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Yesterday, the ratio of males to females working at Gigacorp

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Yesterday, the ratio of males to females working at Gigacorp [#permalink]

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Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

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[Reveal] Spoiler: OA

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Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]

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The answer should be a multiple of 2 as the ratio of male to female originally was 2:3 . Now eliminate ans choice 39. Remaining 16,24,40 and 42.

A. If we choose 16 as 2x , then 3x will be 24 and the total will be (16+24) 40. Adding 81 employees gives total of 121 employees. we know that the new ratio is 5:6. There fore 5x + 6x = 11x. This tells us,the answer has to be divided by 11. Clearly 121 is divisible by 11.
Perform same logic for other options 24, 40 and 42. The end result is not divisible by 11. So going for Option A 16.

There must by easy way to solve this. But this came in handy as we have the options listed out.

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Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]

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GMATPrepNow wrote:
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions


Hi

Nice question.

\((1) 2x + 3x = N\)

\(5x = N\)

\((2) 6y + 5y = N + 81\)

\(11y = N + 81\)

\((2) - (1)\)
\(11y - 5x = 81\)

\(y_0 = 11, x_0 = 8\)

\(2x = 2*8 = 16\)

Answer A

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Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]

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GMATPrepNow wrote:
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42


Yesterday, the ratio of males to females working at Gigacorp was 2:3
There are many scenarios that meet this condition:
- Gigacorp employs 2 males and 3 females (for a TOTAL of 5 employees)
- Gigacorp employs 4 males and 6 females (for a TOTAL of 10 employees)
- Gigacorp employs 6 males and 9 females (for a TOTAL of 15 employees)
- Gigacorp employs 8 males and 23 females (for a TOTAL of 20 employees)
.
.
.
etc.

Notice that the TOTAL number of employees yesterday is a multiple of 5. This is because our ratio of 2:5 tells us that, for every 5 employees, 2 are males and 3 are females. Since the number of males and females must be POSITIVE INTEGERS, the TOTAL number of employees yesterday must be a multiple of 5

Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5
By the same logic, the NEW TOTAL number of employees must be a multiple of 11, since this new information tells us that, for every 11 employees, 6 are males and 5 are females.

So, once we add 81 to yesterday's TOTAL, the NEW TOTAL must be a multiple of 11.

Let's see what happens if there was a TOTAL of 5 employees yesterday.
NEW TOTAL = 5 + 81 = 86.
Since 86 is NOT a multiple of 11, it cannot be the case that there was a TOTAL of 5 employees yesterday.

Let's see what happens if there was a TOTAL of 10 employees yesterday.
NEW TOTAL = 10 + 81 = 91.
Since 91 is NOT a multiple of 11, it cannot be the case that there was a TOTAL of 10 employees yesterday.

Let's see what happens if there was a TOTAL of 15 employees yesterday.
NEW TOTAL = 15 + 81 = 96.
Since 96 is NOT a multiple of 11, it cannot be the case that there was a TOTAL of 15 employees yesterday.

Notice that each NEW TOTAL follows the pattern: 86, 91, 96, 101, etc (the units digit of each number is either 1 or 6.
So, let's continue the pattern until we get to the first multiple of 11
86, 91, 96, 101, 106, 111, 116, 121

BINGO!
When the NEW TOTAL = 121, then the OLD TOTAL = 121 - 81 = 40
So, 40 is the smallest possible number of employees yesterday.
Since the ratio of males to females working at Gigacorp was 2:3 yesterday, we can conclude that there were 16 males and 24 females.

Answer: A

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Yesterday, the ratio of males to females working at Gigacorp [#permalink]

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New post 17 Sep 2017, 22:25
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GMATPrepNow wrote:
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions


Logical Approach for this NICE question -

Original Ratio of Male to Female = 2x:3x
Total Original Population = 5x

After adding 81 employee New Ratio of Male to Female = 6y:5y
Total New Population = 11y

We May Write -
5x + 81 = 11y
Above equation conveys that LHS must be DIVISIBLE by 11
5x + 4+ 77 = 11y

After Reducing
5x + 4 = 11y

Value of 2x is given in the options. Just Plug the value of x in above equation to get the answer.

Only option A would FIT.

Hence Answer A
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Yesterday, the ratio of males to females working at Gigacorp   [#permalink] 17 Sep 2017, 22:25
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Yesterday, the ratio of males to females working at Gigacorp

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