Gmat_mission wrote: ↑Sun Apr 11, 2021 11:27 am
The price of gasoline at a service station increased from $1.65 per gallon last week to $1.82 per gallon this week. Sally paid $26.40 for gasoline last week at the station. How much more will Sally pay this week at the station for the same amount of gasoline?
A. $1.70
B. $2.55
C. $2.64
D. $2.72
E. $2.90
Answer:
D
Source: Official Guide
Since the
amount paid is proportional to the
price per gallon, we can use
equivalent ratios
Let
x = how much Sally will pay THIS WEEK
We get:
26.40/
1.65 =
x/
1.82
Cross multiply to get: 1.65x = (26.40)(1.82)
Divide both sides by 1.65 to get: x = (26.40)(1.82)/1.65
So, the amount Sally pays this week = (26.40)(1.82)/1.65
ASIDE: This expression is a bit of a mess to calculate (without a calculator!!)
Notice that 1.82/1.65 probably won't simplify nicely, but maybe 26.40/1.65 will simplify.
At this point, we have two options.
We can use long division to calculate 26.40/1.65, or we can try to simplify the fraction.
Let's simplify the fraction
Take: 26.40/1.65
Multiply top and bottom by 100 to get: 2640/165
[much easier to work with integers!]
Divide top and bottom by 5 to get: 528/33
[below I have a video that shows a quick way to mentally divide numbers by 5]
Divide top and bottom by 3 to get: 176/11
Divide top and bottom by 11 to get: 16
Since 26.40/1.65 = 16, we know that (26.40)(1.82)/1.65 = (1.82)(26.40/1.65) = (1.82)(16)
=
$29.12
How much more will Sally pay this week at the station for the same amount of gasoline?
Answer =
$29.12 - $26.40
= $2.72
Answer: D
It's not pretty, but it MIGHT be a little faster than long division.
Brent Hanneson - Creator of GMATPrepNow.com
