Executive Assessment Mock Test - 2 - GMAT MCQ

The number of months in which the company generated more than $50,000 of revenue is closest to 0 percent of 48. According to the graph, only one month generated $50,000 in revenue; no months generated more than $50,000.

1. There were 6 furniture items that experienced a decrease in total inventory. Of these, 3 (exactly 50 percent) are Red mahogany. However, all 19 furniture items experienced a decrease in total items sold. Only 6 of these (32 percent) are Red mahogany, so the statement is false.  

2. The furniture type experiencing the greatest percentage increase in total inventory from 2009 to 2010 is the Oak Natural Desk, at 9.7 percent. This same item also experienced the greatest percentage decrease in the total number of items sold (–8.1 percent).  so the statement is true.

3. The furniture type with the highest rank based on total inventory is the Oak Natural Chair. The furniture type with the highest rank based on total items sold is the Maple Natural Chair. so the statement is false

4. The total inventory of Cherry Red mahogany Tables in 2010 was 200,407. This furniture type experienced a 3.1 percent decrease in total inventory, or a drop of about 6,000 items. Its inventory in 2009 was therefore approximately 206,400. so the statement is True.

In E-mail #2, the donations coordinator states that donations are usually received from about 20 percent of those who receive requests. The computer drive had already received 40 donations, and each donor would receive 2 invitations to the thank-you event, for a total of 80 invitees. If requests were extended to 400 local businesses and 20 percent of those made a donation, the drive would receive 80 computers from businesses. That would add 160 invitations to the thank-you event, for a total of 240 invitees.

As the number of weeks increases, the number of complaints also increases. The number of complaints made by customers who received a follow-up call one week after placing their orders is closest to 50 percent of the number of complaints made by customers who received a follow-up call seven weeks after placing their orders. Approximately 30 complaints were made by customers who received a follow-up call one week after placing their orders, and nearly 60 complaints were made by customers who received a call after seven weeks.  If the company wishes to limit its complaints to 40 or fewer per year, it should make follow-up calls no more than two weeks after customers place their orders. If the company waits three weeks or longer, it is likely to receive more than 40 complaints per year.

The tour city with the median rank based on total tickets sold is Denver, CO. Denver has the highest rank based on total sales revenue, so the statement is false.

The total number of tickets sold in Providence, RI, in 2010 was 10,004. Providence experienced a 2.1 percent increase in ticket sales from 2009 to 2010. So, the number of tickets sold in 2009 would be less than 10,000, not greater than 10,000.

Denver, CO, experienced the greatest percentage increase in total sales revenue from 2009 to 2010, at 9.2 percent. It also made more sales revenue in 2010 than any other city on the tour, at $688,095.

Total cost of Setting up magazine = Rs.2800

Total cost of paper and ink = Rs.1600

Total cost of printing = Rs.3200

Total Expenditure on magazines = Rs.7600

Total sale price = 5×1500=7500

Total profit earned =1/4 × 7500 = 1875

So, Sum of money obtained from the advertising in magazine = Rs.1875

The number of products that received more than seven quality assurance inspections is closest to 10 percent of 60. The graph shows that four products received more than seven quality assurance inspections. These four products are 0.067 percent of the total, or 6.7 percent. 

The author clearly states that Ralph Waldo Emerson was not as successful at other pastoral duties (as he was at delivering sermons), so obviously he will never agree with (C), the correct answer.
(A) The author will agree with this, as he states this in the opening lines of the passage.
(B) Out of Scope. The author may or may not agree with this. (The last line of the passage states the opinion of the ‘sexton’ and not that of the ‘author’).
(D) Out of Scope. The author may or may not agree with this.
(E) The author will agree with this, as per the information in the first para.

The opening lines of the passage state that Emerson was born in 1803 and the passage subsequently states that he became a minister in 1826, that is, when he was 23 years of age, so (E) is the correct answer.
(A) Opposite. The first line of the second para states that he did work as a teacher for some time.
(B) The passage mentions no such thing.
(C) Opposite. The second para says that his sermons were ‘couched in spiritual language’.
(D) ‘Hated’ is too strong a word; the passage does not convey such an extreme connotation.

The first para clearly states that people were most impressed with Emerson’s great maturity of mind. Hence, (A) should be the correct answer.
(B) While this is what the quoted line states, the question is WHY the author states this and not WHAT he states.
(C) This fact has no connection with the quoted line.
(D) This was a positive quality of Emerson and not a flaw.
(E) This point is in addition to Emerson’s faultless conduct at Harvard and not a description of the same.

Analyzing the Argument

The argument draws parallels between the mediaeval and modern times and concludes that the dynastic system of sons taking on their fathers’ jobs has not changed over the years. To make the point, the author gives an example of blacksmiths in mediaeval times and baseball players today.

In order to question the credibility of the argument, the correct option must point out that the times are different and that there need not be a parallel between career systems today and in mediaeval times.

Eliminating Options

• Option (A) gives one more example of dynastic systems today. If anything, (A) lending further credibility to the argument and is not refuting it. For the same reason, Option (D) can also be eliminated.

• Option (C) implies that having a father in the same profession increases the possibility of the son following the father’s footsteps. The reasoning and implication in (C) is probably not as evident as in (A) and (D) but ultimately, (C) lends credibility to the argument, if anything.

• Option (E) is possibly a very attractive option. However, the argument does not state that genetic makeup was the reason that people chose a profession; rather it was the accepted practice of the day. Therefore, stating that genetic makeup does not influence the success of a career is irrelevant to the argument. Also, the argument does not discuss “success” in a career at all but just the choice of a career.

• Option (B) works because it implies that there was no choice given to those who lived in mediaeval times. The argument, when discussing the “likelihood” of someone becoming a baseball player implies that anyone today has the choice to become one, if they wanted to. Thus, a difference in the systems today and then has been pointed out and the option weakens the author’s reasoning.

Choice B is the correct answer.

The main issue in this sentence deals with ensuring a concise parallelism in listing the two results of the economic problems.

(1) The economic trouble led to two actions, which should be parallel: (a) write downs of mortgage backed securities (b) fears of a Great Depression-like spiral.

1. the phrase the writing down of..., and, to fears of... is not parallel
2. the phrase the write downs of... and fears of is not parallel as the first the should be removed
3. although this phrase is technically parallel, the inclusion of the before each result makes the sentence awkward and not concise
4. the phrase write downs of... and fears of... is both concise and parallel
5. the phrase write downs of... and, fears of... is not parallel

There are two major problems with this sentence.

(1) A comparison should evaluate two parallel elements. The intention of this sentence is to contrast two World War II battles. However, the original sentence contrasts the Battle of Midway with historians regard the.... The correct contrast should involve two parallel elements: the Battle of Midway and the Battle of Debrecen.

(2) as of marginal importance can be written in a more concise manner (as marginally important). Further, the reference to historians can be omitted as it is clearly understood in the context.

1. A battle (Midway) is incorrectly contrasted with historians regard for a battle; as of marginal importance is wordy
2. The sentence correctly contrasts the two battles; the wordy phrase as of marginal importance is replaced by the concise phrase marginally important
3. A battle (Midway) is incorrectly contrasted with historians regard for a battle; as of being marginal importance is awkward, wordy, and grammatically incorrect
4. The wordy phrase regarded as being of relatively minimal importance should be replaced by the more concise phrase regarded as relatively unimportant
5. The wordy phrase regarded by historians as being relatively unimportant should be replaced by the more concise phrase regarded as relatively unimportant; the phrase by historians is clearly understood in the context of the sentence and does not need to be repeated

There are two main problems with the original sentence.

(1) the infinitive form to enable needs to be replaced by a phrase that modifies to develop faster. The correct modifying phrase cannot be in the infinitive form and should instead be a participle: enabling

(2) it is not grammatically correct to compare AMD employees (i.e., them) to the firm Intel as you cannot compare unlike parts. Instead, you must compare like parts: a firm (i.e., AMD) to a firm (i.e., Intel).

The correct choice should include to gain substantial market share from and not market share with, which changes the meaning of the sentence.

1. to enable improperly modifies the phrase it follows and should be replaced by the participle form enabling; Illogically compares employees (i.e., them, referring to AMD employees) to a firm (i.e., Intel)
2. the word with instead of from in the phrase to gain substantial market share with rival firm Intel entirely changes the meaning of the sentence and is wrong
3. Illogically compares employees (i.e., them, referring to AMD employees) to a firm (i.e., Intel)
4. to enable improperly modifies the phrase it follows and should be replaced by the participle form enabling
5. correctly used the participle form instead of the infinitive to modify the preceding phrase; compares a firm (i.e., AMD) to a firm (i.e., Intel); correctly uses the phrase market share from rival firm

There are two problems with the original sentence.

(1) The subject (The Battle of Bull Run) lacks a verb. was or is must be inserted so that the subject can have a verb.

(2) The phrase in that this historic event was is wordy and could be made more concise.

1. the subject (The Battle of Bull Run) lacks a verb; the phrase in that this historic event was is wordy and could be made more concise
2. the subject (The Battle of Bull Run) lacks a verb; the phrase event in American history marking the first major ground needs to be split up by a comma after history in order to give the correct idea that marking modifies the idea that precedes it
3. the past tense was gives the false impression that the Battle was at some point in the past important, but it is not important today; the past perfect tense had marked is incorrect
4. the subject has a present tense verb; the sentence is concise; the , which modifies what directly precedes it (namely the Civil War) and this modification is logical
5. the phrase resulting in the death of over 500,000 illogically modifies the subject that precedes it (The Battle of Bull Run), giving the false impression that over 500,000 people died in this one battle
   Note: which modifies the word or term immediately preceding the comma (i.e., the Civil War) in the correct answer while resulting in the death of over 500,000 modifies the subject or idea to which it refers (The Battle of Bull Run)

This sentence turns on an idiom: either to x or [to] y where both x and y must be parallel.
The sentence should be: the Federal government...required either to bring...or [to] release
Unfortunately, the current sentence incorrectly reads: the Federal government...required either to bring...or that the government must release. This is not parallel and is wrong.

The correct sentence structure is: the Federal government is required either to bring charges against the individual being held, in which case he is entitled to a lawyer, or release him. Do not be thrown off by in which case he is entitled to a lawyer, which was inserted simply to make spotting the idiom and parallelism more difficult. The phrase in which case he is entitled to a lawyer is merely an elucidation of the preceding idea and is not another item that itself must be parallel.

1. the sentence is not idiomatically correct (i.e., the phrase the Federal government...is required either to bring...or that the government must release is not idiomatically correct)
2. the sentence correctly uses the idiom either to x or [to] y
3. although the sentence follows the correct idiom either to bring...or to proceed, the phrase to proceed in releasing is not concise and can be replaced by [to] release
4. the sentence is not idiomatically correct (i.e., the phrase the Federal government...is required either to bring...or the government must release is not idiomatically correct)
5. the sentence is not idiomatically correct (i.e., the phrase the Federal government...is required either to bring...or they must release is not idiomatically correct); they, which is a plural pronoun, does not agree with the subject the Federal government, which is singular

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 (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 (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.