If the crime rate in a certain region dropped by 28% last year to a ra

Question

If the crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens, what was the approximate rate before the drop?

A. 500 crimes per 128,000 citizens

B. 640 crimes per 128,000 citizens

C. 695 crimes per 128,000 citizens

D. 640 crimes per 100,000 citizens

E. 695 crimes per 100,000 citizens

IanStewart · Accepted Answer

If something drops by 28%, it becomes 72% of what it used to be. So if the crimes per 100,000 people last year was x, and then that figure dropped by 28%, it became 0.72x. We're told it actually became 500, so

0.72x = 500
x = 500*100/72

I'd probably estimate that by reducing the denominator slightly, to 70, but then it's helpful to reduce the numerator slightly also, so I'd reduce the 500 to 490 to get a clean division, and x is roughly 490*100/70 = 700

and the only answer close to 700 per 100,000 is answer E.

If instead you step back before doing any calculation, and realize "per 100,000, if we start with 700 crimes, and that drops by 30%, we get roughly 500 crimes" then only one answer is even plausible -- the others are clearly too small. It's a bit confusing though to think about the rates when they're rephrased "per 128,000", so it might be best just to set up the calculation and estimate from there.

Karan911 · Answer

Hi,

Initially, i got this wrong and selected D, but I found a nice method this :

0.72x = 500

72/100 = 18/25

So, 18/25 x = 500

so x = (25 *250)/9

25 square is 625, and we know that 1/9 is 0.1111

So, I wrote that as 625 (0.1 + 0.01) = 625 + 62.5 = slightly higher than 685 , so E

Rocky25 · Answer

Bunuel , Could you solve this question? How do I know the answer wont be per 128,000?

Ertucinar · Answer

695 per 100,000 equal to 889 per 128,000
It's not a option

shubhim20 · Answer

please help solve this question  Bunuel

Bunuel · Answer

Here is a solution I'd advice to study: https://gmatclub.com/forum/if-the-crime ... l#p2814884

DonBosco7 · Answer

I got this right by working out the answers, here's how -

Remember the question asks for an approximate answer, so there might or might not be a perfect answer but a close one.

Given that - crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens.

From this we know that the crime rate per 100,000 citizens initially would be definitely higher that the drop of 28%.

now look at the answer choices which one hints at that drop of 28% i.e reduced to 72% of original

Option E gives you 695 crimes per 100,000

if we work this out, so initially it was 695 and it dropped by 28%

so 72%*695 = 500.4 which is very close to 500. Hence our answer

Rohanx9 · Answer

Quickest way I think is to eliminate the options. Took 45 seconds.

A. 500 crimes per 128,000 citizens. Cant be - this is a better crime rate than the one given.
B. Both numerator and demoninator increased by 28%. This is the same rate as the one given. 
C. Numerator jumped by >28% (about 200/550 =40%), denominator jumped by 28%. Clearly the rate has changed by <28% as 1.4/1.28 does not equal 1.28.
D. Numerator jumps by 28%, denominator stays the same. This is a we're seeking a decrease of 28% (i.e. 72% of something), which wont be the same as increasing by 28%. 
E. This is the only answer that fits the criteria. Do a rough check 695*0.72 roughly equals 700*0.7 = 490. This is our answer.

If the crime rate in a certain region dropped by 28% last year to a ra

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If the crime rate in a certain region dropped by 28% last year to a ra

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615 to 715 in 15 Days (Ria's Strategies)

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