Solving via options:

A. 64
Rounded off to nearest hundreds = 100
Rounded off to nearest tens = 60
% increase = \(40/60*100 = 200/3 = 66 \frac{2}{3}\) —> YES

IMO Option A

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Assume x='abc'= 100a+b+c

x when rounded to nearest hundred > x when rounded to nearest ten

x when rounded to nearest hundred= 100(a+1)

There are 2 possible cases

1. c<5

100(a+1)=5/3(100a+10b)
4a+b=6

when a=0, b=6.......(1)
60,61,62,63,64

when a=1, b=2........(2)
120, 121,122,123,124

2. c≥5
100(a+1)=5/3[100a+10(b+1)]

4a+b=5

if a=0, b=5.......(2)
55,56,57,58,59

if a=1, b=1.......(4)
115,116,117,118,119


We can solve it using options too

Hello guys , just to make sure, when the stem says "x is rounded to the nearest ten" it means that 133 will turn to 130 and 147 to 150 right?

I am not able to understand why 5/3 was introduced in the equation?

100(a+1)=5/3(100a+10b)


Is there any alternate approach?

Bunuel MathRevolution

Hi, I do not think you should try to do it in the algebraic way. The algebraic way is shown to give the students an idea that it can be done in any way. But during the test, the value testing way should be your approach for this particular problem. Please follow Dillesh's solution as that is the fastest way for this problem.

Since you asked the question, I will try to answer.
The 5/3 is simplification of this -
Let x be the integer.
\(66\frac{2}{3}\)% increase = \(x + 66\frac{2}{3}\)% of \(x\)
\(= x(1+\frac{200}{300})\)
\(= x(1+\frac{2}{3})\)
\(=x(\frac{5}{3})\)

I hope this helps.

GMAT Quant is the dirtiest part of GMAT.
It tasks your dynamism to a breaking point if you want to score high and you're not a physics teacher.
Sometimes it rewards your thinking with no solving sometimes it wants you to solve and not think.

This question wants you to think and not solve. Starred hard at the options from C (bcos it's ascending) till i figured out the ANSWER is less then 99 and can't be 67 bcos moving from 67 to hundred(30) isn't up to 50% of 70 let alone 66%.

% increase formula can be written as Final - Initial / Initial.
When the orginal number is 64. Rounding to nearest tens gives us 60 and rounding to hundreds gives us 100.
Calculating the percentage increase => (100-60)/60 = 40/60 = 2/3 = 66.66 which is the desired increase.
Therefore X is 64. Answer A