GMAT Focus Edition Mock test - 2 - GMAT MCQ

Step 1: Assume cost price and compute marked price

Approach: Assume cost price to be $100.

She had initially marked her goods up by 50%.
Therefore, a 50% mark up would have resulted in her marked price being $100 + 50% of $100 = $100 + $50 = $150.

Step 2: Compute the % discount offered

She finally sells the product at no profit or loss.
i.e., she sells the product at cost price, which in this case is $100.
Therefore, she offers a discount of $50 on her marked price of $150.

Hence, the % discount offered by her = 
Discount offered is 33.33%

Choice E is the correct answer.

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.

Choice C is the correct answer.

Solution:
Condition 1: p > 0, and
Condition 2: x^2 - 11x + p = 0 has integer roots

We know that for a quadratic equation ax^2 + bx + c = 0, sum of the roots is (-b/a) and product of roots is (c/a)
Sum of the roots = −b/a = - (-11/1) = 11
Product of the roots = c/a = p/1 = p > 0 (Accordingly to Condition 1)

We also got sum of roots is 11, i.e. positive
We know, product of two numbers is positive if both the numbers are positive or both the numbers are negative
Since sum of two roots is 11, i.e. positive, both the numbers cannot be negative (sum of two negative numbers cannot be positive). Hence, both the roots must be positive integers.

Let the root be x1 and x2. Therefore, x1 + x2 = 11, in which both x1 and x2 are positive integers. So, we must find various ways of expressing 11 as a sum of two positive integers. Please note that zero is neither positive no negative. Hence, the first positive integer can be 1
Possible roots are (1, 10), (2, 9), (3, 8), (4, 7), and (5, 6)
p is the product of these roots, i.e. 10, 18, 24, 28, 30 = 5 values

The average of 5 positive integers is 40. i.e., the sum of these integers = 5 × 40 = 200

Let the least of these 5 numbers be x.
Because the range of the set is 10, the largest of these 5 numbers will be x + 10.

If we have to maximize the largest of these numbers, we have to minimize all the other numbers.
That is 4 of these numbers are all at the least value possible = x.

So, x + x + x + x + x + 10 = 200
Or x = 38.
So, the maximum value possible for the largest of these 5 integers is 48.

Choice D is the correct answer.

List down possibilities: From only one box containing a green ball to all six boxes containing green balls.

If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
If all 6 boxes have green balls, there is just 1 possibility.

Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.

Choice B is the correct answer.

Method 1: Find the number of such integers existing for a lower power of 10 and extrapolate the results.

Between 10 and 100, that is 10¹ and 10², we have 2 numbers, 11 and 20.

Between 100 and 1000, that is 10² and 10³, we have 3 numbers, 101, 110 and 200.

Therefore, between 10⁶ and 10⁷, one will have 7 integers whose sum will be equal to 2.

Alternative approach

All numbers between 10⁶ and 10⁷ will be 7 digit numbers.
There are two possibilities if the sum of the digits has to be '2'.

Possibility 1: Two of the 7 digits are 1s and the remaining 5 are 0s.
The left most digit has to be one of the 1s. That leaves us with 6 places where the second 1 can appear.
So, a total of six 7-digit numbers comprising two 1s exist, sum of whose digits is '2'.

Possibility 2: One digit is 2 and the remaining are 0s.
The only possibility is 2000000.

Total count is the sum of the counts from these two possibilities = 6 + 1 = 7

Choice B is the correct answer.

Approach: Work with a numerical example

The fastest way to solve problems of this kind is to take numerical examples.

Let the 5 consecutive integers be 1, 2, 3, 4, and 5.
The average of 5 consecutive integers from 1 to 5 is 3.
Therefore, the value of m is 1 and the value of n is 3.

Because m = 1, m + 2 = 3
9 consecutive integers starting from m + 2 will be 3, 4, ... , 11
The average of positive integers from 3 to 11 is 7.
We know n = 3. So, 7 has to be (n + 4).

Choice E is the correct answer.

Step 1: Assign Variables and Frame Equations

Let Jose take 'x' days to complete the task if he worked alone.
Let Jane take 'y' days to complete the task if she worked alone.

Statement 1 of the question: They will complete the task in 20 days if they worked together.

In 1 day, Jose will complete 1/x of the task.
In 1 day, Jane will complete 1/y of the task.
Together, in 1 day they will complete 1/20 of the task.
Therefore, 

Statement 2 of the question: If Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days.

Jose will complete half the task in x/2 days.
Jane will complete half the task in y/2 days.

Or, x + y = 90 or x = 90 - y .... (2)

Step 2: Solve the Two Equations and Compute x and y

Substitute the value of x as (90 - y) in the first equation.

Cross multiply and simplify: 1800 = 90y - y²
Or y² - 90 + 1800 = 0.

The quadratic equation factorizes as (y - 60)(y - 30) = 0
So, y = 60 or y = 30.
If y = 60, then x = 90 - y = 90 - 60 = 30 and
If y = 30, then x = 90 - y = 90 - 30 = 60.

The question states that Jane is more efficient than Jose. Therefore, Jane will take lesser time than Jose.

Hence, Jose will take 60 days to complete the task if he worked alone and Jane will take 30 days to complete the same task.

Choice C is the correct answer.

Approach: Assume cost price to be $100
Let the marked price be S and the cost price of the article be $100.

When the article is sold at 80% of its marked price, selling price is 0.8S.
Selling the article at 0.8S results in a loss of 12% of the cost price.
Therefore, the loss incurred when selling at 0.8S = 12% of 100 = $12.
Hence, when selling at 80% of the marked price, the article is sold at 100 − 12 = $88.
i.e., 0.8S = $88.
or S = 88/0.8 = $110.
If the merchant sells at 95% of the marked price, then the new selling price of the article is 95% of $110 = $104.5

The profit made = 95% of Selling Price − Cost Price = 104.5 − 100 = $4.5.
% Profit = profit/cost price = 4.5/100 = 4.5%
The merchant made 4.5% profit

Choice E is the correct answer.

5x + 4|y| = 55
The equation can be rewritten as 4|y| = 55 - 5x.
Inference 1: Because |y| is non-negative, 4|y| will be non-negative.
Therefore, (55 - 5x) cannot take negative values.

Inference 2: Because x and y are integers, 4|y| will be a multiple of 4.
Therefore, (55 - 5x) will also be a multiple of 4.

Inference 3: 55 is a multiple of 5. 5x is a multiple of 5 for integer x.
So, 55 - 5x will always be a multiple of 5 for any integer value of x.

Combining Inference 2 and Inference 3: 55 - 5x will be a multiple of 4 and 5.
i.e., 55 - 5x will be a multiple of 20.

Integer values of x > 0 that will satisfy the condition that (55 - 5x) is a multiple of 20:

1. x = 3, 55 - 5x = 55 - 15 = 40.
2. x = 7, 55 - 5x = 55 - 35 = 20
3. x = 11, 55 - 5x = 55 - 55 = 0.
When x = 15, (55 - 5x) = (55 - 75) = -20.
Because (55 - 5x) has to non-negative, x = 15 or values greater than 15 are not possible.
So, x can take only 3 values viz., 3, 7, and 11.

Possible values of y when x = 3, x = 7, and x = 11

We have 3 possible values for 55 - 5x. So, we will have these 3 values possible for 4|y|.
Possibility 1: 4|y| = 40 or |y| = 10. So, y = 10 or -10.
Possibility 2: 4|y| = 20 or |y| = 5. So, y = 5 or -5.
Possibility 3: 4|y| = 0 or |y| = 0. So, y = 0.
Number of values possible for y = 5.

The correct choice is (C) and the correct answer is 5.

Step 1: Prime factorize the given expression

a * 4³ * 6² * 13¹¹ can be expressed in terms of its prime factors as a * 2⁸ * 3² * 13¹¹

Step 2: Find factors missing after excluding 'a' to make the number divisible by both 11² and 3³

11² is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 11² is a factor of the number, 11² should be a part of 'a'

3³ is a factor of the given number.
If we do not include 'a', the number has only 3² in it.
Therefore, if 3³ has to be a factor of the given number 'a' has to contain 3¹ in it.

Therefore, 'a' should be at least 11² * 3 = 363 if the given number has 11² and 3³ as its factors.

The question is "what is the smallest possible value of 'a'?"
The smallest value that 'a' can take is 363

Choice C is the correct answer.

Step 1: Compute Total Distance Travelled

Average speed of travel =
Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.
Distance covered in the first 2 hours = speed × time = 40 × 2 = 80 miles.
Distance covered in the next 3 hours = speed × time = 80 × 3 = 240 miles.
Therefore, total distance covered = 80 + 240 = 320 miles.

Step 2: Compute Average Speed

Total time taken = 2 + 3 = 5 hours.
Total distance travelled = 320 miles.

Choice D is the correct answer.

The cost price of 1 apple =
Because Sam wishes to make a profit of 25%, selling price per apple should be 0.10 + 25% of 0.10
= 0.1 + 0.025 = $0.125.
If the selling price of 1 apple is $0.125, the selling price of a dozen apples = 12 × 0.125 = $1.5

Selling price of a dozen apples is $1.5

Choice D is the correct answer.

In quadratic equations of the form ax² + bx + c = 0,  represents the sum of the roots of the quadratic equation and c/a represents the product of the roots of the quadratic equation.

In the equation given a = 1, b = b and c = 72
So, the product of roots of the quadratic equation = 7/21 = 72.
And the sum of roots of this quadratic equation = −b/1 = -b.

We have been asked to find the number of values that 'b' can take.
If we list all possible combinations for the roots of the quadratic equation, we can find out the number of values the sum of the roots of the quadratic equation can take.
Consequently, we will be able to find the number of values that 'b' can take.

The question states that the roots are integers.
If the roots are r₁ and r₂, then r₁ * r₂ = 72, where both r₁ and r₂ are integers.
Possible combinations of integers whose product equal 72 are: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12) and (8, 9) where both r₁ and r₂ are positive. 6 combinations.

For each of these combinations, both r₁ and r₂ could be negative and their product will still be 72.
i.e., r₁ and r₂ can take the following values too: (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12) and (-8, -9). 6 combinations.

Therefore, 12 combinations are possible where the product of r₁ and r₂ is 72.
Hence, 'b' will take 12 possible values.

Alternative method

If a positive integer 'n' has 'x' integral factors, then it can be expressed as a product of two number is x/2 ways.

So, as a first step let us find the number of factors for 72.
Step 1: Express 72 as a product of its prime factors. 2³ * 3²
Step 2: Number of factors = (3 + 1)*(2 + 1) = 12 (Increment the powers of each of the prime factors by 1 and multiply the result)
i.e., 72 has a 12 positive integral factors.
Hence, it can be expressed as a product of two positive integers in 6 ways.

For each such combination, we can have a combination in which both the factors are negative.

Therefore, 6 more combinations are possibile, taking it to a total of 12 combinations.

Choice B is the correct answer.

Find Time Travelled at 60 mph

Let Jane travel 'x' hours at 60 miles per hour.
As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.

Distance covered at 60 miles per hour = Speed × time = 60 × x = 60x miles.
Distance covered at 80 miles per hour = Speed × time = 80 (5 - x) = 400 - 80x miles.

Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.
Therefore, total distance = 60x + 400 - 80x.
Total distance travelled = 340 miles.

Therefore, 340 = 60x + 400 - 80x
20x = 60 or x = 3 hours.

Choice B is the correct answer.

Step 1: Assume a value for cost price

Let the cost price of 1 article be $1.
Therefore, cost price of 20 articles = 20 × 1 = $20
The selling price of 25 articles = cost price of 20 articles = $20.

Step 2: Compute the profit made on sale of 25 articles

Let us find the cost price of 25 articles.
Cost price of 25 articles = 25 × 1 = $25
Therefore, profit made on sale of 25 articles = Selling price of 25 articles − cost price of 25 articles
⇒ 20 − 25 = −$5

Step 3: What is the % Profit or Loss?

Because the profit is in the negative, the merchant has made a loss of $5.
Therefore, % loss = 

The merchant made a loss of 20%

Choice C is the correct answer.

Step 1: Understand the equation and the points (h, 0) and (k, 0)

The given equation is a quadratic equation. A quadratic equation when plotted on a graph sheet (x - y plane) will result in a parabola.
The roots of the quadratic equation are computed by equating the quadratic expression to 0. i.e., the roots are the values that 'x' take when y = 0
So, the roots of the quadratic equation are the points where the parabola cuts the x-axis.
The question mentions that the curve described by the equation cuts the x-axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic equation.
For quadratic equations of the form ax² + bx + c = 0, the sum of the roots = 
The sum of the roots of this equation is 
Note : Higher the value of 'b', i.e., higher the sum of the roots of this quadratic equation, lower the value of b.

For quadratic equations of the form ax² + bx + c = 0, the product of roots = c/a.
Therefore, the product of the roots of this equation = 256/1 = 256.
i.e., h × k = 256 h and k are both integers.
So, h and k are both integral factors of 256.

Step 2: List possible values of h and k and find the least value of ‘b’

This is the step in which number properties concepts kick in. 256 can be expressed as product of two numbers in the following ways:
1 × 256
2 × 128
4 × 64
8 × 32
16 × 16

The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.
∴ The least value possible for b is -257.

Choice D is the correct answer.

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

Choice E is the correct answer.

Step 1: Nature of Roots of Quadratic Equations Theory

D is the Discriminant in a quadratic equation.
D = b² - 4ac for quadratic equations of the form ax² + bx + c = 0.
If D > 0, roots are Real and Unique (Distinct and real roots).
If D = 0, roots are Real and Equal.
If D < 0, roots are Imaginary. The roots of such quadratic equations are NOT real.
The quadratic equation given in this question has real and equal roots. Therefore, its discriminant D = 0.

Step 2: Compute discriminant for the equation in terms of ‘m’ and find the value of ‘m’.

In the given equation x² - mx + 4 = 0, a = 1, b = -m and c = 4.
Therefore, the discriminant b² - 4ac = m² - 4(4)(1) = m² - 16.
The roots of the given equation are real and equal.
Therefore, m² - 16 = 0 or m² = 16 or m = +4 or m = -4.

Choice (D) is the answer to this quadratic equations question.

The group comprises 30 friends.
When the football coach is also included, the average weight of the group becomes 31 kg.
As the new average is 1 kg more than the old average, old average without including the football coach = 30 kg.

Standard Framework to Solve Averages Questions

961 - 900 = 61 kg

The total weight of the 30 friends without including the football coach = 30 * 30 = 900.
After including the football coach, the number of people in the group increases to 31 and the average weight of the group increases by 1 kg.

Therefore, the total weight of the group after including the weight of the football coach = 31 * 31 = 961 kg.
Therefore, the weight of the football coach = 961 - 900 = 61 kg.

Choice B is the correct answer.

Approach to solve: If 1.5 is a root of the quadratic equation, substituting x = 1.5 in the equation will satisfy the equation.

The given quadratic equation is x² + mx + 24 = 0
Substitute x = 1.5 in the above equation because 1.5 is a root of the equation.
(1.5)² + 1.5m + 24 = 0
2.25 + 1.5m + 24 = 0
1.5m = -26.25 Or m = −26.251.5−26.251.5 = -17.5

Alternative Method

Step 1: Sum and Product of Roots of Quadratic Equations Theory

For quadratic equations of the form ax² + bx + c = 0, whose roots are α and β,
Sum of the roots, α + β = , and product of the roots, αβ = c/a.
From the question stem, we know that one of the roots is 1.5. Let α be 1.5.

Step 2: Compute the second root of the equation

Product of the roots of the quadratic equation x² + mx + 24 = 0 is c/a = (24/1) = 24.
i.e., α * β = 24 where α is 1.5.
1.5 * β = 24
β = (24/1.5)
β = 16

Step 3: Compute the value of ‘m’

In the given equation, m is the co-efficient of the x term.
We know that the sum of the roots of quadratic equations of the form ax² + bx + c = 0 is −b/a = −m/1 = -m
Sum of the roots = 16 + 1.5 = 17.5
Sum of the roots = -m
If –m = 17.5, the value of m = -17.5

Choice D is the correct answer.

The credited answer is choice (D). If the town of Dryadia really does flood, then that’s the reason insurers won’t write flood insurance for it! Therefore, the “only reason” cannot be “its similarity to Bayside in terms of where it is situated in the river valley.” Choice (D), if true, obliterates the argument, so this is the best answer.

The argument say that “most insurers” don’t write flood insurance in either town, but if most don’t, this implies that some do. Therefore, choice (A) is actually expected from the argument and does not challenge it at all. Choice (A) is incorrect.

Choice (B) would not be surprising and could be perfectly consistent with the argument. We know Bayside had “catastrophic flooding“, but we don’t know for a fact that every single house was flooded—maybe or maybe not. If some houses were not flooded, it sounds as if the insurers don’t write flood insurance for any house in Bayside, so even those houses that never flooded could not buy flood insurance. Therefore, this would validate (B) without threatening the argument in any way. Choice (B) is incorrect.

Choice (C) is irrelevant. Even if no resident in absolutely any other town up and down the Katonic River Valley can buy flood insurance, that doesn’t necessarily shed light on why folks in a town in a completely different river valley can’t buy insurance. Choice (C) is incorrect.

Choice (E) is too general and vague. Yes, perhaps there are many ways a house can be flooded, and correspondingly, perhaps there are many reasons why an insurer would deny any particular house flood insurance. Even if this is true, it doesn’t shed any light on exactly why the folks in Dryadia have trouble getting flood insurance. Choice (E) is suggestive, but it doesn’t actually tell us anything. Choice (E) is incorrect.

Remains of prehistoric fire were found in Tanzania. The author says that Homo erectus made these fires, and that there’s no reason to assume Homo ergaster did. What is a necessary assumption?

The credited answer is choice (A). Homo erectus had to be as far south as Tanzania—if they were not, there would be no way they could have made those fires there, which would seem to indicate that Homo ergaster made them after all. Negating this statement devastates the argument, which is a confirmation that we have an assumption.

Whatever might have caused Homo erectus to master fire doesn’t clarify who made those fires in Tanzania: Homo erectus or Homo ergaster? Choice (B) is not correct.

Suppose Homo ergaster would have derived as much benefit from the master of fire as did the Homo erectus, or even more benefit. That fact, by itself, would imply nothing about which one of these species created those fires in Tanzania. Denying this doesn’t change the validity of the argument. Choice (C) is not correct.

Choice (D) is intriguing, because it may be true. Both Homo erectus and Homo ergaster evolved from Homo habilis, so it’s quite likely that the Homo habilis was the sole source of cultural knowledge for either of these species. BUT, we know that Homo erectus, presumably without the benefit of cultural knowledge about fire, was able to master fire. If Homo erectus did that, why couldn’t Homo ergaster? In other words, the limits of the cultural knowledge inherited does not necessarily set limits on what these human species could achieve. Therefore, we can draw no conclusion with respect to this argument. Choice (D) is not correct.

If Choice (E) were true, it would support the argument, but a supporting statement is not necessarily an assumption. We have to use the Negation Test. Suppose Homo ergaster was all over in Tanzania, before & during & after the time that those fires were created. Would that prove Homo ergaster started those fires? Not necessarily. It could still be true that both Homo ergaster and Homo erectus occupied that region, that only the latter had mastered fire, and therefore, that the later had to start those fires in Tanzania. Thus, we can deny choice and it doesn’t necessarily contradict the argument. Therefore, it is not an assumption. Choice (E) is not correct.

This is an EXCEPT question. Four of the answer will be perfectly valid explanations, and these will be incorrect. One of the answers will not be good explanation—either it will be irrelevant, or it may even suggest a rise instead of a decline; this oddball choice will be the correct answer.

The credited answer is (B). The new filing system, in essence, never misses the report of a violent crime. This at least implies that perhaps the previous filing system missed some violent crimes on occasion—for whatever reason, some violent crimes that took place slipped through the cracks and failed to be reported. Well, if we were not reporting everything before, and are reporting everything now, if anything this might suggest an increase in the number of reported violent crimes. It most certainly would not, by itself, explain a decrease. This is not in any way a good explanation, so this the correct answer.

We know, over the past decade, “the average income in the city has risen substantially” and “a tremendous amount of capital has flowed into city,” both of which indicate conditions of prosperity. Therefore, according to choice (A), white-collar crimes would increase, and street-crimes would decrease, with a concomitant drop in violent crimes. Choice (A) is a valid explanation, so it’s an incorrect answer.

If the state kept convicts in jail longer, that would mean fewer of them would be back out on the streets committing felonies, most of which are violent. Therefore, it would lead to a drop in the number of violent crimes. Choice (C) is a valid explanation, so it’s an incorrect answer.

Better police and better crime detection means more arrests and fewer violent crimes. Therefore, it would lead to a drop in the number of violent crimes. Choice (D) is a valid explanation, so it’s an incorrect answer.

Better lighting at night and security cameras have some effect in reducing crime. Choice (E) is a valid explanation, so it’s an incorrect answer.

The credited answer is choice (D). If the researcher was able to conclude anything about how an impulse purchase made someone feel, then the researcher first had to know that it was an impulse purchase, that is, that the purchase was not planned. If the researcher had no way to determine whether a purchase was planned or unplanned, then the researcher would have no way of determining which purchases were impulse purchases.

We know the consumer find the impulse purchase of a luxury item more exciting than the planned purchases. We don’t necessarily know how exciting the impulse purchase of an essential need is—maybe it’s less exciting than the impulse purchase of a luxury item, or maybe it’s just as exciting. We suspect from real life that this may be true, but we cannot determine this from information in the prompt, so it can’t be the answer to a “must be true question.” Thus, choice (A) is incorrect.

We only know about the excitement brought about by an impulse purchase of a luxury item, but we have no information about what happens if a purchase is planned but not made. Choice (B) inappropriate extends the pattern into situations the prompt doesn’t cover at all. Choice (B) is incorrect.

We know that the impulse purchase of a luxury item is exciting, but we don’t know whether this is sufficient inducement for a person seeking excitement to make this kind of purchase frequently. The expense, for example, might be a mitigating factor. We can conclude nothing for certain about this, so choice (C) is incorrect.

This is a tempting one—we certainly might suspect that the luxury items of higher price would be bought as impulse purchases less frequently. We might suspect this, but notice that the prompt says nothing about high price vs. low price items. This answer choice invites us to bring in irrelevant outside knowledge, so, like (A), it can’t be the answer to a “must be true question.” Choice (E) is incorrect.

The author makes it clear in the first line of the passage that the study of Physics is profitable to everyone and then provides examples of how the same would benefit our Members of Parliament as well as the common man. Hence (C) is the best answer
A: The author makes no such extreme advocacy in the passage
B: While the passage does discuss this, the primary purpose of the entire passage is broader than just doing this
D: The author makes no such proposal
E: Again a specific detail from the passage but the primary purpose of the entire passage is broader than just doing this

The opening para clearly states that Members of Parliament are at times called upon to legislate on matters that they are ignorant of. Thus it is not a prerequisite that they have to be knowledgeable about the matter on which they are legislating i.e. (D) should be the correct answer
A: Extreme. It's true that some of them are ignorant of physics but this cannot be generalised to the entire group
B: Opposite as explained above
C: No such preference is mentioned in the passage
E: While this may be true in the real world, there is nothing in the passage to suggest the same

According to the last para, the knowledge of Physics can help keep temptation at bay by providing man another pursuit to channelize his energies on and NOT ‘by educating him about the negative aspects of temptation’. Hence (B) should be the correct answer
A: This is the main idea of the passage
C: This can be inferred from these lines in the 2nd para – ‘A man's reformation oftener depends upon the indirect, than upon the direct action of the will. The will must be exerted in the choice of employment which shall break the force of temptation by erecting a barrier against it’
D and E: This is the gist of the 2nd para

Step 1: 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.

Step 2: 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.

Step 1: Analyzing the Argument

The argument presents a contradiction in the behavior of college welfare-aid applicants. While they understate the extent to which they have certain items, in order to maximize the loan, they also seem to overstate the extent to which they have some items.

To resolve the discrepancy, the correct answer option must explain their motivation to overstate certain things. Why they understate certain items is explained in the argument itself - to maximize the amount of loan. So, even though understating can possibly maximize their loan, why do many of these applicants overstate some items? That is the question that the correct option must answer.

Step 2: Process of Elimination

• Option (A) does not work for a couple of reasons. The option states that the city wants people to already have certain things. That is contrary to the very notion of welfare-aid. Moreover, if the city just wants people to already have certain things, why not just claim that they have a TV? The option does not specify what the city expects the people to already have.

• Option (B) explains why candidates for aid would understate the extent to which they have certain things. But why would they claim to have running water when they do not? If option (B) were true, would not their application be treated even more favourably if they do not have water. Essentially, the option repeats one part of what is already given in the argument and provides no justification for the other part.

• Option (D) has no impact on the argument. What does the percentage of people understating or overstating matter when attempting to explain WHY they do so?

• Option (E) like Option (D), has no impact on the argument. Whether the people were the same or different does not explain WHY they under or overstated what they had.

• Option (C) explains why they would overstate certain things such as running water - they were too embarrassed to confide that they did not have necessities. However, they understated other things to maximize aid.

Choice C is the correct answer.