Percent Nail it

If z is x percent of y, then what is the square root of z? (1) (√y) percent of (√x) is 8. (2) (√y) percent of (√y) is 16.

A Correct. This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) you're asked about. The issue is percent translation. The combination of square roots of variables and percents make plugging in difficult for this question. Instead, translate the math into English using the percent translation table (see summary): Begin with the question stem. z is x percent of y, so z = (x/100) · y = xy/100. The question asks for the square root of z, so √z = √(xy/100) = √xy/10. To find this expression, you need the value of √xy. See if the statement(s) provide you with the missing pieces of the puzzle. Stat. (1): Translate the statement: (√y/100) · √x = 8. In other words: (√y) · (√x)/100 = √xy/100 = 8. This determines a single value for the required expression, so Stat.(1)->S->AD. Stat. (2) tells a convoluted story about y, but tells you nothing about x. Thus, no single value can be determined for √z, so Stat.(2)->IS->A.

Although percent problems are common in the GMAT, most of the problems concern percent increase or decrease, rather than just percent translation. Consider the following example; During spring the Attine ant collects 5 grams of seeds per day. During fall, the Attine ant's collection rate decreases to 4 grams per day, up until the end of winter, when the Attine increases its collection rate to 5 grams per day, again. What is the increase in percent of the Attine ant's collection rate from winter to spring? (A) 15% (B) 20% (C) 25% (D) 30% (E) 35%

A percent increase/decrease is in fact percent change, which warrants the percent change formula; Percent Change = Difference / Original * 100 Memorize this formula. It will come in handy. Try to use the percent change formula to figure out the Attine ant's percent increase. Fill in the missing pieces of the formula; The difference is 5-4=1, but the original may be more confusing to identify. In your opinion, which is the original ? 4 5 A) 4 Correct. The question asks about the percent increase from winter to spring, therefore the original is the Attine ant's collection rate in winter time, that is 4 grams per day. Correct. Fill in the blanks in the percent change formula; Percent Change = 1/4 * 100 = 25%

Andrew decreased his hourly rate by 25% to accommodate more clients. However, he realized that his rate was too low and decided to revert to his original hourly rates. By what percent must Andrew now increase his current rate to bring it back to its original amount? 25% 33.3% 50% 66.7% 75%

B Correct. Whenever there's an invisible variable in the problem plug in a good number. If the problem asks about percents use 100 or multiples of it. Remember that a percent increase/decrease warrants the use of the percent change formula. Plug in 100 for Andrew's hourly rate (the invisible variable). A 25% decrease brings his rate down to 100-25=75. In order to revert to the initial rate Andrew needs to increase his rate by 25. Use the percent change formula,. Percent Change = Difference / Original * 100 Thus, to go up from 75 to 100 the percent change is (25/75)×100=33.3%.

Sometimes the question asks you to find different percentages: How large a tip, in dollars, must Jenny pay for a $240 dinner tab, if the restaurant charges a 15% tip? $30 $36 $40

B Correct. Since 10%+5%=15%, use the 10% block to figure out this one. 10% of 240.0 is 24. 5% of 240 is one half of that, 12. Add them up 24+12=36. As you already know by now, your goal on the GMAT is to find the correct answer. This does not necessarily mean that you have to calculate all the way through, but rather to spot the right answer as quickly as you can. Often, a calculated estimation will suffice.

Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ? 0.5% 1% 5% 50% 500%

C Correct. For every percent problem in the GMAT, follow these steps: Translate, Reduce, Solve. Use the four-worded percent language as your guide and pay attention to basic math skills like multiplying and reducing. Some problems do require dirty work, so be prepared. First, translate "30% of 40% of 50 is 60% of what % of 200?" into an equation using the percent language. Use the percent language to figure out this confusing clump of words: Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred Translate: Reduce: Multiply by 100 twice on both sides to get rid of the denominator and come down to --> 30 · 40 · 50 = 60 · x · 200 Now, divide by 10 three times on both sides to get rid of all the zeros, simplifying further to --> 3 · 4 · 5 = 6 · x · 2 --> 60 = 12· x Solve: 5 = x That is, of course 5%.

Imagine yourself in the GMAT, dealing with a wordy, lengthy problem... The last step is to figure out the value of 37570/85386 These are some ugly numbers! Try to choose the best answer from the following: 22% 33% 44% 55% 66%

C Correct. Instead of messing around with the numbers, try to estimate like so: If 40,000/80,000 is 50%, then 37570/85386≈37,000/80,000, which is somewhat less than 50%. Therefore, the correct answer is C.

In a group of 250 adults, is the number of married (not necessarily to other group members) people at least 75? (1) At least 65 percent of the men in the group are married. (2) At least 30 percent of the women in the group are married.

C Correct. This is a Yes/No DS question. Answering a definite "Yes" or a definite "No" means Sufficient. If the answer is sometimes "Yes" and sometimes "No", it means Maybe which means Insufficient. The issue is percents. Plug in numbers that satisfy the statements and show that more than 75 people are married and the answer is "Yes". Then ask yourself "is this always true, for any number?" Think of other numbers to reach an answer of "No" and prove the statement(s) insufficient. In order to "break" the question, try plugging in the extremes: 250 men, 0 women, or the other extreme 0 men, 250 women. Stat. (1): You do not have any data about the percent of married women, nor about the relative ratio of men to women in the group. Thus, the answer is "Maybe", so Stat.(1)->Maybe->IS->BCE. Stat. (2) alone does not provide any data about the percent of married men, nor about the relative ratio of men to women in the group. Thus, the answer is "Maybe", so Stat.(2)->IS->CE. Stat. (1+2): Together, the two statements provide some data about both men and women. plug in the extremes: If the group consists of 250 men, then 65% of 250 is definitely over 75 married (50% of 250 = 125 is already over 75). If the group consists of 250 women, then 30% of 250 is 3·25 = 75 are married, and the answer is "Yes". Any mix of the two will necessrily have more than 75 married people, as there is nothing in either statement to drag the number under 75. Thus, the answer is "Yes", and Stat.(1+2)->S->C.

The Cactus-Bird cocktail is a mix of two beverages, A and B. In the Cactus-Bird cocktail, the ratio of A to B may vary from 1:4 to 2:3. If beverage A contains 40% alcohol, and beverage B contains 60% alcohol, what is the maximum possible alcohol percent in a Cactus-Bird cocktail? 44% 48% 52% 55% 56%

D Correct. This problem has several layers. First, choose the right ratio to maximize the alcohol percent in the cocktail. Since B has a greater alcohol percentage than A, choose the ratio that maximizes the amount of B in the cocktail. Write the ratio as a fraction of B/A: thus the ratio of 1:4 becomes 4/1 = 4, while the ratio of 2:3 becomes 3/2. The first ratio is greater, so choose the ratio of 1:4. Now, to calculate the percent of alcohol in a cocktail with a ratio of 1:4. Notice that the problem contains no real numbers - only ratios and percents. This is a surefire sign for an invisible plug in - in this case, plug in 100. Assume that a barman prepares a 100 ml of the Cactus-Bird cocktail at a ratio of A to B at 1:4. Place the information in a ratio box to find the Real quantities of each beverage, then find the alcohol content stemming from each beverage. The ratio of A to B is 1 to 4, for a total ratio of 5. The corresponding real number is the 100 ml you plugged in. Ratio Multiplier Real A 1 ×20 20 B 4 ×20 80 Total 1+4=5 100/5 = ×20 100 The multiplier is therefore 100/5 = 20. Since the multiplier is the same for all ratios in the box, use it to find the real quantities of A and B: 20 ml and 80 ml, respectively. Finally, find the alcohol quantity from each beverage: 20 ml of 40% A beverage contains 40%·20 = 4·2 = 8 ml of alcohol. 80 ml of 60% B beverage contains 60%·80 = 6·8 = 48 ml of alcohol Together, 100 ml of the cocktail contain 48+8=56 ml of alcohol, which is 56%.

Aaron's accountant accidentally decreased the salary of an employee by 25% instead of giving her a 25% increase. After receiving her paycheck, the employee complained to Aaron. The accountant was asked to fix the mistake and make up the difference in the next pay period. By approximately what percent of the short paycheck must the accountant increase the employee's next paycheck to make up for his mistake? 25% 33% 50% 67% 75%

E Incorrect. Whenever there's an invisible variable in the problem plug in a good number. If the problem asks about percents use 100 or multiples of it. In this case, plug in a good number for the employee's initial salary. Remember that a percent increase/decrease warrants the use of the percent change formula. D Correct. Plug in 100 for the employee's original salary (the invisible variable). After the accidental decrease of 25% the employee's salary becomes 100-25=75. The intended increase in the employee's salary should have resulted in 100+25=125. To fix that, the accountant needs to add 50 to the next paycheck. Use the percent change formula . Pay attention to the original, % change= (50/75)×100= 66.7%. Therefore, 66.7% of the short paycheck ($50) must be added to the corrected, increased amount of $125 during the next pay period.

Let's review the basics of percent change problems; Words like percent increase, percent decrease, percent more, percent less can help you identify percent change problems.

If the question asks about percent more or percent increase, the original is the smaller number. If the question asks about percent less, percent decrease, the original is the larger number.

Percent means: out of a hundred. The use of "cent" meaning "hundred" is derived from a Roman army rank - "centurion". These officers commanded a hundred soldiers each. GMAC just loves percentages. That's why they're so common in the GMAT not only as standalone problems, but also as part of a problem. "Percent" is a fraction with denominator 100 (20% means 20 over a 100 or 20/100) To convert from fraction-->percent use the form x/100, where x is the percentage.

Like fractions, percents are also defined as part/whole. Only that percents have denominator 100. For instance, 3% means 3 over a 100 or 3/100. What is 4/25 as a percent? A percent is a fraction with denominator 100, therefore 4/25=x/100, and so x=16. Eventually, 4/25=16/100=16%.

Let's review the basics of Percents Ballparking:

To find 10% of a number, divide it by 10 by moving the decimal point one place to the left. Use the 10% block to quickly find percents that are multiples of ten (i.e 20%, 30%, 40% etc.) To find 1% of a number, divide it by 100 by moving the decimal point two places to the left. To find other percents use combinations of these techniques (i.e 5% is half of 10%) Don't hesitate to estimate ugly numbers to save precious time.

Consider the following example: 7.5 is what percent of 1500 ? (A) 0.5% (B) 1% (C) 5% (D) 50% (E) 500% Before you go on to solving this problem consider the four words of the percent language; English word....................Math translation percent, % ......................../100 of............................................ · (times) what.....................x, y... (any variable you like) is, are, were (any form of to be)....=

Translate the problem using the percent language, 7.5 is what percent of 1500 ? 7.5 = x/100 · 1500 Now, reduce and solve. Incorrect. Ouch! You fell for yet another GMAC trick. Reduce your translation: 7.5 = · 1500 Now solve: 7.5 = x · 15 0.5 = x If x equals 0.5, then the correct answer is 0.5%. Don't go where GMAC intended, deducing 0.5 to 50%. This is wrong. Let's review percent translation: For every percent problem in the GMAT follow these steps; Translate - using the percent language Reduce Solve

Percent problems are perhaps one of the best opportunities to ballpark on the GMAT. In a test that's mostly about time management and making quick decisions, ballparking is extremely useful. Let's look at some common examples.

What is 10% of 1023? Getting 10% of something is similar to multiplying it by 10/100 or by 1/10, namely dividing it by 10. And so, divide 1023 by 10, moving the decimal point one place to the left. Hence, 10% of 1023 is 102.3. This is the 10% block. In the same manner, What is 1% of 1025 ? 102.5 10.25 1.025 B Correct. Getting 1% of something is similar to multiplying it by 1/100, namely dividing by 100. And so, to divide 1025 by 100, is to move the decimal point two places to the left. Hence, 1% of 1025 is 10.25.

GMAC tends to complicate percent problems with needless wordiness. Trying to wade yourself out of such problems sometimes becomes messy, as you try to find the right equation to solve the problem.

You may have good or bad memories of percentages, but the fact is that in order to solve GMAT percent problems all you need to know is the percent language. The good news is that it's a four-word language.