Which of the following could be the sum of the reciprocals of two

Question

Which of the following could be the sum of the reciprocals of two different prime numbers?

A. 7/13
B. 10/12
C. 11/30
D. 23/50
E. 19/77

Bunuel · Accepted Answer

Which of the following could be the sum of the reciprocals of two different prime numbers? 
A. 7/13
B. 10/12
C. 11/30
D. 23/50
E. 19/77

Let  x  and  y  be two different primes, then their sum will be  \frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy} . So, the denominator of the reduced fraction must be the product of two different primes: only B,  \frac{10}{12}=\frac{5}{6}=\frac{5}{2*3} , and E,  \frac{19}{77}=\frac{19}{7*11} , have such denominators and nominator must be the sum of the primes in denominator, thus only B is left:  \frac{10}{12}=\frac{5}{6}=\frac{2+3}{2*3} .

Answer: B.

Hope it's clear.

nitya34 · Answer

10/12 it is 10/12=5/6=(1/2) + (1/3)

jullysabat · Answer

Was it a guess ??? or how do we approach to this kind of problem...

prab · Answer

are there any theories for these kinds of problems? haven't came across any yet, i think hit and trial is the best one!

jullysabat · Answer

Hey Bunnel,

Thank u so much.. for this explanation...
very very simple and robust way of explaning things...

prasannajeet · Answer

Hi Bunuel

Why not the ans would be 11/30? Pls explain

If we take 2 prime number as 5 and 6 then by equation it is 5+6/5*6=11/30 ans.....
 
Apart from this PS question I have a query..that is currently I am doing practice from GMAT club. Is it enough or I must follow some other source ?

Needless to say +Kudos to your simplistic approach for every question.

Rgds
Prasannajeet

svitozar · Answer

Hi Bunuel

Why not the ans would be 11/30? Pls explain

If we take 2 prime number as 5 and 6 then by equation it is 5+6/5*6=11/30 ans.....

Because 6 is not a prime)

Bunuel · Answer

6=2*3 is not a prime number.

Bunuel · Answer

I think that we have more than enough questions and theory topics on the site. Though you can check Best GMAT Books: best-gmat-math-prep-books-reviews-recommendations-77291.html books-to-read-improve-verbal-score-and-enjoy-a-good-read-76079.html Hope it helps.

prasannajeet · Answer

Hi Sivtozar & Bunuel

Thank you . I made a felony not a mistake to identify the prime number.
Also thanx for the thread.

Rgds
Prasannajeet

TeamGMATIFY · Answer

This question has to be solved by taking on option at a time.
However, we do not need to check all the options here as some can be eliminated by checking the given condition.

We have to find the sum of reciprocals of two different prime numbers.
This means that the denominator will be the multiplication of the two different prime numbers.

Checking the options for this.

Option A  = 13*1. Does not satisfy the condition of two prime numbers
 Option B  = 10/12 = 5/6, Here 6 = 2*3. This is what we need. 
To cross check, see that 1/2 + 1/3 = 5/6 = 10/12 Our answer.

Let us check for the others too
 Option C : 30 = 5*6 or 3*10. Does not satisfy the condition of two prime numbers
 Option D : 50 = 25*2 or 50*1. Does not satisfy the condition of two prime numbers
 Option E : 77 = 7*11. This satisfies our condition. 
Checking for the numerator: 1/11 + 1/7 = 18/77
But option has 19/77. Hence not the correct answer.

Correct answer: Option B

Temurkhon · Answer

num=sum of prime numbers

denom=product of those numbers

A. 7/13, no such primes exist

B. 10/12=5/6, the numbers are 3 and 2

C. 11/30, no such primes

D. 23/50, no such primes
 
E. 19/77, no such primes

B

mvictor · Answer

what a brain tease...
to have an odd number in the numerator, it must be that one of the prime numbers is 2.
2*3=6.
2+2=5
5/6 *2 = 10/12

B.

we can also rewrite:
a+b/ab
where ab must be either the result of 2 prime numbers multiplied, or we must have a factor as well: abx - where x is the factor.
A. 7/13 - ab=13 - can't have such option. 
B. 10/12 = ab=2*3*2 => so 2 primes multiplied by a factor of 2. numerator must also be the sum of 2 prime numbers multiplied by 2.
C. 11/30 = ab=5*3*2 => so either ab is multiplied by 5, 3, or by 2. in this case, a+b as well needs to be multiplied by the same factor. but 11 is not a multiple of 5, 3, or 2. so out.
D. 23/50 = 5x2x5 -> 23 is not a factor of 5 or 2. so out.
E. 19/77 = 7x11 => so 2 primes. a+b must be equal to 18. so definitely not what we need.

only B works.

gauravk · Answer

Missed reducing the fraction and got it wrong even after the correct approach.

Good question.

shashankism · Answer

Here we have to find the number which is sum of reciprocals of two prime numbers say x ,y
So, 1/x + 1/y = (x+y)/xy, which means denominator must be multiple of two prime numbers.

In the given options we can see that only option B fulfills this. 10/12 = 5/6 = 5/3*2

Now 1/3+1/2 = 5/6

Answer B

RashedVai · Answer

try to reduce the answer choices to prime. Look every choices has prime numbers except (B).
If answer choice (B) were 5/6, you would pick choice (B) easily.

Posted from my mobile device

BrentGMATPrepNow · Answer

Let  x  be one of the prime numbers
Let  y  be the other prime number

So, the sum of their reciprocals  = \frac{1}{x}+\frac{1}{y} = \frac{y}{xy}+\frac{x}{xy}=\frac{x+y}{xy}

So, we're looking for an answer choice such that the denominator can be written as the product of two primes, and the numerator can be written as the sum of two primes.

Notice that the fraction in answer choice B ( \frac{10}{12} ) isn't expressed in simplest terms. 
When we simplify  \frac{10}{12} , we get  \frac{5}{6} , which can be expressed as:  \frac{2+3}{(2)(3)} 
So, if the two prime numbers are  2  and  3 , the sum of the reciprocals  = \frac{5}{6}

Answer: B

Kinshook · Answer

Asked: Which of the following could be the sum of the reciprocals of two different prime numbers?

1/p1 + 1/p2 = (p1+p2)/p1p2

A. 7/13
B. 10/12 = 5/6 = (2+3)/2*3
C. 11/30
D. 23/50
E. 19/77

IMO B

GmatPoint · Answer

Let a and b be two prime numbers.

Now, 1/a + 1/b = (a+b)/ab

Consider the options:

I)7/13: Here, ab = 13. Since 1 is not a prime number, this is not a possibility.
II)10/12 = 5/6: Here, ab = 6. Thus one of them is 2, and the other is 3. Since 2+3 = 5, thus, this is the correct option.
III)11/30: Here, ab = 30. Since it is not possible to for 30 with the product of two prime numbers, this is not a possibility.
IV)23/50: Same as (III)
V) 19/77: Here, ab = 77. Thus, one of them is 7, and the other is 11. Since 11+7 = 18, and the numerator is 19, this is not a possibility.

Thus, the correct option is B.

Which of the following could be the sum of the reciprocals of two

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GMAT Problem Solving (PS) Questions

Which of the following could be the sum of the reciprocals of two

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