Solution

Given:

• The price of gasoline at a service station increased from $1.65 per gallon to $1.82 per gallon
• Sally paid $26.40 for last gasoline last week

To find:

• What will be the equivalent price Sally have to pay this week, due to price increase

Approach and Working:

• Increase in price per gallon = \(($1.82 - $1.65) = $0.17\)

Therefore, we can say:

• In $1.65 the cost increases $0.17
Or, in $26.40 the cost increases \(\frac{0.17}{1.65} * 26.40 = $2.72\)

Hence, the correct answer is option D.

Answer: D
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The hardest part of the problem is meeting the time constraint.

The in the approach that I used I tried to avoid dividing and multiplying large numbers, as this is one of the things I struggle with.

First find the size of the tank by 26.40/1.65. For this I took both numbers to their prime factorization to get (2^4 x3x5x11)/(3x5x11).
From there everything cancels pretty nicely to leave 2^4 which yields 16; which is the size of the tank.

Then take the size of the tank by the price increase per gallon to get the total cost increase, which is:

16x.17 = 2.72

Answer D

Answer is D.

Gasoline = 26.40/1.65 = 16 galloons
Price difference = (1.82-1.65) = $0.17 per gallon

Price difference for 16 gallons = (0.17*16) = 2.72

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

Since the price of gasoline goes up from $1.65 to $1.82 from last week to now,
the amount that Sally spends on gasoline also goes up by a similar margin.

As, 1.65 -> 26.40 | 1.82 -> x(amount Sally spent on gasoline)

\(1.65 * x = 26.40 * 1.82\) ->\(x = 26.40 * \frac{1.82}{1.65} = $29.12\)

Therefore, Sally spends \($29.12 - $26.40 = $2.72\)(Option D) more on gasoline this week.
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Since $26.40 bought 26.40/1.65 = 16 gallons last week, and this week she has to pay 1.82 - 1.65 = $0.17 more per gallon, she has to pay 16 x 0.17 = $2.72 more this week for the same amount of gasoline.

Answer: D
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Gasoline = 26.40/1.65 = 16 galloons
16*1.82 = 29.12
29.12-26.40=2.72

Hello egmat Pyal the problem here is the process i mentioned to solve this question is more natural to me but the problem is it takes lot of calculation i am unable to map out the clean and easy way in any GMAT question as you have done. if you could help me find how to do fewer calculations like your method. i would be really obliged.
Thanks

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.

VIDEO ON MENTALLY DIVIDING BY 5

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Let,
Number of gallon = x
So,
1.65x=26.40

=> x = 26.40/1.65=16 gallons


More price per gallon = (1.82-1.65)=0.17

Thus,

More price should be given for total gallons = 16*0.17= 2.72


Answer is D

Posted from my mobile device

I knew conceptually how to approach this question but dividing 26.40/1.65 was the tricky bit for me and affecting my timing. As bcal95 explained, try using prime factorization when having to divide big numbers like this. So my approach is:

26.40/1.65

Remove the decimal points

= 2640/165

Do prime factorization on top and bottom (numerator and denominator)

2640 = 2*2*3*4*5*11
165 = 3*5*11

Therefore (2*2*3*4*5*11)/(3*5*11)

Cancel relevant factors and you get 2*2*4 = 16

Then follow through with the rest of the calculation:
1.82 * 16 = 29.12

29.12-26.40 = 2.72

Answer D

Hi!

I prefer mental math in such questions. We know there is a 17 point increase on 165. it'd be a 10% rise had it been on 170. a drop of 5 in the denominator would skew result by just over 0.3 points. so for final payment we know its definitely more than 2.64 ie more than 10%. 2.90 is almost 11% i figured hence it should be 2.72

While this question is straightforward, it's tricky in the sense that there's some very difficult division.

Identify the question: How much more will Sally pay this week at the station for the same amount of gasoline?

If Sally paid $26.4 for gas last week, and gas was $1.65 per gallon;
1.65x = 26.40
x = \(\frac{2640}{165}\)
To deal with this, you can either directly divide 2640/165, or put each number in prime factorization form
\(\frac{(2^4 * 3 * 5 * 11)}{(3*11*5)}\) = 16

So sally bought 16 gallons of gas

The price of gas is $0.17 more than last week, so 0.17*16 = $2.72
Quick Tip: 6*7 has its last digit is 2, so only answer D has 2. Saves time rather than calculating everything out

The Answer is D!

Answer: Option D

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2640/165 = 16

165*10 = 1650, which leaves 2640-1650 = 990 left.

165*2 = 330, taken three times is 990.


16*0,17 --> 16*17 = 160 + 16*7 (=112) = 272.

GMAT Problem Solving - A disguised percentage question? (Silent Video)


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Here's my approach:
One gallon of gasoline costs $1.65. To make this number a little manageable, I found the price of 2 gallons (which is 2*1.65 = $3.30). It costed Sally $26.40 to fill up tank last week. So, I multiplied $3.3 by 8 (gallons) and got $26.40. I came to 8 gallons by using an educated guess. So, last week Sally filled 16 gallons of gasoline.
The price increase of gasoline from last to this week was $0.17 ($1.82-$1.65). So, I multiplied 16 gallons with $0.17 and came to $2.72.

Difference between unit price 1.82$-1.65$=0.17$;
total gallons (that she filled this week or last week since both are same) = 26.4/1.65

two approaches,
1st one (time to solve approx. to 1.5mins)
if you could solve this quickly 26.4/1.65=16, then diff amount will be
0.17$*16=
(16*10+16*7)/100=(160+112)/100=272/100=[b]2.72 Ans is D

2nd one (time to solve approx. to 2mins)
26.4*0.17/1.65 remove decimals 264*17/(165*10), next approximation = 264*17/(170*10) =264/100=2.64, the approximation was to increase the denominator by 5, so the result should be slightly higher than 2.64, which is 2.72 Ans - D

Gasoline = 26.40/1.65 = 16 galloons
Price difference = (1.82-1.65) = $0.17 per gallon

Price difference for 16 gallons = (0.17*16) = 2.72

D

Posted from my mobile device
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Try to practice divisions with decimals before the real test of GMAT.
Generally, the author prepares the questions in a way that the arithmetic calculations are easy, but during the test you can be nervous and make unnecessary mistakes.

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