Company P had 15 percent more employees in December than it had in Jan

Question

Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January?

(A) 391
(B) 400
(C) 410
(D) 423
(E) 445

MacFauz · Accepted Answer

If 100 is increased by 50%, we get 150.
However if 150 is decreased by 50% we do not get 100 and instead we get 75.
The mistake you are doing is thinking that a 15% decrease from 460 is the same as a 15% increase from the right answer choice.
From the above illustration, we can see that equating as such is incorrect.

Bunuel · Answer

SOLUTION

Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January?

(A) 391
(B) 400
(C) 410
(D) 423
(E) 445

Given: January*1.15=December --> January*1.15=460 --> January=460/1.15=400.

Answer: B.

MacFauz · Answer

No. of employees in December = 1.15 * No. of employees in January
No. of employees in January = No. of employees in december / 1.15 = 460/1.15
 = 400

Answer is B.

EvaJager · Answer

Since  15%=\frac{15}{100}=\frac{3}{20} , it means that  460  represents  23/20  of the number of employees in January. Then,  1/20  of that number is  460/23 = 20. 
Therefore, the number of employees in January was  20\cdot20=400.

Answer B.

PS Bunuel, just another small typo...see above ( slution ). And I am mad at myself, why I didn't see it before...

hamm0 · Answer

If J = # of employees in January, and D = # of employees in December..
D = (J + 15% of J) = (1.15)*J  Plug in known values (D = 460) 
Therefore, (1.15)*J = 460  Solve for J 
J = 460/(1.15) =  400 B

thevenus · Answer

Let the no. of employees in Jan=x
Therefore the no.of employees in Dec will be =Total employees in Jan  PLUS  increased no of employees 
=>{x + (15% of x)} 
=> 1.15x

It is given that;
Total no.of employees in Dec = 460
so, 1.15x=460
solve for x , we will get x= 400

Answer: B

Vips0000 · Answer

First, we need to determine which one to use for base January or December, that is whether,
J= 1.15D 
Or 
0.85J = D

The question says . employees in December are 15%  more than in January . Therefore we are actually taking J as base and hence get number of employees in December as D=115% of J => 1.15J
Or 1.15J =460 => J =400 Ans (B)

thinktank · Answer

Okay, so now i ve fallen into this really Stupid trap here . I got  A) 391  . 15% of 460 is 69 . So i did 460-69 = 391 . I know i am wrong now and this is a dumb mistake . But what am i missing here ?? 
Kindly Help..
Thanks in Advance

selfishmofo · Answer

I solved the problem by estimation, I won't try to explain that, just for the fact that 410 could be a trap. So I'll try to explain on BackSolving the problem.

Jan = 10% + +5% = December
391 39.1 (Stop Here) 
400 40 20 460
410 41 (Stop here) 
423 42.3 (Stop here) 
445 44.5(Stop here)

Both Numbers must be divisible in order to arrive at 460

or Try to Solve this way:

J=15%+D
D=460

Solve for J = .15+460
Multiply by 100 
 
46000/115 = 400

bytatia · Answer

I'm having a problem. 
 I started solving this problem when December is x and January is 0.85x. IF x=460 shouldn't January be 460x0.85=391

Where am I going wrong?

Bunuel · Answer

x is 15% more than y means, that  x=1.15y , or that  y=\frac{x}{1.15}\approx{0.87x} .

y=0.85x  means that y is 15% less than x, which is not the same as x is 15% more than y.

JeffTargetTestPrep · Answer

There are actually two great methods to solving a problem such like this. The first is create a simple word translation. We are given that Company P had 15 percent more employees in December than it had in January and that it had 460 employees in December.

So we can say:

D = number of employees in December

J = number of employees in January

J x 1.15 = D

J x 1.15 = 460

J = 460/1.15

J = 46,000/115 = 400

Alternately, we could have looked at our answer choices and used divisibility and a little logic. We know that the answer choices represent the number of employees in January.

Thus we can say the following:

(Answer Choice)(1.15) = 460

Answer Choice x 115/100 = 460

Right away we can see that answer choice B stands out because it is divisible by 100. If we do the arithmetic, we see that:

400 x 115/100 = 400/100 x 115 = 4 x 115 = 460.

Thus B is the correct answer.

BrentGMATPrepNow · Answer

Let J = # of employees in Jan So, 1.15J = # of employees in Dec This means that 1.15J = 460 So, J = 460/1.15 = 400 Answer: B ASIDE: Many people will conclude that, if the December population is 15% greater than the January population, then it must be the case that the January population is 15% less than the December population. If you have this common misconception then you would have (incorrectly) answered A To better understand the issue, examine the following example: A = 100 B = 150 Notice that B is 50% greater than A. HOWEVER, A is not 50% less than B. In fact, A is 33 1/3% less than B. For more on this misconception, read the following article: https://www.gmatprepnow.com/articles/co ... 93-part-ii Cheers, Brent

Abhishek009 · Answer

Plain and simple -

\frac{460}{115}*100 = 400 , Answer must be (B)

ag153 · Answer

how can we calculate 460/1.15 quickly?

Bunuel · Answer

\frac{460}{1.15} = \frac{460*100}{115}=4*100=400

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=nNvH0AdGPNU

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=FHhx0GCpRZk

ArnauG · Answer

According to the given information, the number of employees in December is 15% more than in January. Mathematically, this can be represented as:

X + 0.15X = 460

Simplifying the equation:

1.15X = 460

Dividing both sides by 1.15:

X = 460 / 1.15 ≈ 400

Therefore, Company P had approximately 400 employees in January.

The answer is option (B) 400.

Company P had 15 percent more employees in December than it had in Jan

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Company P had 15 percent more employees in December than it had in Jan

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