How to find the whole from the part - GRE Quantitative Reasoning

divide: 36/145 = 0.248; multiply by 100 to get percent

24.8%

Let's first pick numbers. If y = 25, x = 100. It's tempting to pick 25% as the answer, but x is greater than y, so the percentage must be greater than 100%. x is four times y, or 400% of y.

Belinda walks faster than Max, so she should walk over a mile in the same time that Max walks 1 mile. We can eliminate the answer choices that aren't over a mile. It takes Max 3 minutes longer to walk a mile, so Belinda will walk for 3 more minutes after she finishes her first mile. If she walks 1 mile in 12 minutes, she walks 1/12 miles in 1 minute, or 3/12 = 1/4 mile in 3 minutes. So she walks 1 1/4 miles, or 5/4 miles.

This problem requires you to work backwards from stop 5 to the passengers present at stop 1. If 2 person gets out at stop 5, that means there were 3 people on board at stop 5. This means there were 9 people present at stop 4 (9 total, 2/3 (6) got off, leaving the 3 for stop 5), 27 people present at stop 3 (27 total, 2/3 (18) got off, leaving 9 for stop 4), 81 people present at stop 2 and 243 passengers present at stop 1. That is, the number of passengers on board the train at any stop follows a logarithmic reduction along powers of three, from 35 at stop 1 to 31 at stop 5.

21.21/ 4.25 = 5 pounds paid for. Since a pound is given for every 2 pounds sold, that is 5/2 = 2.5 so an extra 2 pounds is given to Lauren, totaling 7 pounds.

First solve for z by multiplying 2/7 by the reciprocal of 4/13.

Then multiply this number by 8/11 to find the solution.

In setting up the problem, notice how “of” means to multiply z by 4/13 and “is” means to set (4/13)z equal to 2/7.

If 3 senior men = 30% * All Men →

All Men = 3/30% = 10 Men.

The Ratio Men : Women = 5 : 3 = 10 : 6.

Thus there are 6 Women. 6 + 10 = 16.

Say cost of each pair of socks = y and pairs of socks = x.

Since \[quantity x cost per item = total cost\]:

First, xy = 50.

Secondly, (x + 5) \[y (1 - 20%)\] = 50

Simplify the second equation:

80%y(x + 5) = 50 or

0.8xy + 4y = 50

Insert xy =50 here.

.8(50) + 4y = 50

40 + 4y = 50 or 4y = 10

Thus y = 10/4 = 5/2

Need to find x = pairs of socks.

xy = 50 = x(5/2)

So 5x = 100 or x = 20

We need to convert 5 hours into minutes. There are 60 minutes in an hour, so 5 hours = 5 * 60 minutes = 300 minutes. Therefore, you go 20 meters/minute for 300 minutes, or 20 * 300 = 6000 meters.

36 is x% of 133

that means that 36 = (x%)(133)

x% = 36/133 X 100 = 27%

divide: 36/145 = 0.248; multiply by 100 to get percent

24.8%

Let's first pick numbers. If y = 25, x = 100. It's tempting to pick 25% as the answer, but x is greater than y, so the percentage must be greater than 100%. x is four times y, or 400% of y.

Belinda walks faster than Max, so she should walk over a mile in the same time that Max walks 1 mile. We can eliminate the answer choices that aren't over a mile. It takes Max 3 minutes longer to walk a mile, so Belinda will walk for 3 more minutes after she finishes her first mile. If she walks 1 mile in 12 minutes, she walks 1/12 miles in 1 minute, or 3/12 = 1/4 mile in 3 minutes. So she walks 1 1/4 miles, or 5/4 miles.

This problem requires you to work backwards from stop 5 to the passengers present at stop 1. If 2 person gets out at stop 5, that means there were 3 people on board at stop 5. This means there were 9 people present at stop 4 (9 total, 2/3 (6) got off, leaving the 3 for stop 5), 27 people present at stop 3 (27 total, 2/3 (18) got off, leaving 9 for stop 4), 81 people present at stop 2 and 243 passengers present at stop 1. That is, the number of passengers on board the train at any stop follows a logarithmic reduction along powers of three, from 35 at stop 1 to 31 at stop 5.

21.21/ 4.25 = 5 pounds paid for. Since a pound is given for every 2 pounds sold, that is 5/2 = 2.5 so an extra 2 pounds is given to Lauren, totaling 7 pounds.

First solve for z by multiplying 2/7 by the reciprocal of 4/13.

Then multiply this number by 8/11 to find the solution.

In setting up the problem, notice how “of” means to multiply z by 4/13 and “is” means to set (4/13)z equal to 2/7.

If 3 senior men = 30% * All Men →

All Men = 3/30% = 10 Men.

The Ratio Men : Women = 5 : 3 = 10 : 6.

Thus there are 6 Women. 6 + 10 = 16.

Say cost of each pair of socks = y and pairs of socks = x.

Since \[quantity x cost per item = total cost\]:

First, xy = 50.

Secondly, (x + 5) \[y (1 - 20%)\] = 50

Simplify the second equation:

80%y(x + 5) = 50 or

0.8xy + 4y = 50

Insert xy =50 here.

.8(50) + 4y = 50

40 + 4y = 50 or 4y = 10

Thus y = 10/4 = 5/2

Need to find x = pairs of socks.

xy = 50 = x(5/2)

So 5x = 100 or x = 20

We need to convert 5 hours into minutes. There are 60 minutes in an hour, so 5 hours = 5 * 60 minutes = 300 minutes. Therefore, you go 20 meters/minute for 300 minutes, or 20 * 300 = 6000 meters.