GMAT Focus Edition Mock test - 4 - GMAT MCQ

N = total number of tests
x = overall average per test
Sum of scores for N tests = Nx
Sum of scores for first 10 tests = 600*10 = 6000
Sum of scores for last 10 tests = 700*10 = 7000
Therefore, sum of scores for (N − 20)tests = Nx − (6000 + 7000) = Nx − 13000
Average without the last 10 tests
Average without the first 10 tests 
We are given that

and

Solving (1) and (2) we get, N = 60

Given number is of the form 3x + 1 and 7y + 5
=> 3x + 1 = 7y + 5
=> x = (7y + 4)/3
The lowest integer values which satisfies this are y = 2 and x = 6
and number = 7y + 5 = 19
Therefore lowest value to be added to 19 make it divisible by 21 is 2

7 < 2x − 3 < 15

3 is added to each side to isolate the x term:

10 < 2x < 18

Then each side is divided by 2 to find the range of x:

5 < x < 9

The only integers that are between 5 and 9 are 6, 7, and 8.

The answer is 3 integers.

Given X < 0, i.e. X has to be -ve value.
When X is +ve or -ve |+X| = |-X| = |X|.
We know that -ve * -ve will lead to +ve.
- ( X ) |X| = +ve as we required this.
Then only option D fits the bill.

For AB to be a terminating decimal b must have the form 2^a ∗ 5^b.
Every option except 128 contains a 77, and since A and B do not share any factor (are co-prime) 7 will not cancel out of the denominator.
So B can only be 128 = 2⁷.

There are two situations, either the son takes car A1 or car A2:

In each of these situations the rest of the cars can be assigned in 5!5! different ways.

5!∗25!∗2
= 240

We are given that rate of work of 1 narrow pipe : rate of work of 1 wide pipe = 1 : 2
If we can find the ratio of rate of work of 2 wide pipes : rate of work of all pipes together, then we can easily get the ratio of time taken by 2 wide pipes : time taken by all pipes together. This is because ratio of time taken will be inverse of the ratio of rate of work since work done in both the cases is the same. (For a further explanation of this concept, check out the previous post)
In ratio terms, rate of work of 3 narrow pipes is 1 * 3 and rate of work of 2 wide pipes is 2 * 2
Therefore, rate of work of 3 narrow pipes : rate of work of 2 wide pipes = 3 : 4
Or we can say rate of work of 2 wide pipes : rate of work of all pipes together = 4 : (3 + 4) = 4 : 7
Then, time taken by 2 wide pipes : time taken by all pipes together = 7 : 4 (i.e. inverse of 4 : 7)
So all the pipes together will take 4/7 th of the time taken by the two wide pipes.

Total no of circuit boards inspected = 1600
64 CBs failed in inspection, so 64 nos are indeed faulty.
#boards those are process certified or passed in inspection = 1600 - 64 = 1536
Given, 1/8 of those that pass are also faulty, So, #additional faulty boards=1536/8 = 192
Therefore, total #of faulty circuit boards = #boards indeed faulty + #boards also faulty(addl.) = 64 + 192 = 256

When p = 9
Units sold = 130000 - 90000 = 40000
Revenue = 9(40000) = 360000
Cost = 100000 + 5(40000) - 1600000000/100000 = 100000 + 200000 - 16000 = 284000
Profit = 360000 - 284000 = 76000
When p=8
Units sold = 130000 - 80000 = 50000
Revenue = 8(50000) = 400000
Cost = 100000 + 5(50000) - 2500000000/100000 = 100000 + 250000 - 25000 = 325000
Profit = 400000 - 325000 = 75000
Profit decreased by 1000.

Step 1: Deduce profit for Effort and Investments
Total profit earned will be divided into two parts: 1/3 will be for efforts and 2/3 for investments made.
Mary and Mike get equal share for their efforts.
If x is the share that each of Mike and Mary get for efforts, 2x is the share of profit for total efforts.
1/3 of total profit goes toward effort.
Hence, the total profit earned will be 6x.

Step 2: Share of profit for investments made

4x is the profit to be distributed for investments made.
4x will be divided in the ratio of amount invested by Mary and Mike.
As Mary and Mike invested $700 and $300 respectively, share of profit on investments will be divided in the ratio 7 : 3
Hence, if Mary receives 7y, Mike will receive 3y.
Total profit on investments is 10y which is equal to 4x
10y = 4x ... (1)

Step 3: Compute total profit earned

Difference between amount shared between Mike and Mary is $800.
7y − 3y = 800
y = $200
Total profits on investment 10y = 2000
From equation 1, 10y = 4x
So, x = 2000/4 = $500
Total profit earned 6x = $3000

First let’s try to figure out what is meant by ‘consume 20% less fuel than the company’s cars’. It means that if company’s each car consumes 1 lt per hour, the hired cars consume only 4/5 lt per hour. So renting 5 more cars is equivalent to renting 4 cars which are same as the company’s cars. Hence, the total number of cars that will be run for the next 6 days is 8 company-equivalent cars.

4 cars running 10 hrs for 10 days consume 1200 lt of fuel

8 cars running 12 hrs for 6 days consume x lt of fuel

We multiply by 8/4 because more cars implies more fuel so we multiply by a number greater than 1.

We multiply by 12/10 because more hours implies more fuel so we multiply by a number greater than 1.

We multiply by 6/10 because fewer days implies less fuel so we multiply by a number smaller than 1.

First, we need to know: how many combinations of four distinct single-digit numbers have a sum of 28?  Start with the three highest digits: 9 + 8 + 7 = 24, so {9, 8, 7, 4} is one such combination.  First, keep the 9 & 8, and bring the other two closer together: {9, 8, 6, 5}.  OK: that exhausts possibilities with 9 & 8 as the highest numbers.  Now, omit 8, and try 9 & 7: even with the largest available digits, 9 + 7 + 6 + 5 = 27, so this will not be big enough.  Similarly, without 9, even with the largest available digits, 8 + 7 + 6 + 5 = 26, also is not big enough.  If we omit either 9 or 8, the sum is not big enough, and with both 9 & 8, there are only two possibilities: {9, 8, 7, 4} or {9, 8, 6, 5}.   Thus, only two possible sets of four digits.

For each one of these, we could permutate the number in any order.  4! = 24, so for each of the two sets, there are 24 different four-digit numbers we could form.  That’s a total of 2 * 24 = 48 different four-digit numbers.

Answer = D

We want to see what values of x satisfy the equation.  x² − 4 is under a radical, so it must be positive.

x² − 4 ≥ 0

x² ≥ 4

x ≥ 2, x ≤ −2

Objective: Compute number of students who enrolled for only English

Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.

Then, (A ∪ B) is the set of students who have enrolled for at least one of the two languages.
Because the students of the class have enrolled for at least one of the two languages, we will not find anyone outside A ∪ B in this class.
Therefore, n(A ∪ B) = number of students in the class
So, n(A ∪ B) = 40

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

i.e., 40 = n(A) + 22 - 12
Or n(A) = 30
n(A) is the number of students who have enrolled for English.
This number is the sum of those who have enrolled for only English and those who have enrolled for both the languages.

What we have to compute the number of students who have enrolled for only English.
n(only English) = n(English) - n(A ∩ B)
= 30 - 12 = 18.

Can we say that 10 people can finish the work in 100 days? No. If that were the case, after 20 days, only 1/5th of the work would have been over. But actually 1/4th of the work is over. This means that ‘10 people can complete the work in 100 days’ was just the contractor’s estimate (which turned out to be incorrect). Actually 10 people can do 1/4th of the work in 20 days. The contractor fires 2 people. So the question is how many days are needed to complete 3/4th of the work if 8 people are working?

We need to find the number of days. How is ‘no. of days’ related to ‘no. of people’ and ‘work done’?

If we have more ‘no. of days’ available, we need fewer people. So ‘no. of days’ varies inversely with ‘no. of people’.

If we have more ‘no. of days’ available, ‘work done’ will be more too. So ‘no. of days’ varies directly with ‘work done’.

Therefore,
‘no. of days’ * ‘no. of people’/’work done’ = constant

No. of days = 75

So, the work will get done in 75 days if 8 people are working.

We can also do this question using simpler logic. The concept used is joint variation only. Just the thought process is simpler.

10 people can do 1/4th of the work in 20 days.

8 people can do 3/4th of the work in x days.

Start with the no. of days since you want to find the no of days:

From where do we get 10/8? No. of people decreases from 10 to 8. If no. of people is lower, the no of days taken to do the work will be more. So 20 (the initial no. of days) is multiplied by 10/8, a number greater than 1, to increase the number of days.

From where do we get (3/1)? Amount of work increases from 1/4 to 3/4. If more work has to be done, no. of days required will be more. So we further multiply by (3/4)/(1/4) i.e. 3/1, a number greater than 1 to further increase the number of days.

This gives us the expression 
We get that the work will be complete in another 75 days.

Ratio of Boys to Girls = 4 : 3, So let’s consider there are “4x” boys and “3x” girls in the class.

Let’s also consider the average weight of the boys = “y” kgs. Therefore, average weight of girls will be “y - 7” kgs.

The average weight of Class = (Average weight of Boys * Number of Boys + (Average weight of Girls * Number of Girls)/(Total Number of Students)

=> 45 = y × 4x + (y - 7) × 3x/4x + 3x

=> 45 = 7y - 21/7

y = 48, and also, y - 7 = 41

Therefore, ratio of Average weight of Boys to Average weight of Girls = 48 : 41

The correct answer is B.

K = L * M + N

K/L = L * M/L + N/L
K/L = M + N/L = 80 + 0.025

M = 80
N/L = 0.025 = 1/40
L = 40N

K = 40M * 80 + N = 3201N

−3x + 7 ≥ 13 

−3x ≥ 6

When multiplying or dividing by a negative number on both sides of an inequality, the direction of the inequality changes.

x ≤ −2

As the ratio is 25 : 4, hence the total number of people will be 29 or multiple of 29.

Let us assume that the total number of people was 145: Professors: 20 and Students: 125.

University expelled eighty students for acts of civil disobedience, seventeen professors quit in protest. Therefore,

Students: 125 - 80 = 45 and Professors: 20 - 17 = 3

New ratio of student: the professor is 45 : 3 or 15:1

Given ratio is 25 : 4 which is 6.xx. Option A has value 5.xx, Option B has value 5.5x - ELIMINATED

We have professors as 20(Even) - 17(Odd) = 3(odd). Hence, D (55 : 6) - ELIMINATED

15 : 1 is higher than 25 : 4 and as we increase the numbers of professors and students, the ratio 15 : 1 will get lower but will still be higher than 25 : 4.

4 < −x + 7 < 15 

Subtract 7:

4 − 7 < −x + 7 − 7 < 15 − 7

−3 < −x < 8

Divide by -1. Don't forget to switch the direction of the inequality signs since we're dividing by a negative number:

−3 ⋅ (−1) > −x ⋅ (−1) > 8 ⋅ (−1)

Simplify:

3 > x > −8 or in interval form, (−8, 3).

Solving |2x – 15| < 2 first to get range of x
(2x – 15) < 2
x < 8.5
-(2x – 15) < 2
x > 6.5
Range of x 6.5 < x < 8.5
y = |2 + x| - |2 – x| to see that there is only 1 solution.
|2 + x| = 2 + x ...... is always +ve , x > 2 as (6.5 < x < 8.5)
|2 – x| = −(2 − x) ...... range of x > 2 , so 2 - x will be negative
y = |2 + x| − |2 – x|
y = 2 + x − (−(2−x))
y = 4;
so y is only taking one value ie 4

constant value

This choice suggests that a significant proportion of Hawaii's population is genetically predisposed to be long lived. Since Louisianans are not necessarily so predisposed, and since the Louisianans' children will acquire their genetic characteristics from their parents, not from their birthplace, this choice presents a reason to doubt that Hawaiian born children of native Louisianans will have an increased life expectancy. Therefore, this choice is the best answer. Because the conclusion concerns people born in Hawaii, not the average Louisianan, A does not weaken the conclusion. Because the governor's allegation is false, it cannot affect the conclusion. D fails to weaken the conclusion because it is consistent with the information given and the conclusion about life expectancy. By suggesting that Hawaii's environment is in one respect particularly healthy, E supports the conclusion.

In this argument, view #1 is that of the optimistic politicians, who look to the first piece of evidence #1, the jobless rate decline, for proof.  That first piece of evidence is the first bold statement.  Then view #2 is that of the economists.  They cite more evidence, evidence that calls into question the politician’s optimism in view #1.  Finally, we get the economist’s conclusion, view #2, the second underlined statement.

How to express that?  The second is definitely the main conclusion of the argument, but the first, evidence #1, is not necessarily something the economists would reject, not something that opposes the economists or calls their view into question.  The economists are well aware that the jobless rate has declined: they simply cite additional facts that cast this first fact in a different light.  One way to say it is  — the first underlined statement, evidence #1, was used to support one conclusion, view #1, and the second underlined statement is a second conclusion, view #2, that calls the first into question.

This is what (E) says.  (E) is the credited response.

Insurance companies can improve the ratio of revenues to claims paid, thus minimizing losses, if they insure as many people belonging to low-risk groups as they can. Because the strategy described in A adds a low-risk group to the pool of policyholders, this choice is the best answer. B is irrelevant, since no link is established between childhood diseases and diseases affecting the elderly. C is inappropriate, since increasing the number of services covered is unlikely to minimize losses. D is inappropriate, since it would increase the likelihood that claims against the policy will be made. Because policyholders will file claims against the policy for services covered rather than pay for the cost of the services themselves, E is irrelevant.

The first statement is a fact: everyone agrees with that.  The second sentence is a conclusion (signal words: “argue that“) — the first underlined section is conclusion #1, the conclusion of the community activities.  Then more facts — the results of scientific investigations are always facts!  The final sentence is another conclusion (signal words: “suggest that“), conclusion #2, the conclusion of the professors. Both underlined statements are conclusions, and the argument ultimately disagrees with the first and accepts the second — the second is the conclusion of the argument as a whole.

This is what (D) says. The first is a conclusion, a position, that the argument opposes, and the second is the conclusion of the argument. (D) is the credited response.

The correct answer to this question will be a claim that must follow from text contained in the passage. This question does not provide any clues as to where the justifying text will be found.
(A) The first paragraph mentions that the the Javan rhino is the most endangered species of large mammal. However, it does not have to be true that it is one of the most endangered animals, a category that is far broader than mammals.
(B) CORRECT. The first paragraph states that very little is known about the life of the Javan rhino. The passage does indicate, however, that scientists have been able to extract information on the species’ DNA from gathered dung. The paragraph also suggests that very little information about female Javan rhinos has been gained, given that scientists only recently discovered whether or not females of the species even have horns. Thus, one can infer that more is known about the genetics of the Javan rhino than its mating patterns.
(C) The second paragraph indicates that hunters slaughtered many rhinos, but it does not mention where. Furthermore, it does not have to be true that more rhinos were killed in Vietnam simply because fewer rhinos remain there.
(D) The passage only discusses the Javan rhino; therefore, a generalization about the extinction of "most animals" is not supported by the passage.
(E) The passage does not mention other survival factors for a species or rank them; therefore, this inference is not supported by the passage.

In the second paragraph, after citing human actions as the cause of the Javan rhino’s plight, the author goes on to mention that the population in Vietnam is probably not viable and that human efforts in Indonesia, such as the protection of the rhino on the Ujung Kulun peninsula, have had mixed results. The passage ends with the thought that human benevolence is not helping the rhinos much more than past maltreatment. Thus, the correct answer will note the problems with current human efforts.
(A) The author is certainly not optimistic, as the passage mentions that in Vietnam the outlook is doubtful and in Indonesia, problems plague the effort. It is possible, although not certain, that the author considers the effort worthwhile.
(B) The author gives no indication that he or she believes the effort is pointless. Furthermore, especially in Indonesia, the passage does not indicate a certainty that it will fail.
(C) The passage does not at all discuss the profitability of the effort. It is possible, although not certain, that the author considers the effort idealistic.
(D) CORRECT. The discussion of the mixed results and poor prognosis for the population in Vietnam justifies “problematic.” The last sentence of the passage, observing that benevolence has proved little better than maltreatment justifies “ironic.” Also, the author references the ironic quality of human protection of the Javan rhino in the 8th sentence in the 2nd paragraph, “Ironically, however, the lack of human disturbance allows mature forests to replace the shrubby vegetation the animals prefer.”
(E) The passage indicates that the efforts have been much less than entirely successful but does not indicate any confusion related to the current efforts. It is possible for efforts to be less than fully successful without being confused. Furthermore, it does not at all address the idea that any particular heroism is involved.

The author mentions the number of horns in the first paragraph in the course of describing the Javan rhino. The correct answer must follow from this text.
(A) Although the Javan rhino is described as rare, the discussion of extinction is in the second paragraph,. Furthermore, the vitality of the African rhino is not mentioned.
(B) The passage contrasts the number of horns of the Javan rhino to that of the African and Sumatran rhinos. However, the author makes a parallel comparison to the Indian rhino because both species have one horn.
(C) The passage only discusses the Javan rhino’s evolution into a separate subspecies in the second paragraph in a completely different context,; no direct link is drawn between this evolution and the Javan rhino’s single horn.
(D) CORRECT. The author mentions the Javan rhino’s single horn in conjunction with a general description of the Javan rhino. The passage then goes on to discuss its habitat and the scientific knowledge to date. Thus, the author included this detail to add depth to his or her description.
(E) The passage only states that until recently scientists were unsure if females had horns, and no definitive answer is given. Furthermore, this point is mentioned in a different context, after the passage has finished describing the Javan rhino.

Both (B) and (E) make the paradox harder to explain. Answers (A) and (C) are off-the-wall irrelevant. Choice (A) says that cheese has more fat then cream, but the French are eating both of those, so it doesn’t matter: either way, the French are eating high fat food. (C) changes the topic to imports, which is completely unrelated to the direct relationship of diet and epidemiology.
Only (D) resolves the paradox. Since the French drink red wine, which in moderation cleans the arteries, this explains how they could eat high fat foods and have a much lower risk of heart disease

The plan proposes that high-speed ground transportation would be a less expensive solution to airport congestion than would airport expansion. B indicates that between the cities to be served by the plan there is substantial air travel to which ground transportation would represent an alternative. Therefore, B is the best answer. No other choice could be cited appropriately. A and D both provide some evidence against the plan. A by emphasizing the likely costs of providing high-speed ground transportation is not by itself a solution to airport congestion. D by indicating that such an alternative is not by itself a solution to airport congestion. C and E say that there are many travelers for whom the proposed system would actually provide no alternative.