If (x+500)/510+(x+510)/515+(x+520)/520+(x+530)/525+(x+540)/530=10

Question

If  \frac{x+500}{510}+\frac{x+510}{515} + \frac{x+520}{520} + \frac{x+530}{525}+ \frac{x+540}{530}=10 , what is the value of x ?

A. 515
B. 520
C. 525
D. 530
E. 535

I know that chances of getting such question on an actual test is slim to none. I also know that it's not that hard to solve the question using back-solving. But it's interesting to see if you can find a neat algebraic trick which allows to crack it in less than a minute (if you know/get the trick that is).

gmatophobia · Accepted Answer

Used a combination of algebra and observation to solve this question. Look forward to see better methods.

The working is attached below

IMO B

Regor60 · Answer

Using perhaps faulty intuition, we can see that the differences between the numbers in the numerator and denominator range from -10 to +10, with the middle term being 0.

This suggests these terms offset.

Likewise, the average of the denominators is 520.

Coupled with the 10 and 5 Xs, a multiple of 520 is likely on the right, which is likely to be X.

Another, more simple observation, is that the average of the terms is 2, and since the middle term appears to equal the average (intuition), this suggests

(X+520)/520 = 2

Which means X=520

Posted from my mobile device

rachanarc · Answer

1> The given equation -> Sum of 5 numbers is 10
2> From the answer choices we understand that x >= 315 and hence these numbers that add up to 10 cannot be negative values

Possible value of these 5 numbers that add up to 10 would be : \(2+2+2+2+2=10 \)

\(\frac{x+500}{510}=2\)

\(x+500=1020\)
\(x=520\)

Similarly,
\(\frac{x+510}{515}=2\)

\(x+510=1030\)
\(x=520\)

Same applies for other numbers as well, hence x=520

Here I have not considered decimals numbers that add up to 10, as the first instinct I had was to try with whole number

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If (x+500)/510+(x+510)/515+(x+520)/520+(x+530)/525+(x+540)/530=10

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If (x+500)/510+(x+510)/515+(x+520)/520+(x+530)/525+(x+540)/530=10

Prep Toolkit

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My Rewards