What is the smallest positive integer that's less than 1/3% greater..

Question

What is the smallest positive integer that's less than 1/3% greater than the largest integer smaller than the aforementioned integer?

(A) 299
(B) 300
(C) 301
(D) 302
(E) 303

HarshavardhanR · Answer

- Let the "aforementioned integer" be x.
- Largest integer smaller than the "aforementioned integer" = x - 1

- Given Condition:

\(\frac{x - (x-1)}{(x-1)}\) x 100% < 1/3

Simplifying this.
1 < (1/300)(x-1)
300 < x - 1
which gives
x > 301.
Smallest positive integer x that is >301 is 302. Choice D.

Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com

ajay0520 · Answer

i think you're confused with 1/3% = 0.33%, but i think, 1/3% equals 33.33%. 
and if the integer is less than 33.33% greater than previous then all options are incorrect. please let me know if i am worngy seeing this question.

HarshavardhanR · Answer

I sense some confusion regarding percentages here. Let me try to help.

- 10% of something (say P) is (10/100) x P
- 1/3 is 0.33..
- So, similar to the above example, 1/3% of P would be 0.33% of P. So, 1/3% of P is the same as 0.33% of P. NOT 33.33% of P.

Some useful points:

1/3 of X = 33.33% of X

Because   1/3 of X converted to % is  \frac{(1/3)X}{X}  x 100 = 100/3 = 33.33%

1/3 % of X is different.

1/3% of X is 0.0033X

Because   1/3 % of X =  \frac{(1/3)}{100}  x X = (1/300)X = 0.0033X (in other words (0.33/100)X = 0.0033X).

What is given in the question:   
if x is that "smallest positive integer" we are trying to find,

x is less than  1/3%  greater than x - 1.

\frac{(x - (x-1)}{(x-1)  x 100% < 1/3 (note -> 1/3 here refers to %).

A parallel example. Say x = 11, x - 1 = 10.

(11-10)/10 X 100% = 10%.

Just like the RHS here is 10%, the RHS in the above relation ("1/3") refers to (1/3)%.

Hope this helps. 
___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com

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