If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?

Question

If  \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x} , which of the following must be an integer?

I.  \frac{x}{8}

II.  \frac{x}{12}

III.  \frac{x}{24}

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

GMATinsight · Answer

\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x} 
i.e. 13/12 = 13/x
i.e. x = 12

i.e. x will be divisible by ONLY 12 and every factor of 12 hence

Answer: option B

EgmatQuantExpert · Answer

Solution 
  Given:  
 •  \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}

To find:  
 • Which of the given options is always an integer?

Approach and Working:   
 • Multiplying the equation,  \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x} , by x on both sides gives,
 o  \frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 13 
o  \frac{13x}{12} = 13 
o Implies, x = 12

Thus, only II is true

Hence, the correct answer is option B.

Answer: B

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-Algebra-e1533292089856.jpg

abhishekdadarwal2009 · Answer

1/2+1/3+1/4=13/12. Thus x=12.

Not just put 12 in place of x in all three options we get only 2 II to be an integer.

Option B.

T1101 · Answer

If the question used "COULD be true" instead of "must be true", would the answer be D?

Because we know that  \frac{13}{12}  =  \frac{13}{x}

So x could also be a multiple of 12, therefore  \frac{x}{24}  could also be true.

Am I correct?

ArjunJag1328 · Answer

1/2 + 1/3 + 1/4 = 13/x

=>13/12 = 13/x
=>13x = 156
=>x = 156/13
=>x=12

A. 12/8 = 3/2 - Not an Integer
B. 12/12 = 1 - Integer
C. 12/24 = 1/2 - Not an integer

Hence B is the answer

ScottTargetTestPrep · Answer

Multiplying by 12x we have:

6x + 4x + 3x = 156

13x = 156

x = 12; thus, x/12 must be an integer.

Answer: B

Kinshook · Answer

Given:  \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}

Asked: Which of the following must be an integer?

\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}

\frac{(6+4+3)}{12} = \frac{13}{x}

\frac{13}{12} = \frac{13}{x}

\frac{1}{12} = \frac{1}{x}

x = 12

I.  \frac{x}{8}

\frac{12}{8} = \frac{3}{2} = 1.5

NOT AN INTEGER

II.  \frac{x}{12}

\frac{12}{12} = 1

INTEGER

III.  \frac{x}{24}

\frac{12}{24} = \frac{1}{2} = 0.5

NOT AN INTEGER

IMO B

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If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?

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If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?

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