Lesson: Word Problems with Fractions

Comment on Word Problems with Fractions

I solved the candy question slightly different, but still got $4 as the answer. 1/3+5/9=24/27 (spent on movie and hat). So the remainder she spent on candy is 3/27. Then i multiplied 3/27*36 and got $4. Thanks!
-Yvonne
gmat-admin's picture

Perfectly valid approach!

Brent,

I have a doubt on the question 189 from the O.G. (2017 edition). Could you explain me in a different answer from the OG Answer Explanations, please?

Thank you in advance.
gmat-admin's picture

No problem.

Please see my solution here: http://www.beatthegmat.com/problems-151-and-226-in-the-og-13-t283699.html

Cheers,
Brent

Thank you very much!

Cheers,
Pedro
gmat-admin's picture

Aha! I had a hunch your name wasn't Phlemos!

Yulia's picture

Hi Brent,

The question asks what fraction of all the boxes loaded by the two crews did the day crew load?
I thought that all boxes dived by day crew workers.

Could you please tell me why you take number of day crew divided by total number of boxes? While I was typing it, I think I got it but would love to hear your excellent explanation to back up my understanding.

Thank you.
gmat-admin's picture

Question: What fraction of all the boxes loaded by the two crews did the day crew load?
So, we want: (# boxes loaded by DAY CREW)/(TOTAL # of boxes loaded by both crews)

The DAY crew loaded 20 boxes
The NIGHT crew loaded 12 boxes
So, the crews COMBINED loaded 32 boxes.

The question becomes "What fraction of 32 boxes is 20 boxes?"
The desired fraction = 20/32 = 5/8

Does that help?

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

A. 5/6
B. 1/5
C. 1/6
D. 1/7
E. 1/24

Hi Brent, I am failing to get an answer to this question:

30=U+N

and U=1/5*N making N=6U

therefore my answer = 1/6 but apparently, the answer is 1/7. Could you please help.
gmat-admin's picture

Hi Brent,

Don't we interpret this statement " If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport" as Miami = 1/2(Kennedy) + 4*(Logan)? In that case we cannot take 1/4 of 6 million.

Let me know what I am missing out on.

Problem Link: https://gmatclub.com/forum/in-1979-approximately-1-3-of-the-37-3-million-airline-passengers-trave-208035.html

Warm Regards,
Pritish
gmat-admin's picture

Great question, Pritish.

Question link: https://gmatclub.com/forum/in-1979-approximately-1-3-of-the-37-3-million...

Consider this analogous sentence: Joe is twice as old as Karen and three times as old as Mark.
The "AND" here does not mean addition.
We are comparing Joe's age with Karen's age, AND we are Joe's age with Mark's age.
So, we can read the information as: Joe is twice as old as Karen, and JOE IS three times as old as Mark.

The same applies to the question: "If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport,..."

We can read that information as: "The number of passengers that used Miami Airport was 1/2 the number that used Kennedy Airport, and THE NUMBER OF PASSENGERS THAT USED MIAMI AIRPORT WAS 4 times the number that used Logan Airport,..."

Does that help?

Cheers,
Brent

Hi Brent,

Thanks for the explanation. The analogous sentence made it crystal clear to me.

Warm Regards,
Pritish

Hi Brent,

https://gmatclub.com/forum/the-price-of-gasoline-at-a-service-station-increased-from-1-65-per-ga-268776.html

Could you please suggest some easy way to handle such calcs.

Thankyou !
gmat-admin's picture

The calculations required are a little tricky.
Here's my solution: https://gmatclub.com/forum/the-price-of-gasoline-at-a-service-station-in...

Cheers,
Brent

Yulia's picture

Hi Brent,
Could you please help me to understand something?

Question 1: https://gmatclub.com/forum/a-satellite-is-composed-of-30-modular-units-each-of-which-119751.html

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

A. 5/6
B. 1/5
C. 1/6
D. 1/7
E. 1/24

Why do you assume that total of upgraded sensors on the entire satellite is 5 and then you multiply (1/5)(5) = 1?
gmat-admin's picture

Question link: https://gmatclub.com/forum/a-satellite-is-composed-of-30-modular-units-e...

The question asks, "What FRACTION of the sensors on the satellite have been upgraded?"
Since we're not asked to find specific values, we can start with a "nice" value for the number of upgraded sensors.

Given: the number of non-upgraded sensors on one modular unit is 1/5 the TOTAL number of upgraded sensors on the entire satellite
If we let 5 = the TOTAL number of upgraded sensors on the entire satellite....,
...then there will be 1 non-upgraded sensor on one modular unit (since 1/5 of 5 = 1)
With 30 modular units, the TOTAL number of non-upgraded sensors = (30)(1) = 30.
The TOTAL number of sensors = (number of non-upgrades) + (number of upgraded)
= 30 + 5 = 35
So, the fraction of the upgraded sensors on the satellite = 5/35 = 1/7
------------------------
You'll see that, if we choose a different starting value, we still get the same answer:
If we let 15 = the TOTAL number of upgraded sensors on the entire satellite....,
...then there will be 3 non-upgraded sensor on one modular unit (since 1/5 of 15 = 3)
With 30 modular units, the TOTAL number of non-upgraded sensors = (30)(3) = 90.
The TOTAL number of sensors = (number of non-upgrades) + (number of upgraded)
= 90 + 15 = 105
So, the fraction of the upgraded sensors on the satellite = 15/105 = 1/7

And so on...
Does that help?

I should also note that, later in the forum thread, I provide some illustrations to show exactly what's happening: https://gmatclub.com/forum/a-satellite-is-composed-of-30-modular-units-e...

Cheers,
Brent

Yulia's picture

Thank you Brent.
It is a great explanation.
Yulia's picture

Hi Brent,
Could you please explain me something?

Question 1: https://gmatclub.com/forum/at-a-supermarket-john-spent-1-2-of-his-money-on-fresh-fruit-136879.html#p1110612

At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

The questions is easy and did solve it by use fractions: 1/2x + 1/3x+ 1/10x + 6 = x > x will be equal to 90

However, when I converted fractions into decimal 0.5x + 0.33x + 0.1x + 6 = x my answer is x= 85.7… Why the answer is different with decimals?
gmat-admin's picture

Question link: https://gmatclub.com/forum/at-a-supermarket-john-spent-1-2-of-his-money-...
The problem is that your decimal approximation of 1/3 is slightly changing the equation.

Keep in mind that 1/3 = 0.3333333333333...(forever)
So, rounding 0.3333333333333... to 0.33 will change the solution.

Notice what happens when we get a little more precise and say that 1/3 = 0.333
We get: 0.5x + 0.333x + 0.1x + 6 = x
The solution to this (slightly more precise) equation is x = 89.55
So just by using 0.333 instead of 0.33, our solution already becomes closer to 90.

Does that help?

Cheers,
Brent

Hi Brent, could you please help on this one ? thank you

Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month ?
A.1/2, B.1/3, C.1/4, D. 1/5, E. 1/6

Dear Brent, could please help on this one ? thanks

in a field day at school, each child who competed in n events and scored a total of p points was given an overall score of p/n+n. Andrew competed in 1 event and scored 9 points. Jason competed in 3 events and scored 5,6 and 7 points, respectively. What was the ratio of Andrew's overall score to Jason's overall score ?

A. 10/23
B.7/10
C. 4/5
D. 10/9
E.12/7
gmat-admin's picture

for this question https://gmatclub.com/forum/if-3-4-of-the-number-of-women-working-at-company-x-is-equal-to-2-3-of-229184.html

I just dont like fraction, how can man be a fraction? so managed the function a bit, w = 8/9 m, let man equal to 9 so women has 8, then (8+9)/17 and get the answer
gmat-admin's picture

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