GMAT Classic Mock Test - 3 - GMAT MCQ

1. To find the prime numbers between 40 and 50, inclusive, begin by eliminating all even numbers and multiples of 5.
   Original List: 43, 44, 45, 46, 47, 48, 49, 50
   Possible Primes Remaining: 43, 47, 49
2. Since 7 x 7 = 49, 49 cannot be a prime number since 7 is a factor.
   Possible Primes Remaining: 43, 47
3. Apply the relevant divisibility rules to each number remaining.
   43 will not be divisible by 3 since the sum of its digits is 7, which is not divisible by 3
   43 will not be divisible by 6 since it is not divisible by 3
   43 will not be divisible by 8 since it is not even
   43 will not be divisible by 9 since the sum of its digits is 7, which is not divisible by 9
   Since 7 x 6 = 42, you know 43 is not divisible by 7
   43 is prime.
   7 will not be divisible by 3 since the sum of its digits is 11, which is not divisible by 3
   47 will not be divisible by 6 since it is not divisible by 3
   47 will not be divisible by 8 since it is not even
   47 will not be divisible by 9 since the sum of its digits is 7, which is not divisible by 9
   Since 7 x 7 = 49, you know 47 is not divisible by 7
   The only number remaining is 49, which is not prime since 7 x 7 = 49
4. Having determined the prime numbers, you can multiply them together:
   43 x 47 = 2,021

1. Using the basic distance equation, Distance = Rate(Time), you can write the following equation:
   D = RT
   100 Meter Run: x = r₁₀₀(5)
   r₁₀₀ = x/5
2. Since the question states that Peter will run 200 meters "at the same rate," you can write the following equation:
   D = RT
   z = r₂₀₀(T)
   Since r₁₀₀ = r₂₀₀
   z = (x/5)(T)
3. Since the question asks for the time, variable T, you need to solve for T:
   z = (x/5)(T)
   T = 5z/x

1. Start by combining the two equations. Since the second equation is already solved for y, plug it into the first equation to yield:
   2x + 3y = 16
   Since y = -6x
   2x + 3(-6x)=16
2. Simplify like terms:
   2x + 3(-6x) = 16
   2x + (-18x) = 16
   -16x = 16.
3. Divide by -16 to yield x = -1. Be careful though: the question asks for the value of -x, not x.
4. Since x = -1, -x = 1. So the correct answer is E.

1. We are interested in the sales of the old month. We know that the new month had 25% more sales than the old. Since a 25% increase is equal to multiplying a number by 1.25 (=100% + 25% = 1 + .25), we can write the following equation:
   1.25(Old month sales) = $1,000,000
   Divide both sides by 1.25 to yield $800,000 for the value of sales for the past month.
   (Old month sales) = $800,000
2. Be careful that you are not tricked into choosing answer B at this point. The question asks for the amount per day, not per month.
3. To get the amount per day, divide the monthly amount by 30 to yield $26,666 per day (=$800,000/30).
4. The question asks for an approximate value, so answer D, $27,000, is the closest and is correct.

1. In order to find out "how many more liters of water than liters of oil are in 200 liters of solution x", we must first find out the quantity of each component in 200 liters.
2. For water, 75% of 200 liters is 150 liters of water:
   (200 liters)(0.75 water concentration) = 150 liters of water
3. For oil, 25% of 200 liters is 50 liters of oil:
   (200 liters)(0.25 oil concentration) = 50 liters of oil
4. The difference between the two is 150-50, which equals 100 liters. Thus, 200 liters of solution x contains 100 liters more water than it does oil. The correct answer is E.

In order to solve this problem, it is extremely helpful to set up a matrix, organizing the information and methodically filling it in.

If 30% of the computers are laptops, 70% of the computers are desktops (note: you could not make this inference unless the problem said that all the computers are "desktops or laptops").

If 80% of the computers have more than 1GB of RAM, 20% of the computers have less than 1GB of RAM. (Note: The problem stated that no computers had exactly 1GM of RAM).

If 10% of the computers with less than 1GB of RAM [known to be 20% of all computers] are laptops, then (.1)(.2) = .02 or 2% of all computers are laptops with less than 1GB of RAM.
Laptop Desktop
< 1GB of RAM 2% 20%
> 1GB of RAM 80%
30% 70% x

Since the percents rows must add up, you can fill in the values:
Laptop Desktop
< 1GB of RAM 10% of 20% = 2% 90% of 20% = 18% 20%
> 1GB of RAM 28% 52% 80%
30% 70% x

The final graph is as follows:
Laptop Desktop
< 1GB of RAM 2% 18% 20%
> 1GB of RAM 28% 52% 80%
30% 70% x

Since the question asks "what percent of the desktops [not total number of computers] have more than 1GB of RAM," the correct answer is (percent of desktops with more than 1GB of RAM) / (percent of desktops) = 52%/70% = about 75%

Note: If the concept of dividing percents is causing you trouble, let x = 100 and fill in accordingly.
Laptop Desktop
< 1GB of RAM 2% or 2 18% or 18 20% or 20
> 1GB of RAM 28% or 28 52% or 52 80% or 80
30% or 30 70% or 70 x = 100

1. The number of individuals that had infection A is 1/3 of N, or N/3.
   Infection A: N/3
2. The number of individuals that also had infection B is 1/5 of the number that had infection A. In other words, it is (1/5)A = (1/5)(N/3) = N/15.
   Infection B: (1/5)A = (1/5)(N/3) = N/15
3. If N/15 of the N individuals have infection A and B, then N – (N/15) did not have both infection A and B. Consequently, 14N/15 individuals did not have both infection A and infection B.
   Neither A or B: N - (N/15) = 14N/15

1. Each time the pump is used, 2/3 of the remaining gas stays and 1/3 of the remaining gas is removed.
2. The first time running the pump removed 1/3 of the full tank, leaving 2/3 of a full tank of gas. So, after running the pump once, 1/3 of the total gas in the tank has been removed.
3. The second time running the pump removed 1/3 of the 2/3 of a full tank that remained after running the pump for the first time. So, after running the pump twice, (1/3) + (1/3 of the 2/3) of the remaining tank had been removed. Thus far, 5/9 of the total gas in the tank has been removed.
4. The third time running the pump removed 1/3 of the 4/9 of a full tank that remained after running the pump for the second time. So, after running the pump three times, 5/9 + 1/3 of 4/9 of the remaining tank had been removed. In total, 5/9 + 4/27 = 19/27 of the total gas in the tank at the beginning was removed after running the pump three times.

1. Although this question can be solved using algebra, it is significantly easier to solve by picking small numbers and observing the changes.
2. Although x is defined as a positive integer divisible by 4 from 1824 to 1896, there is no reason you cannot seek to determine whether the equations increase by using x = 2 and x = 4. The equations will behave the same for x = 2 and x = 1824. To be safe and convince yourself that the patterns between 2 and 4 will hold, you could also check x = 6, although this is not necessary and will consume extra time
   
3. Evaluate equation I. As x increases, equation I must increase. Any answer choice that includes I is wrong.
4. Evaluate equation II. The pattern that emerges is that as x increases, a smaller number is subtracted from a negative number. Subtracting a smaller number from a negative number actually makes the overall value increase (e.g., -10 – 20 = -30, which is less than -10 – 15 = -25). Consequently, as x increases, equation II must increase. Any answer choice that includes II is wrong.
5. Evaluate equation III. Both by looking at the equation and by observing the values, it is clear that as x increases, the value of equation III decreases since four is being divided by a larger number.

1. o determine f(-1), we must first know (-1)⁵⁹, (-1)⁵⁷, and (-1)⁵⁶. You should never multiply out hundreds of numbers.
2. Instead, look for a pattern:
   (-1)¹=-1
   (-1)²=+1
   (-1)³=-1
   (-1)⁴=+1
   ...
   (-1)^{(odd number)}=-1
   (-1)^{(even number)}=+1
3. This means (-1)⁵⁶=+1 since 56 is an even number, (-1)⁵⁷=-1 since 57 is an odd number, and (-1)⁵⁹=-1.
4. This simplifies the numerator to:
   5(-1) - 3(-1) + 4(1)
   -5 + 3 + 4 = 2
5. Plugging in -1 for x in the denominator yields:
   2(-1 )+ 1
   -2 + 1 = -1
6. Combining the top and bottom of the fraction yields an answer of f(-1) = 2/-1 = -2. The correct answer is A.

1. Finding P(at least two students with the same birthday) directly will be extremely difficult. Consequently, we must look for a different way. If we find the complement of P(at least two students with the same birthday), we can find P(at least two students with the same birthday) since it will be equal to 1 - P(complement).
   P(A) = 1 - P(complement of A)
   P(at least two students with the same birthday) = 1 – P(all birthdays are unique)
2. Find P(all birthdays are unique).
3. If every birthday is unique, then with 85 students, there are 85 different days on which a birthday occurs.
   Let N = Total Students Selected After Student S Selected
   Let M = Total Students Selected Before Student S Selected
   Let U = Unique Days of Year Remaining Before Student S Selected on Which Future Students Can Have Unique Birthday
   Let P = P(Unique Birthday)
   Let O = Students Remaining After Student S Selected
   You can draw a table to help solve this problem.
   
4. For P(Unique Birthday with 1 student already selected [i.e., the M=1 row]): Since there are 365 possible days of the year yet only 364 days will satisfy the condition of all birthdays being unique since 1 day already has a birthday occupying it from the first student selected, P = 364/365
5. P(all birthdays are unique) = P(unique birthday for 1st person selected) *P(unique birthday for 2nd person selected) *P(unique birthday for 3rd person selected) ... *P(unique birthday for 84th person selected) *P(unique birthday for 85th person selected)
6. Translating this into math by multiplying the values in column P:
   P(all birthdays are unique) = 
7. At this stage, you should simplify the expression that equals P(all birthdays are unique).
   From 365 to 281, there are (365-281)+1 = 85 numbers (remember that you need to add 1 since it is 365 to 281, inclusive).
8. In the denominator, you know that 365 will be multiplied together 85 times:
   Denominator = 365⁸⁵
9. In the numerator, it is not as easy to simplify. However, you may notice that there appears to be something resembling a factorial. Specifically, the numerator is 365! truncated just before 280. If you take 365! and divide it by 280!, every term beneath 281 will cancel out, leaving you with the expression you are looking for in the numerator.
   
10. Combine the numerator and denominator:
11. Use the complement to find the answer to the original question:
    P(at least two students with the same birthday) = 1 – P(all birthdays are unique)
    P(at least two students with the same birthday) = 

1. The authors of the test do not want you to do the calculations long-hand. This would consume an incredible amount of time and is absolutely unnecessary.
2. In order to determine the units digit of the difference of these three terms, it is essential to know the units digit of each individual term. Since a digit raised to integer exponent follows a pattern in its units digit, you need to identify this pattern.
3. In identifying the pattern of the units digit of an exponential expression, it is essential to remember that you do not need to carry out the entire multiplication process to determine the units digit of a product. Simply multiply the units digit of each number being multiplied and the units digit of this product will be the units digit of the entire expression. For example: (2389283)(24892489) will have a units digit of 7 because 9*3=27 has a units digit of 7.
4. The units digit of 6 raised to an integer exponent follows a definitive pattern. Consequently, with minimal calculations, you know that the units digit of 6¹⁵ is 6.
   6¹ = 6 → units digit of 6
   6² = 36 → units digit of 6
   6³ = 216 → units digit of 6
   6⁴ = 1,296 → units digit of 6
   6^{any integer} → units digit of 6
5. The units digit of 7 raised to an integer exponent follows a definitive pattern.
   7¹ = 7 → units digit of 7
   7² = 49 → units digit of 9
   7³ = 343 → units digit of 3
   7⁴ → 3 x 7 {take units digit of 3 from 343 and multiply by 7} → units digit of 1
   7⁵ → 1 x 7 {take units digit of 1 from 7⁴ and multiply by 7} → units digit of 7
   7⁶ → 7*7 {take units digit of 7 from 7⁵ and multiply by 7} → units digit of 9
   7⁷ → 9*7 → units digit of 3
   7⁸ → 3*7 → units digit of 1
   
   Based upon this pattern, you know that the units digit of 7⁴ is 1.
6. The units digit of 9 raised to an integer exponent follows a definitive pattern.
   9¹ = 9 → units digit of 9
   9² = 81 → units digit of 1
   9³ → 1 x 9 → units digit of 9
   9⁴ → 9 x 9 → units digit of 1
   9⁵ → 1 x 9 → units digit of 9
   9 raised to an odd integer has a units digit of 9.
   Consequently, you know that the units digit of 9³ is 9.
7. Thus far you know that the units digit of 6¹⁵ – 7⁴ – 9³ = units digit of 6 – units digit of 1 – units digit of 9.
8. Simplify the first two terms of this expression: units digit of 6 – units digit of 1 = units digit of 5
   Note: If you are having trouble believing that this will always hold true, try a few numbers. For example, 796 - 11 = 785, 56 - 501 = -445, 86 - 271 = -185
9. The expression now reads: units digit of 5 - units digit of 9.
10. This is perhaps the trickiest part of the question. Some students think that since 5-9=-4, the units digit of the entire expression will be 4. However, this fails to consider that the left term could be larger than the right, resulting in a units digit of 6. For example:
    15 - 9 = 6 {left term is larger}
    155 - 99 = 56 {left term is larger}
    155 - 999 = -844 {right term is larger}
    15 - 99 = -84 {right term is larger}
11. Consequently, the crucial question in determining whether the units digit of the final expression is a 6 or a 4 is whether the left expression is larger than the right. In other words, "is (6¹⁵ - 7⁴) greater than 9³?"
12. In order to figure this out, take an approximate guess at the value of each term. You know that 9³ will be less than 1000, which is 10³, so the question of whether the units digit is 6 or 4 really rests on whether 6¹⁵ - 7⁴ is greater than 1000 (in which case the left term will be larger than the right term and the units digit will be 6) or whether 6¹⁵ - 7⁴ is less than a thousand (in which case the right term will be larger than the left term and the units digit will be 4).
13. The test does not require long tedious calculations and these are not necessary here. It should be rather clear that 6¹⁵ - 7⁴ is greater than 1000, in which case the units digit will be 6, not 4.
14. Units digit of 5 - units digit of 9 = units digit of 6 since the left term (i.e., the one with a 5) is larger than the right term. The final answer is a units digit of 6.
15. Answer choice C is correct.
16. FYI. The expression is: 470,184,984,576 – 2,401 – 729 = 470,184,981,446

From statement I:

N is a multiple of 13. It can be 13, 26, 39, and so on. But, N cannot be determined uniquely.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

N is not a composite number. So, N can be any prime number or it can be 1(note that 1 is neither prime nor composite). But, N cannot be determined uniquely.
∴ Statement II alone is not sufficient to answer the question.
From statements I and II together:
N is a mutiple of 13. It can be 13 or any multiple of 13 less than 100.
N is not a composite number. So, N can be any prime number or it can be 1(note that 1 is neither prime nor composite).
Any multiple of 13 will be composite, except 13 itself. Also, 1 is not a multiple of 13. So, only possible value N can take is 13.
∴ Using both the statements together, we can answer the given question.

1. Rewrite the terms on the left-side with common prime bases.
   (243^{9 + 18z})(81^-18z)(27^{15 – 9z})
   = (3^{5(9 + 18z)})(3^4(-18z))(3^{3(15 – 9z)})
   = (3^{45 + 90z})(3^-72z)(3^{(45 – 27z)})
2. Simplify by combining terms with like bases.
   (3^{45 + 90z})(3^-72z)(3^{(45 – 27z)})
   = 3^{45 + 45 + 90z – 72z – 27z}
   = 3^{90 -9z}
3. As a result of this simplification, the equation is much easier to deal with.
   3^{90 -9z} = 1
4. At this point, the problem may appear unsolvable as different bases and exponents exist. However, remember that any number raised to the 0th power is 1. Consequently, 1 can be rewritten as 3⁰. The equation now reads:
   3^{90 -9z} = 1
   3^{90 -9z} = 1 = 3⁰
5. Since the bases are the same, you can set the exponents equal to each other. The equation becomes:
   90 – 9z = 0
   90 = 9z
   z = 10

1. The general approach to solving this question is that we want to find:
   (Area of Square – Area of Circle)/4
   = .25(Area of Square – Area of Circle)
   Note: We divide by 4 since we are only interested in the bottom left gray region. This will be one fourth of the total region between the circle and the square since the circle is perfectly inscribed into the square due to the circle being tangent with each side of the square.
2. Since the x-coordinate of point a is x₁, point a is x₁ units away from the y-axis. This distance from the y-axis to point a is the exact same distance as the length of the radius AF. Consequently, AF = x₁ = length of radius. As a result:
   Diameter_circle = 2(Radius)
   Diameter_circle = 2x₁
   Note: The diameter is not important for the next step, but it will be important later.
3. We can now calculate the area of the circle:
   Area_circle = πr²
   Area_circle = π(x₁)²
4. The area of the square is the length of a side of the square multiplied by itself. Although we are not told directly the length of a side, since the circle is tangent with the square on all sides, we know that the circle will just fit within the square. Consequently, the length of the side of the square is the same as the length of the diameter of the circle:
   Diameter_circle = Length_square
   2x₁ = Length of Side of Square
5. The area of the square:
   Area_square = side²
   Area_square = (2x₁)²
6. Calculate the area of the gray region:
   =.25(Area of Square – Area of Circle)
   .25[(2x₁)² - (x₁)²π]
   .25[4(x₁)² - (x₁)²π]
   .25[(x₁)²4 - (x₁)²π]
   .25*x₁²(4 – π)

The correct response is (A).

The first statement allows us to express the total number of children in the first two groups in terms of the number of children in the third group. Let’s call the smaller groups A and B, and the largest group C. Thus, we can express the first statement: A + B = C.

We know from the question-stem that A + B + C = 50
So we know C = 50 – (A + B).

Using substitution, C = 50 – C.
2C = 50
C = 25. Sufficient.

The second statement tells us the value of A, the smallest group.

This only tells us that 6 + B + C = 50. Without knowing B, we cannot determine a unique value for C.

The correct answer is (B).

(1) If it costs more than $1,000 annually to feed 4 raccoons, we do not have enough information to answer either yes or no to the original question. It could cost $2,000 to feed 4 raccoons, in which case it WOULD cost more than $2,000 to feed 7 raccoons. Or, it could cost only $1,000 and one cent to feed 4 raccoons, in which case feeding 3 more would be less than an additional $1,000, and the answer would be no. This statement is insufficient.

(2) If it costs more than $1,500 annually to feed 5 raccoons, then the smallest cost for each animal is a little over $300. $300 x 7 raccoons = $2,100. Sufficient.

The correct response is (D).

The missing information here is the value of s. Both statements allow us to find s. Statement (1) allows us to do so by simplifying and solving the equation for s. From Statement (2) we know we can find “z” from the information given in the question stem. Once we find z, we can plug in for s. From the question stem we can calculate z% as follows:

Simple interest = principal x rate x time. $450 = $8000 * z/100 * 1, so z = 5.625%. Now that we know z, we can plug in to solve for s in Statement (2).

The correct response is (C).

(1) If no additional voters are added to the bloc, and 4 of the current voters leave the bloc, there will be fewer than 20 voters.

We can translate the given information into an inequality: x – 4 < 20, where “x” is the number of current voters. We know x < 24, but we cannot determine an exact value for x.

(2) If 4 more voters join the bloc and all of the present voters remain, there will be at least 27 voters.

We can translate the given information into an inequality: x + 4 ≥ 27. “At least” means there could be 27 OR more than 27 in the bloc. This inequality simplifies to x ≥ 23. We do not know the exact value of x based on this inequality.

Combining both statements we know 23 ≤ x < 24. If x must be less than 24, but greater or equal to 23, the only number that satisfies both conditions is 23.

If you chose (D), keep in mind that each statement alone only allows us to limit the range of possible values for “x,” but not find the actual numerical value. For a “value” DS question, if more than one number is possible, the statement cannot be sufficient.

If you chose (E), you may not have realized that we could have expressed the information in the statements as inequalities. Both statements combined then allow us to limit the range of possible values to one, so combined they are sufficient.

The correct response is (B).

(1) 7y is an integer.

If you chose (A), note that it is possible for 7y to be an integer when y is an integer. For example, if y = 1, 7y = 7. However, it is also possible for 7y to be an integer when y is not an integer. For example, if 7y = 1, then y =1/7.

(2) y/7 is an integer.

If y/7 is an integer, then y must be a multiple of 7. All multiples of 7 are themselves integers (7, 14, 21, etc.).

If you chose (C), you failed to recognize that Statement (2) was sufficient by itself, as there is no value we can choose for y that makes y/7 an integer that is not itself an integer. Picking numbers can help you see this relationship more clearly.

The correct answer is (E).

If you chose (A), from Statement 1, the possible values for the digits are 0 and 5, 1 and 4, or 2 and 3. So the possible numbers are: 50, 14, 41, 23, or 32. We don’t know which of these is x.

If you chose (B), from Statement 2, we know x is prime, but there are many two-digit prime numbers: 11, 13, 17, 19, etc.

If you chose (C), remember that both 23 and 41 are prime numbers.

If you chose (D), both statements offer limiting information, but because this is a “value” question, a statement can only be considered sufficient if it allows us to limit our range of possible x’s to ONE value only.

The answer is (E). Statement 1 limits our possible x’s to 5 integers, and Statement 2 narrows that list to 2 integers. However, we still do not know whether x is 23 or 41.

The correct response is (B).

We know from the question that each family member got at least 1 present, that they all got the same number of presents, and that no presents were left over. Based on this information, we can write the following inequality:

(1) The first statement would be useful if we needed to know the number of family members, but it doesn't help to answer this yes/no question.

(2) Based on the information in statement (2), we can write the following inequality:

Combining the information in statement (2) and the information in the question stem, we find that:

Since each family member got at least one present, and the number of presents per family member is less than 2, we can conclude that each family member received only one present.

The answer to the original question is NO. However, if we can answer YES/NO to a data sufficiency question based on the information in a statement, then that statement is sufficient. Statement (2) is sufficient.

The correct response is (D).

Statement (1) is sufficient. If the box is 18 inches long and 9 cylinders fit along that length, then they must each have a diameter of 2.

Statement (2) is also sufficient. In order to find the value of x, we need to know the diameter of each cylinder. This is given by Statement (2), since twice the radius of the ball bearing will equal the cylinder’s diameter. If each cylinder has a diameter of 2, then 9 will fit along the length of the box and 5 will fit along the width. A total of 9 x 5 = 45 cylinders will fit inside the box.

The correct response is (C).

To find the number of girls who are members of BOTH teams, we must find the overlap of this set. From Statement (1), we know that there are 18 girls total. Some are members of the Diving Team-only, some are members of the Swim Team-only, and some are members of both. But we do not have enough information to determine the number of girls who are members of both teams. Statement (1) alone is not sufficient.

From Statement (2), we know that 1/3 of the 27 Diving Team members are girls, so there are 9 girls in the Diving Team. We’re also told that 1/2 of the 24 Swim Team members are girls, so there are 12 girls in the Swim Team. Combined, that is a head-count of 9 + 12 = 21 girls. However, we still cannot determine how many girls are members of both teams. Statement (2) alone is not sufficient.

Combining both statements, we know that there are only 18 girls total who are members of these two clubs. Therefore, the extra 3 girls from our “headcount” must come from the number of girls who are members of both clubs.

The correct response is (B).

Statement (1) says that JK < 1. In order for this to be true, at least one of these numbers must be a positive fraction. We can quickly choose numbers to test this: If J = 1 and K = ½, their product is ½ and this less than 1. In this case, the answer to the question would be “YES” since 1 ÷ ½ = 2, which is greater than 1. But what if J = ½ and K = 1? J/K would be equal to ½. In this case, the answer to the question would be “NO”. Since the answer to the question can be “YES” or “NO” depending on the values of J and K, Statement (1) alone is not sufficient to answer the question.

Statement (2) tells us that J – K > 0. Let’s quickly choose values again. If J = 1 and K = ½, we satisfy the statement and get a “YES” answer. In fact, for all values we choose we will get a “YES” since J – K > 0 can be manipulated to read J > K. If J is always greater than K, then J/K will always be greater than 1. Statement (2) Alone is sufficient to answer the question.

The correct response is (D). We do not need to know the exact amount of espresso and sugar in the new drink. We only need to know the relationship between the amounts, since this question only asks for the ratio of espresso to sugar in the new drink.

If you chose (A), remember that we can find the ratio between ingredients as soon as we know the amount of each ingredient in the beverage or if we know the amount of one ingredient in relation to the set amount of the drink (part to part , or one part to whole). Since there are only two ingredients in the new drink, 20 ounces must be espresso. The ratio in (1) would be 20:15, or 4:3. However, (B) is also sufficient, since 30 ounces would be sugar.

If you chose (B), since the new drink consists only of espresso and sugar, we can find the ratio of espresso to sugar. The 30 ounces difference here must be made up of sugar. Therefore, the ratio is 40:30, or 4:3.

If you chose (C), you failed to recognize that each statement alone is sufficient. This is because the question is asking only for a ratio. We don’t need all of the “real-world” values to come up with a ratio, only the part-to-part or part-to-whole in a given circumstance to express the ratio. Each statement is sufficient to do this.

If you chose (E), you missed the idea that you can figure out the amount of espresso and the amount of sugar for a given amount of the new drink based on either statement (you just need to subtract).

The correct response is (E). There are three numbers we must know in order to find the percent of women with blue eyes: number of men in the group, number of women in the group, number of women with blue eyes.

If you chose (A), we know that 5% of the women have blue eyes, but we do not know how many members of the group are women, thus we cannot answer the question.

If you chose (B), this only gives us information on the men in the group, but the question concerns the number of women who fit a certain criteria.

If you chose (C), the information in the second statement does not tell us anything about the women in the group, and the first statement only tells us the percentage with blue eyes, not enough to determine the actual number.

If you chose (D), both statements are insufficient for different reasons. Statement (1) tells us the percentage, but not the actual number of women in the group, so we cannot turn that percentage into a number as this “value” question requires. Statement (2) does not relate at all to the women in the group and is therefore insufficient.

The correct response is (A). The probability that a substitute will be chosen can be found if we know the ratio of substitutes to total members OR if we know both values exactly. Here we are given the ratio = 1/6, so it is sufficient. If you chose (B), we know 18 are NOT substitutes, but we do not know how many ARE substitutes, so we cannot determine the probability.

The correct response is (B). This question asks about gross profit, which we know is derived from subtracting the total cost from the total selling price. If we know the cost of each mannequin and the selling price of each mannequin we can determine the designer’s gross profit. From the given information, we can write the following equation: P = 20 (s – c), where s = selling price and c = cost. So either we’ll need a value for s and a value for c, or we’ll need the value of (s – c).

Statement (1) tells us that $2400 = (20(2s – c)) or 2400 = 40s – 20c. We can divide both sides by 20 and simplify the equation to get: 120 = 2s – c. We still don’t know s and c. Insufficient.

Statement (2) tells us that 440 = 20(s + 2 – c). Let’s simplify:
440 = 20s + 40 – 20c
400 = 20s – 20c
400 = 20 (s – c)

Sufficient. Even though we didn’t solve for s and c separately, we were able to find the value of (s – c).

The correct response is (B). Let’ start with our most basic Profit formula: Profit = Revenue – Cost.

Using Statement (1), we can say that 200,000 = R – C.
Profit in 2010 = R – C
Profit in 2011 = 1.1R – 1.08C

Without knowing R or C, we cannot determine the percentage change in this case. Notice that if we knew R or some other relationship between R and C, we could substitute into the equation R-C = 200,000 to solve for the missing piece.

Statement 1 is insufficient.

Using Statement (2), R = 1.5C

The last step was not necessary if you realized that substituting R=1.5C into the expression for calculating the percentage change will give you an expression in which the Cs cancel out, giving you an actual percentage.

Statement 2 is sufficient.