Two fractions are inserted between 1/4 and 1/2 so that the

Question

Two fractions are inserted between 1/4 and 1/2 so that the difference between any two successive fractions is the same. Find the sum of the four fractions.

A. 18/12
B. 16/12
C. 5/2
D. 9/19
E. 24/32

My ans is 16/12
but OA is 18/12...
Can someone please explain the OA.....

Bunuel · Accepted Answer

As the difference of any two successive fractions is the same then we have evenly spaced set (arithmetic progression). Sum of the terms of AP is  \frac{first \ term + last \ term}{2}*(number \ of \ terms)  -->  sum=\frac{\frac{1}{4}+\frac{1}{2}}{2}*4=(\frac{1}{4}+\frac{1}{2})*2=\frac{3}{2} .

Answer: A.

prasannajeet · Answer

Hi Bunuel...

Can we solve it like in following procedure...

Let a/b and c/d two fraction..so the sequence 1/2,a/b,c/d,1/4

As given- 1/2-a/b=c/d-1/4=>a/b+c/d=3/4
Question ask us to find 1/2+a/b+c/d+1/4=>1/2+3/4+1/4=3/2 ans....

Rgds
Prasannajeet

vy3rgc · Answer

Think of this as 4 points on the number line...

(1/4).....(X).....(Y).....(1/2)

OR

(3/12)....(X).....(Y).....(6/12)

You can easily see that X & Y should be 4/12 and 5/12 respectively. Add and you'll get the sum as 3/2.

Bunuel · Answer

Yes, that's correct.

GMATtracted · Answer

Let the fractions inserted b/w  \frac{1}{4} & \frac{1}{2}  be  \frac{1}{x} and \frac{1}{y} We can easily calculate the value of  \frac{1}{x}  by:-
 2(\frac{1}{x}-\frac{1}{4})=\frac{1}{2}-\frac{1}{x} Solving we get,  \frac{1}{x}=\frac{1}{3} Also,  \frac{2}{y}=\frac{1}{3}+\frac{1}{2} 
Solving we get  \frac{1}{y}=\frac{5}{12} Hence, the 4 fractions are  \frac{1}{4}, \frac{1}{3}, \frac{5}{12} and \frac{1}{2} 
The required sum is thus:-
 sum=\frac{1}{4}+ \frac{1}{3}+ \frac{5}{12}+ \frac{1}{2}=\frac{18}{12}

PareshGmat · Answer

Let the 2 fractions be a & b

\frac{1}{2}  ........... a ............... b ................  \frac{1}{4}

\frac{1}{2} - a = a - b

a - b = b - \frac{1}{4}

Solving the above, we get

a = \frac{5}{12}

b = \frac{1}{3}

Addition

= \frac{1}{2} + \frac{5}{12} + \frac{1}{3} + \frac{1}{4}

= \frac{18}{12}

Answer = A

abdurgiki · Answer

Write 1/4 as 3/12 and 1/2 as 6/12

therefore,

3/12, 4/12, 5/12, 6/12

Sum 18/12

ikneet · Answer

Let the two fractions be X and Y

1/4.... X.....Y....1/2

Since we know that the difference between all of them is same

X-1/4 = 1/2-Y

X+Y = 1/2+1/4

X+Y = 3/4....... (1)

And

Y-X = X - 1/4

Y-X-X = -1/4

Y-2X = -1/4

2X - Y = 1/4........ (2)

Slove equations (1) and (2)

X+Y = 3/4.....(1)
2X-Y = 1/4.... (2)

This gives X=1/3 and Y=5/12

So add (1/4)+(1/3)+(5/12)+(1/2) = 18/12.

Hence (A).

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matteotchodi · Answer

doesn't usually the gmat present the correct answer choice as a simplified fraction??? i was able to attain 3/2 but with the rush i was not able to identify 18/12 as 3/2 since i was searching 3/2...... it made me guess an answer choice.... i hope to not make the same mistake on the exam

yalembagrad · Answer

The midpoint of 1/4 and 1/2 is 3/8 (1/4+1/2 divided by 2). Let the Two fractions be a and b, since they have to be the same distance from the midpoint, thus 1/4 ---a--3/8-----b---1/3.

3/8 - a = b+3/8
a+b = 3/8 + 3/8 = 6/8

sum of 4 fractions

6/8+1/4+1/2= 3/2

option A. (18/12 simplified is 3/2)

arbazfatmi1994 · Answer

The question clearly states that - The difference between any two successive fractions is the same.

What does that mean?

It simply means that these numbers are evenly spaced - hence, these numbers are in arithmetic progression

Sum of the terms of an AP = (first term+last term)/2∗(number of terms)

3/2 = 18/12 (Don't get nervous if the options are not in the same form)

I hope it helps!

Rance14 · Answer

If A.P doesn't come to mind (though it should)

I think you can simply solve this by

1/4, X, Y, 1/2 -> difference btw and two successive fractions is the same

Hence, 
1/2-Y = X-1/4
X+Y=1/2+1/4
X+Y=3/4

so we have the sum of the two unknown fractions and we just need the sum of all the 4 fractions

that would be -> 1/4+1/2+3/4 = 3/2

option A. -> 18/12 on simplification gives 3/2

saynchalk · Answer

Between 1/4 and 1/2 there are 2 digits, each increasing by a specific amount.

1/4 increases evenly 3 times to reach 1/2

(1/4) + 3x = (1/2)

x = 1/12

therefore the numbers are  1/4 , (1/4) + (1/12) =  1/3 , (1/3) + (1/12) =  5/12 , and  1/2

Sum = 18/12

MoeKo · Answer

Let two fractions be X & Y.
Then 1/4 , X , Y , 1/2.
X-1/4 = Y-X = 1/2 - Y

Just pick X-1/4 = 1/2 - Y => X+Y = 1/2 + 1/4
To answer the question, 1/4 + X + Y + 1/2 = 1/4 + 1/2 + 1/4 + 1/2 = 3/2. ( 18/12 )
Ans : A. 18/12.

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