
B) 5
C) 7
D) 9
E) 11
The OA is C.
Should I solve the equation 1/(2k+1) + 1/(2k+3) = 12/35? Or there is another way to solve it?
If the sum of the reciprocals of two consecutive
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Let us assume that two consecutive odd integers are a and b where b = a+2. Then, sum of their reciprocal is (a+b)/ab. We have been given that sum of two consecutive odd integers is 12/35.
As GCD of two consecutive integers is always 1, sum of these two is 12 and multiplication of these two integers is 35.
Obviously, these two odd integers are 5 and 7.
Thus, larger integer is 7. So, answer is C.
As GCD of two consecutive integers is always 1, sum of these two is 12 and multiplication of these two integers is 35.
Obviously, these two odd integers are 5 and 7.
Thus, larger integer is 7. So, answer is C.
Last edited by pannalal on Sun Sep 24, 2017 7:22 am, edited 1 time in total.
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Since the denominator of the sum is 35, and since 35 equals the product of 5 and 7 (two consecutive odd integers), let's start by testing whether 5 and 7 are the integers in question.Vincen wrote:If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is
A) 3
B) 5
C) 7
D) 9
E) 11
So, the RECIPROCALS are 1/5 and 1/7
1/5 + 1/7 = 7/35 + 5/35
= 12/35
Voila!!
So, the odd integers are 5 and 7
The greater of the two integers is 7
Answer: C
Cheers,
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Hi Vincen,
We're told that the sum of the reciprocals of two CONSECUTIVE ODD integers is 12/35. We're asked for the GREATER of the two integers. This question can be solved by TESTing THE ANSWERS.
Let's TEST Answer B: 5
IF.... the values are 3 and 5....
then the sum of the reciprocals is 1/3 + 1/5 = 5/15 + 3/15 = 8/15
This is clearly not the correct answer, but the denominator ends in a '5', so it's likely that 12/35 will ALSO include a 5...
Let's TEST Answer C: 7
IF.... the values are 5 and 7....
then the sum of the reciprocals is 1/5 + 1/7 = 7/35 + 5/35 = 12/35
This is an exact match for what we were told, so this MUST be the answer.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that the sum of the reciprocals of two CONSECUTIVE ODD integers is 12/35. We're asked for the GREATER of the two integers. This question can be solved by TESTing THE ANSWERS.
Let's TEST Answer B: 5
IF.... the values are 3 and 5....
then the sum of the reciprocals is 1/3 + 1/5 = 5/15 + 3/15 = 8/15
This is clearly not the correct answer, but the denominator ends in a '5', so it's likely that 12/35 will ALSO include a 5...
Let's TEST Answer C: 7
IF.... the values are 5 and 7....
then the sum of the reciprocals is 1/5 + 1/7 = 7/35 + 5/35 = 12/35
This is an exact match for what we were told, so this MUST be the answer.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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We can let the first odd integer = x and the next odd integer = x + 2; thus, the reciprocals are 1/x and 1/(x + 2). Thus:Vincen wrote:If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is
A) 3
B) 5
C) 7
D) 9
E) 11
1/x + 1/(x+2) = 12/35
Multiplying by 35x(x+2), we have:
35(x + 2) + 35x = 12x(x + 2)
35x + 70 + 35x = 12x^2 + 24x
12x^2 - 46x - 70 = 0
6x^2 - 23x - 35 = 0
(6x + 7)(x - 5) = 0
Thus, x = -7/6 or x = 5.
Since x is an integer, x must be 5 and the greater integer is x + 2 = 7.
Alternate solution:
We are given that the sum of the reciprocals of two consecutive odd integers is 12/35. We see that the denominator is 35. It's not difficult to conjecture that the integers have to be 5 and 7 since 5 x 7 = 35. Finally, we can check the sum of 1/5 and 1/7 to see if they sum to 12/35:
1/5 + 1/7 = 7/35 + 5/35 = 12/35
Since they do add up to 12/35, the larger integer is 7.
Answer: C
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