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Company P had 15 percent more employees in December than it

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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

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Re: Company P had 15 percent more employees in December than it [#permalink]

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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.
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Re: Company P had 15 percent more employees in December than it [#permalink]

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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.
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Re: Company P had 15 percent more employees in December than it [#permalink]

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Number of employees in Jan = 460 /1.15 = 400
Answer B
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Re: Company P had 15 percent more employees in December than it [#permalink]

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Bunuel wrote:
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


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...
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Last edited by EvaJager on 08 Oct 2012, 06:11, edited 2 times in total.

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Re: Company P had 15 percent more employees in December than it [#permalink]

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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
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Re: Company P had 15 percent more employees in December than it [#permalink]

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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
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Re: Company P had 15 percent more employees in December than it [#permalink]

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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)
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Re: Company P had 15 percent more employees in December than it [#permalink]

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please. experts can give an opinion about the level (real) of this question ?? of course I know that is not important the level but to solve it 300 or 700 no matter what

back to question.

J --------------- D

X 1.15

1.15 x = 460 X = 400 B in 30 seconds ( thanks to sleepless nights)

or 1.15 is what % of 460 ----> translate 1.15 = x/100 * 460 -----> = 4 only B fits the bill

C should not possible following this process of reasoning
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New post 16 Feb 2013, 11:19
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..
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thinktank wrote:
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


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.
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Re: Company P had 15 percent more employees in December than it [#permalink]

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thinktank wrote:
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



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

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Re: Company P had 15 percent more employees in December than it [#permalink]

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just use the answer choices.

400*15/100=60 === 60+400=460. Ans B.
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Re: Company P had 15 percent more employees in December than it [#permalink]

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New post 25 May 2014, 13:05
Bunuel wrote:
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

Practice Questions
Question: 57
Page: 159
Difficulty: 550


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?

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Re: Company P had 15 percent more employees in December than it [#permalink]

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bytatia wrote:
Bunuel wrote:
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


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?


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.
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Re: Company P had 15 percent more employees in December than it [#permalink]

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Bunuel wrote:
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


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.
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Re: Company P had 15 percent more employees in December than it [#permalink]

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New post 16 Aug 2017, 09:09
15% more in December = 115% (taking employees in January = 100%)

SO,
115% = 460
100% = (?) -> 460 x 100 / 115
= 400 (b)

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Company P had 15 percent more employees in December than it [#permalink]

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New post 14 Sep 2017, 23:16
115/100 = 460
then no of employee = 460*100/115
divide by 5
460*20/23
20*20 = 400
answer B
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