Percentages

A number x is 150% greater than 200. What percent greater is x than 50% of 500? (A) 0 (B) 20 (C) 50 (D) 100 (E) 200

"150% greater than 200" means 150% of 200, or 300, added back to 200. This is the not the same figure as 150% of 200. Thus, 150% greater than 200 is 200 + (200)(1.5) = 500.

Suppose they have given 25% decrease Then after decreasing by 25%, only 75% will be left out so multiply with (0.75) to get the quantity left out after decrease If you want to find by how much it has decreased then in this case it has decreased by 25% so it has decreased by (0.25)*(original quantity)

thats a very important concept

y is what percentage of x

then use the proportion form and check what is the base. In this case the base is x so x---100 y----?

A cockroach population doubles every three days. If there were c cockroaches on June 1st, what was the percent increase in the population on July 1st? (June has 30 days.) (A) 900% (B) 1,000% (C) 9,999% (D) 102,300% (E) 102,400%

The percent increase is the difference between the amounts divided by the original, converted to a percentage. If the population doubles, mathematically the increase can be written as a power of 2. In the 30-day interval, if the original population is 1, it will double to 2 after three days — so, 21 represents the population after the first increase, the second increase would then be 22 and so on. Since there are ten increases, the final population would be 210 or 1,024. Therefore, the difference, 1024 - 1, is 1023. Use the percent change formula to calculate percent increase:

QuantityA QuantityB 50 as a percent of 30 The percent increase from 30 to 80

1. (C). 50 as a percent of 30 is . (Note: it's incorrect to calculate "50 percent of 30," which is 15. This asked for 50 as a percent of 30, which is equivalent to asking, "What percent of 30 is 50?") To find the percent increase from 30 to 80, use the percent change formula: Percent Change = Percent Change = The two quantities are the same. Note that if you set up both quantities first, you will be able to see that the two quantities are equal without solving (because both equal ).

25% of 400

400*.25 = 100

70. A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture? (A) 1.6 ounces (B) 3.2 ounces (C) 4.8 ounces (D) 6.4 ounces (E) 8 ounces

A). "200% larger" means "three times as big as" the original; "200% as large as" would mean twice as big. If the pitcher is three times as big as the glass, then pouring the contents of the glass into the pitcher will make the pitcher 1/3 full. If adding another 16 ounces fills up the pitcher, the 16 ounces must be equal to the remaining 2/3 of the pitcher's capacity. 1/3 of the pitcher's capacity, then, is 16/2, or 8 ounces. The juice mixture totals 8 ounces. 20% of the juice is grape juice, so there are (8)(0.2) = 1.6 ounces of grape juice.

If 35% of the acreage of a national forest was destroyed in a wildfire, and the remainder regenerates at a rate of 10% a year, after how many years, assuming no further losses, will the forest exceed its original acreage? (A) 10 (B) 8 (C) 5 (D) 4 (E) 3

BEWARE! Total calculation is incorrect. We have to proceed with each year since the area is increaseed every year for eg it was 65% in first year then it changed to 71.5 and now we have to calculate 110% of 71.5 so thats where i went wrong. Dont do that Picking numbers is a good strategy here. If the forest had 100 acres: After the fire: After 1 year: After 2 years: After 3 years: After 4 years: After 5 years: 65 acres (65)(1.1) = 71.5 acres (71.5)(1.1) = 78.65 acres (78.65)(1.1) = 86.515 acres (86.515)(1.1) = 95.1665 acres (95.1665)(1.1) = 104.68315 acres Note that each solution is multiplied by 1.1, so you can keep multiplying by 1.1 using the calculator — just be extra careful to keep track of how many times you multiply! Alternatively, write an inequality in which a is the original acreage and y is the number of years: (0.65a)(1.1)y > aNotice that the a values cancel out: (0.65)(1.1)y > 1 The GRE calculator is not equipped to solve this directly (you would need to use a logarithm, a topic not tested on the GRE), so instead plug in the answer choices for y, starting with the smallest value (3), until you find the smallest one that works. 5 is the smallest value that makes the inequality true.

75. In 2011, each member of a committee voted for one of two possible candidates for president. Candidate A received 40% of the vote and Candidate B received the remainder. In 2012, the same two candidates ran for president. Candidate A received 3 more votes than the previous year, a 5% increase in his total number of votes. How many votes did Candidate B receive in 2011? (A) 40 (B) 60 (C) 75 (D) 90 (E) 150

Candidate A had a 5% increase in votes between 2011 and 2012; a percent increase is calculated based upon the "original" number, which in this case was the number of votes for Candidate A in 2011. This 5% increase was equivalent to 3 total votes. You can use algebra to solve; let x equal the number of votes for Candidate A in 2011. Alternatively, if 5% = 3, then 50% = 30 (multiply both sides by 10) and 100% = 60 (multiply both sides by 2). Therefore, Candidate A received 60 votes in 2011. The problem also indicates that Candidate A received 40% of the total vote in 2011. You can solve for the total votes and subtract to find the number of votes for Candidate B: Let T equal the total number of votes in 2011. 60 = (0.4)T150 = T T - A = 150 = 60 = 90 votes for Candidate B in 2011. Alternatively, you could set up a proportion to solve. The advantage of this method: you won't solve for the total number of votes, so you won't get distracted by trap wrong answer (E). 60 votes represent 40% of the total, and you want to solve for 60% of the total:

A chemist is mixing a solution of acetone and water. She currently has 30 ounces mixed, 10 of which are acetone. How many ounces of acetone should she add to her current mixture to attain a 50/50 mixture of acetone and water if no additional water is added? (A) 2.5 (B) 5 (C) 10 (D) 15 (E) 20

EYES WIDE OPEN and solve