How to find proportion - GRE Quantitative Reasoning

First, add up the four parts of the ratio. This equals 25 parts. These 25 parts make up the 75 pound mixture, which means the 75 pound mixture is composed of 3 times the 25 parts (25x = 75 so x = 3).

This allows you to know that the number of pounds of chocolate chips is 3 times the ratio, i.e. 3 * 5 = 15. The mixture includes 15 pounds of chocolate chips. The answer is 15.

The best approach is to add the numerator and denominator of the ratio (5 + 1 = 6), and then divide the total by that sum (120/6 = 20). This gives you the value for 1 part when the total is divided into 6 parts and, luckily for us, there is only 1 part women for every 5 parts men. Now set up equal ratios: men/women = 5/1 = x/20. Solve for the number of men by cross multiplying (5 * 20 = 1x). So there are 100 men and 20 women, which makes 80 more men than women.

Answer: 25
Explanation: For this type of problem, build an equation that represents the relationships between the quantities and solve for the quantitiy you need. The problem states that b=1/4c and a = 1/3b. Thus, a = 1/3(1/4)c, or 1/12 of c. Now put everything in terms of c, thus 1/12c + 1/4c +c = 400. Now comes the tricky step--combine like terms and create the improper fraction (1/12c + 3/12c + 12/12c = 16/12c). Reduce the fraction to 4/3. So 400 is 4/3 of c. Thus c is 3/4 of 400, or 300. a is 1/12 of 300, or 25.

Since she spent 1/4 on the ticket, 3/5 of the remaining 3/4 of the money was spent on popcorn: 3/5 x 3/4 = 9/20. This means 9/20 of the money was spent on popcorn so in total: 1/4 + 9/20 = 14/20 = 7/10 of her money was spent. This leaves 3/10 of her money behind: 3/10x 10 = 3.00.

Set up a proportion: 18.50/5 = x/2. Cross multiply and solve for x: 37 = 5x.... x = 7.40.

It's tempting to pick 1 hour, but that is a trick answer! Picture 3 men each painting 1 room. All 3 of the rooms are done after 3 hours, so each man actually spends 3 hours painting his room, not 1 hour.

The easiest way to solve this is with a rate formula: 1 / combined time = 1 / Bob's time + 1 / Ron's time. We know the combined time and Bob's time, so we can solve for Ron's time:

1/2 = 1/3 + 1/Ron's time

1/Ron's time = 1/2 – 1/3 = 1/6

Ron's time = 6 hours

Although it seems as though "Quantity B is greater" is the correct answer at first glance, a further analysis indicates that this answer is a trap. If and are negative numbers, such as and , then would be the larger number. Similarly, is larger if both and are positive numbers. Thus, it cannot be determined which variable is larger simply based on the information given.

First count the total number of parts in the ratio.

Then we can set up a proportion representing .

As the initial ratio shows, there are 6 pennies for every 14 total coins. In the total set, we have X pennies and 42 total coins. Plugging these numbers into the proportion gives .

Finally, we multiply both sides times 42 to isolate x.

2 gallons of lemonade equals 8 quarts of lemonade. To make 3 quarts of lemonade, you need of the amount needed to make 2 gallons of lemonade, or 6 ounces of mix.

This problem states that there are students in the class taking Calculus. Because the class has a total of students, that means there are only students in the class not taking Calculus. The problem also states that there are students in the class taking Chinese. Because only students in the class aren't taking Calculus, this means that there is a minimum of students in the class that are taking both Calculus and Chinese.

For this problem, you must do conversions of from hours to seconds.

Two hours is equal 120 minutes

.

120 minutes is equal to 7200 second

.

The train travels 8 feet per second so in 7200 seconds it travels 57600 feet

.

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

Answer: 25
Explanation: For this type of problem, build an equation that represents the relationships between the quantities and solve for the quantitiy you need. The problem states that b=1/4c and a = 1/3b. Thus, a = 1/3(1/4)c, or 1/12 of c. Now put everything in terms of c, thus 1/12c + 1/4c +c = 400. Now comes the tricky step--combine like terms and create the improper fraction (1/12c + 3/12c + 12/12c = 16/12c). Reduce the fraction to 4/3. So 400 is 4/3 of c. Thus c is 3/4 of 400, or 300. a is 1/12 of 300, or 25.

Since she spent 1/4 on the ticket, 3/5 of the remaining 3/4 of the money was spent on popcorn: 3/5 x 3/4 = 9/20. This means 9/20 of the money was spent on popcorn so in total: 1/4 + 9/20 = 14/20 = 7/10 of her money was spent. This leaves 3/10 of her money behind: 3/10x 10 = 3.00.

Set up a proportion: 18.50/5 = x/2. Cross multiply and solve for x: 37 = 5x.... x = 7.40.

It's tempting to pick 1 hour, but that is a trick answer! Picture 3 men each painting 1 room. All 3 of the rooms are done after 3 hours, so each man actually spends 3 hours painting his room, not 1 hour.

The easiest way to solve this is with a rate formula: 1 / combined time = 1 / Bob's time + 1 / Ron's time. We know the combined time and Bob's time, so we can solve for Ron's time:

1/2 = 1/3 + 1/Ron's time

1/Ron's time = 1/2 – 1/3 = 1/6

Ron's time = 6 hours

Although it seems as though "Quantity B is greater" is the correct answer at first glance, a further analysis indicates that this answer is a trap. If and are negative numbers, such as and , then would be the larger number. Similarly, is larger if both and are positive numbers. Thus, it cannot be determined which variable is larger simply based on the information given.