Ratio and proportion- Plug-in values

Question

Hi All, Would anyone please help with how to decide/narrow in on what values to plug-in to solve for the ratio..? Thanks, Mallika

Rich.C@EMPOWERgmat.com · Answer

Hi mallika,

This question has a number of subtle 'hints' built into it (and the answer choices) that would help you to TEST VALUES. Most of the TESTs that you could do will involve fractions though (which is part of what makes this question harder than average). Here's how I approached it:

We're told Tom gets paid $X per hour for each of the first N hours worked.
Then Tom gets paid $1.375X per hour for each additional hour thereafter.

The first "hint" is that 0.375 = 3/8, so Tom gets paid (1 3/8)X for each overtime hour. This means that making X a multiple of 8 should help to simplify the math a bit.

We're then asked for the ratio of OVERTIME hours to REGULAR hours needed to DOUBLE his daily pay.

IF....
X = 8
N = 2
Tom earns $8(2 hours) = $16 of normal pay

(1 3/8)(8) = $11/hour for each overtime hour.

To DOUBLE his pay, the overtime pay must ALSO equal $16, so...

$11(Z overtime hours) = $16
Z = 16/11

So the ratio of overtime hours to regular hours is...

16/11: 2

This ratio needs to be "cleaned up" though, so let's multiply both sides by 11...

16: 22

And then reduce....

8:11

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

mallika hunsur · Answer

Rich.C@EMPOWERgmat.com wrote:Hi mallika, This question has a number of subtle 'hints' built into it (and the answer choices) that would help you to TEST VALUES. Most of the TESTs that you could do will involve fractions though (which is part of what makes this question harder than average). Here's how I approached it: We're told Tom gets paid $X per hour for each of the first N hours worked. Then Tom gets paid $1.375X per hour for each additional hour thereafter. The first "hint" is that 0.375 = 3/8, so Tom gets paid (1 3/8)X for each overtime hour. This means that making X a multiple of 8 should help to simplify the math a bit. We're then asked for the ratio of OVERTIME hours to REGULAR hours needed to DOUBLE his daily pay. IF.... X = 8 N = 2 Tom earns $8(2 hours) = $16 of normal pay (1 3/8)(8) = $11/hour for each overtime hour. To DOUBLE his pay, the overtime pay must ALSO equal $16, so... $11(Z overtime hours) = $16 Z = 16/11 So the ratio of overtime hours to regular hours is... 16/11: 2 This ratio needs to be "cleaned up" though, so let's multiply both sides by 11... 16: 22 And then reduce.... 8:11 Final Answer: E GMAT assassins aren't born, they're made, Rich Many thanks Rich! I see that the hint is 0.375.

Tmoni26 · Answer

Now that's a solid question,

Rick, I prefer your approach to mine

I did not want awkward fractions, so I had to play around to get something that would can be divided by 11 easily

So I picked as 11 hours as "normal", which meant he worked 11 hour days(probably a MBB consultant) and it fit in well with the second calculation

Although, I did not have to clean up the ratio, I "wasted" time in picking a number that would divide easily

Brent@GMATPrepNow · Answer

Tmoni26 wrote: I did not want awkward fractions, so I had to play around to get something that would can be divided by 11 easily Hi Tmoni26, In my opinion, the GMAT's test-makers typically reward test-takers who work with fractions (rather than converting all fractions to decimals). Cheers, Brent

Brent@GMATPrepNow · Answer

REGULAR hours: Tom earns $n/hour
OVERTIME hours: Tom earns $(1.375n)/hour

Since we've memorized some of the base conversions, we recognize that 0.375 = 3/8, so 1.375 = 1 3/8 = 11/8. So, we can rewrite the overtime information as....
OVERTIME hours: Tom earns $(11n/8)/hour

Let R = number of REGULAR hours worked
Let 0 = number of OVERTIME hours worked

IMPORTANT: To double his daily income, Tom's OVERTIME income must EQUAL his REGULAR income.
Income = (hourly rate)(hours worked)
So, we can write: (11n/8)(O) = (n)(R)

The question asks us to find the ratio of overtime hours to regular hours.
In other words, we must find the value of O : R or O/R

Take (11n/8)(O) = (n)(R) and rewrite as follows:
O/R = (n)/(11n/8)
Simplify to get: O/R = 8/11 [aka 8:11]

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Rich.C@EMPOWERgmat.com · Answer

Hi Tmoni26,

On tougher questions, there's always a balance between finding an effective approach and finding work that is "easy." Remember that the clock is always ticking, so you have to look for an approach that YOU can handle (and hopefully isn't too difficult or long-winded). If you're comfortable doing Arithmetic with fractions and decimals, then sometimes you just have to say "I know this number I've chosen is a little "ugly", but I can work with it."

To Brent's point, there WILL be questions on Test Day that are easier to deal with if you convert the data into fractions. Not all questions will fit this idea though, so it's important to note the data that you're given, the exact question that is asked and the 'format' of the answer choices - those elements should help you to make the choice of whether to use fractions or decimals.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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