GMAT Classic Mock Test - 1 - GMAT MCQ

Since the numerator of aU of the fractions in the answer choices is 0.03, the least of the fractions will, be the fraction with the greatest denominator. The greatest denominator is 7.1, and so the least of the fractions is 0.03/7.1

Substitute 140 for R in the given equation and solve for x.
140 = 176 - 0.8x
-36 = -0.8x
-36/-0.8 = x
45 = x

Arthmetic means = sum of total numbers /numbers
(j + j + 5 + 2j-1 + 4j - 2 + 5j - 1)/5 = 8
(13j + 5 - 4)/5 = 8
(13j + 1) = 40
13j = 40 – 1 = 39
j = 39/13 = 3 ans.

The area of a rectangle can be found by multiplying the length and width of the rectangle. Therefore, the combined area, in square meters, of the 2 rectangular tracts of land is (300)(500) + (250)(630) = 150,000 + 157,500 = 307,500.

We can create the following equations:

A = 2E
B = E + 3
C = 2B
D = B + E
Let’s substitute B = E + 3 in the last two equations:
C = 2(E + 3) = 2E + 6
D = (E + 3) + E = 2E + 3
Now, we have everything expressed in terms of E; thus it just remains to compare the quantities 2E, E + 3, 2E + 6, 2E + 3 and E. Since E is the number of properties sold by Ellen, it is a positive integer. Thus, the greatest expression among the five possibilities is 2E + 6, which belongs to Cary.

Andrew participated in 1 event and scored 9 points, so his overall score was 9/1 + 1 = 10. Jason participated in 3 events and scored 5 + 6 + 7 = 18 points, so his overall score was 18/3 + 3 = 9. The ratio of Andrew’s overall score to Jason’s overall score was 10/9.

The work plan requires that the team produce an average of 200 items per day in September. Because the team has only produced an average of 150 items per day in the first half of September, it has a shortfall of 200 - 150 = 50 items per day for the first half of the month. The team must make up for this shortfall in tire second half of the month, which has an equal number of days as the first half of the month. The team must therefore produce in the second half of the month an average amount per day that is 50 items greater than the required average of 200 items per day for the entire month. This amount for the second half of September is 250 items per day.
The correct answer is B.

The vendor’s gross profit on the sale of the shirts is equal to the total revenue from the shirts that were sold minus the total cost for all of the shirts. The total cost for all of the shirts is equal to the number of shirts the vendor purchased multiplied by the price paid by the vendor for each shirt: 1,000 x $5 = $5,000. The total revenue from the shirts that were sold is equal to the total revenue from the 600 shirts sold for $12 each plus the total revenue from the 300 shirts that were sold for $4 each: 600 x $12 + 300 x $4 - $7,200 + $1,200 - $8,400. The gross profit is therefore $8,400 - $5,000 = $3,400.
The correct answer is E.

Let number of plants ordered be: n

3n + 0.05(3n) + 6.95 = 69.95

1.05 (3n) = 69.95 - 6.95 = 63

n = 63 / (3 x 1.05) = 20

Therefore the company ordered 20 plants.

Maureen’s initial investment was $16,800, and it has decreased by 5.8%. Its current value is therefore (100% - 5.8%) = 94.2% of $16,800, which is equal to 0.942 x $16,800. To make the multiplication simpler, this can be expressed as $(942 X 16.8). Thus multiplying, we obtain the result of $15,825.60.
The correct answer is C.

Maureen’s initial investment was $16,800, and it has decreased by 5.8%. Its current value is therefore (100% - 5.8%) = 94.2% of $16,800, which is equal to 0.942 x $16,800. To make the multiplication simpler, this can be expressed as $(942 x 16.8). Thus multiplying, we obtain the result of $15,825.60.

The company’s gross profit on the 500 toy trucks is the company’s revenue from selling the trucks minus the company’s cost of producing the trucks. The revenue is (500)($10.00) = $5,000.The cost for the first 100 trucks is (100)($5.00) = $500, and the cost for the other 400 trucks is (400)($3.50) = $1,400 for a total cost of $500 + $1,400 = $1,900. Thus, the company's gross profit is $5,000 - $1,900 = $3,100.
The correct answer is C.

If, during the first hour, 25 percent of the total displays were assembled, then 280(0.25) = 70 displays were assembled, leaving 280 - 70 = 210 displays remaining to be assembled. Since 40 percent of the remaining displays were assembled during the second hour, 0.40(210) = 84 displays were assembled during the second hour. Thus, 70 + 84 = 154 displays were assembled during the first two hours and 280 - 154 = 126 displays had not been assembled by the end of the second hour.

let's calculate the absolute values of the profits/losses for each division over the three consecutive years.

Here is the data provided:

• Division A:
  • 1991–1993: -0.4
  • 1992–1994: 0.5
  • 1993–1995: 4.5
• Division B:
  • 1991–1993: -1.3
  • 1992–1994: 4.9
  • 1993–1995: -3.5
• Division C:
  • 1991–1993: 8.7
  • 1992–1994: -0.2
  • 1993–1995: 3.4

Let's calculate the absolute value of the sums:

1. Division A:

   • 1991–1993: |-0.4| = 0.4
   • 1992–1994: |0.5| = 0.5
   • 1993–1995: |4.5| = 4.5

2. Division B:

   • 1991–1993: |-1.3| = 1.3
   • 1992–1994: |4.9| = 4.9
   • 1993–1995: |-3.5| = 3.5

3. Division C:

   • 1991–1993: |8.7| = 8.7
   • 1992–1994: |-0.2| = 0.2
   • 1993–1995: |3.4| = 3.4

Among these values, the smallest absolute value (closest to 0) is 0.2 for Division C for the years 1992–1994.

Therefore, the correct answer is:

Option E: Division C for 1992-1994

Note that this question asks for a specific number, not a ratio. Consequently, keep in mind that knowing y percent of the total staff is composed of women from outside the United States is not sufficient.

Evaluate Statement (1) alone.

• If 25% of the staff are men, 75% must be women.
• There is not enough information to determine the number of women from outside the United States. Statement (1) alone is NOT SUFFICIENT.

Evaluate Statement (2) alone

• Since 20 men from the U.S. represent 20% of the staff, the total staff is 100. We also know that there are 20 men from the U.S. and 2(20)=40 women from the U.S. for a total of 20+40=60 employees from the U.S. Consequently, 100-60=40 employees must be from outside the U.S.
• Since we cannot determine the breakdown of the 40 employees from outside the U.S., it is impossible to determine the number of women from outside the U.S.; Statement (2) alone is NOT SUFFICIENT.

Evaluate Statements (1) and (2) together.

• Fill in as much information as possible from Statements (1) and (2). We now know that there are a total .25(x) =. 25(100) = 25 men and .75(x) = .75(100) = 75 women.
• 35 members of the staff of Advanced Computer Technology Consulting are women from outside the United States.

Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, but Statements (1) and (2), when taken together, are SUFFICIENT, answer C is correct.

Given: Each student gets an equal number of candies and an equal number of few bars

Do not assume! Number of candies = Number of bars

To find out: The number of students in the class

Statement 1:

We know that each student received an equal number of candies and an equal number of bars.

Thus, the GCD of the number of candies and the number of bars is the largest possible number of students in the class.

180 = 2² × 3² × 5

40 = 2³ × 5

The terms common to both: 2²  5 = 20
⇒ GCD of 40 and 180 = 20

Thus, the number of students could be 20 or a factor of 20 (that is, 1, 2, 4, 5, 10):

Scenario #1

Number of students = 20 (Maximum possible number of students):

Number of candies received by each student: 180 / 20 = 9
Number of bars received by each student: 4 / 20 = 2

Scenario #2

Number of students = 10

Number of candies received by each student: 180 / 10 = 18
Number of bars received by each student: 40 / 10 = 4

Scenario #3

Number of students = 5

Number of candies received by each student: 180 / 5 = 36
Number of bars received by each student: 40 / 5 = 8

There are three more possible cases for the number of students, i.e. 4 or 2 or 1. Of these, the possibility of the number of students being 1 can be rejected because the question explicitly mentions students in the plural.

So, the number of students can be 20, 10, 5, 4, or 2.

Thus, there is no unique answer. – Insufficient

Statement 2:

There is no information about the number of candies and the number of bars distributed. – Insufficient

Statement 1 & 2 together:

Combining both statements, we find that since the total number of items received by each student is less than 20, the only possible scenario is Scenario #1, where:
i. the number of students is 20.
ii. Total number of items received by each student: 9 + 2 = 11< 20.
The total number of items received by each student in other scenarios is more than 20. – Therefore, we’ve arrived at a unique answer: the number of students is 20. Sufficient

Statement 1:

We are given that the combined price of 39 oranges and 36 apples is $111.

Looking at the numbers (13,12) in the question statement and (39,36) in Statement (1), it must click that 39 is 3 times of 13, and 36 is also 3 times of 12. Thus, we have:

The combined price of 39 (= 13 × 3) oranges and 36 ( = 12 × 3) apples is $111.

Thus, the combined price of 13 oranges and 12 apples is $111 / 3. - Sufficient

Note: Since in Data Sufficiency questions, you only have to assess whether a statement can lead you to a unique answer or not, do not waste time in calculating the exact answer. This is why the value $1113 has not been further simplified. There is simply no need to do so.

Statement 2:

We are given that the combined price of 3 oranges and 2 apples is $7.

Getting a cue from dealing with Statement (1), we see that 12 is 6 times of 2, but 13 is not 6 times of 3. So, by multiplying the information "the combined price of 3 oranges and 2 apples is $7" by 6, we cannot reach "the combined price of 13 oranges and 12 apples…"

We would rather get:

6 × (Combined price of 3 oranges and 2 apples is $7)
= Combined price of 18 oranges and 12 apples is $42, which is not asked for. - Insufficient

Statement 1:

We are given that the combined price of 3 oranges and 2 apples is $7:

3(Price of 1 orange)+2(Price of 1 apple)=7
This is a linear equation with two variables. From it alone, we cannot get the unique value of the price of an orange.

Let's take two cases.

1. Say the price of an apple = $1, then the price of an orange is 

2. Say the price of an apple = $2, then the price of an orange is 

No unique value of the price of an orange. Insufficient!

Statement 2:

Merely knowing that the price of an orange and the price of an apple are integers is not sufficient.

Statement 1 & 2 together:

Say the price of an orange = x and the price of an apple = y;

Thus, from Statement 1, we get,

3x + 2y = 7
From Statement 2, we know that the price of an orange and the price of an apple are integers, thus they must be positive. That is,

x ≥ 1
y ≥ 1
Let's assume a few possible integer values of the price of an apple (y) and see whether it results in a unique positive integer value of the price of an orange (x).

We get only one valid value of x, i.e. the price of an orange = $1, a unique value.

So, our analysis has yielded a unique value of x (=1). Sufficient!

We are given that the amount spent on buying Product X, Product Y, and Product Z is $500,000.

Say the amounts spent on buying Product X, Product Y, and Product Z are x,y, and z, respectively.

⇒ x + y + z = 500,000 (Equation 1)

We have to determine whether z>200,000.

Statement 1:

We are given that the sum the trader paid for Product X and Product Y combined was 3 times the sum the trader paid for Product X.

⇒ x + y = 3x
y = 2x (Equation 2)

Substituting equation (2) in equation (1):

⇒ x + 2x + z = 500,000
⇒ 3x + z = 500,000
We have an unknown x. So, we cannot determine whether z > 200,000. Insufficient!

Statement 2:

We are given that the trader paid more to purchase Product Z than to purchase Product Y.

⇒ z > y (Inequality 3)

With the help of equation (1): x + y + z = 500,000 and inequality (3): z > y, we cannot determine whether z > 200,000. Insufficient!

Statement 1 & 2 together:

Let's put down the two equations (1) and (2) and the inequality (3).

x + y + z = 500,000 (Equation 1)

y = 2x (Equation 2)

z > y (Inequality 3)

Since equation (3) has only z and y variables, let's eliminate variable x from equation (1) and (2).

From equation (2), we have x = y/2. By plugging in the value x in equation (1), we get:

y/2 + y + z = 500,000
y + 2y + 2z = 1,000,000
3y + 2z = 1,000,000 (Equation 4)

Substituting (5) in (3):

5z > 1,000,000 
z > 200,000
So, the answer is 'Yes'. The two statements together are sufficient!

Alternate approach:

Alternate way of solving further after Equation (4): 3y + 2z = 1,000,000
Let's assume that y = z, and see what are their values. Say y = z = p
Thus, 3p+2p = 1,000,000
⇒5p = 1,000,000
⇒p = 200,000
Thus, y = z = 200,000;

However, this goes against the fact given in inequality (3): z > y.

Thus, y < 200,000 & z > 200,000. The answer is 'Yes'. Sufficient!

We are given that a teacher gave an equal number of pens, an equal number of pencils, and an equal number of erasers to each student of this class.

You must NOT assume:

(Number of pens per student) = (Numbers of pencils per student) = (Number of erasers per student)

The number of pens that a student - say Student A - got may be different from the number of pencils and from the number of erasers he got; however, every student in the class got as many pens as Student A gets (and likewise, as many pencils and erasers as Student A gets).

Let the total number of students in the class be n, and each student got x number of pens, y number of pencils, and z number of erasers. We have to find out n.

Statement 1:

Each student got pens, pencils, and erasers in the ratio 3:4:5, respectively.

Thus, we have:

x : y : z = 3 : 4 : 5
⇒ x = 3k, y = 4k, z = 5k,where k is a constant of proportionality.
However, we have no information on n. - Insufficient

Statement 2:

We know that the teacher distributed a total of 27 pens, 36 pencils, and 45 erasers.

Thus, nx = 27,ny = 36,nz = 45
We have no information about x, y, z.

Hence, we cannot determine the value of n. - Insufficient

Statement 1 & 2 together:

Substituting the values of x, or y, or z from Statement 1 in the information from Statement 2, we have:

nx = 27 = 3k
n = 9k
Since k is unknown, we cannot determine n.

The valid values of k can be 1, 3, and 9, rendering the values of n = 9, 3, and 1. (k cannot be greater than 9 because n, the number of students, cannot be a fraction. And, k cannot be a fraction, for example, 1/2 etc., because we know that x = 3k, y = 4k, & z = 5k. Since x, y, & z denote the number of items, they cannot be fractions. For x, y, & z to have integer values, k must be an integer.)

No unique value of n. - Insufficient

We have to find out whether 3x − 2y = 0.

Alternatively, we can write 3x − 2y = 0 as x = (2 / 3)y.

Thus, we have to determine whether x = (2 / 3)y.

Statement 1:

We are given that 27x³ − 8y3 = 0.

⇒ 27x³ = 8y³
⇒ x³ = (8 / 27)y³
⇒ x = 2 / 3y; taking the cube root of both the sides. (Remember that the real number x³ has only one real cube root.)

The answer is Yes. - Sufficient!

Statement 2:

We are given that 9x² − 4y² = 0
⇒ 9x² = 4y²
⇒ x² = (4 / 9)y²
⇒ x = ±2 / 3y; taking the square root of both the sides. (Remember that the positive number x² has two square roots, one positive and the other negative.)

If x = (2 / 3)y, the answer is Yes; however, if x = −(2 / 3)y, the answer is No.

No unique value of x. - Insufficient!

Statement 1:

We are given that Thrice the number of questions that David solved in the test was greater than 6 less than thrice the number of questions that Steve solved in the test.

⇒ 3x > 3y − 6
⇒ x > y − 2
We cannot determine whether x > y, since x is greater than a quantity y, which is reduced by a certain amount, 2.

Let us take an example.

Say y = 10, thus x > 10−2 ⇒ x > 8.

If x = 9, then x ≯ y and the answer is No. However, if x = 11, then x > y and the answer is Yes. No unique answer. Insufficient!

Statement 2:

We are given that Twice the number of questions that David solved in the test was greater than 4 less than twice the number of questions that Steve solved in the test.

⇒ 2x > 2y − 4
⇒ x > y − 2
This is the same inequality that we got in Statement 1. Insufficient!

Statement 1 & 2:

Since each statement renders the same inequality, even combining both the statements cannot help. Insufficient!

Conclusion:

Each statement renders that same inequality, thus combining both the statements will not help.

You may have deduced a wrong conclusion with the inequality x > y − 2.

We see that x is greater than a number y minus 2; thus, x may or may not be greater than y.

Had the situation been x > y + 2, then it's for certain that x > y; since x is greater than a number (y + 2), then x must be greater than a relatively smaller number y.

We are given that each of the 25 books on bookshelf X is thinner than each of the 25 books on bookshelf Y.

⇒ (Thickness of the thickest book on bookshelf X) < (Thickness of the thinnest book on bookshelf Y)
You must not assume that the thickness of each of the 25 books on bookshelf X is the same; they all may be of different thickness; they all may be of the same thickness or a few of them may be of the same thickness. The same goes for the books on bookshelf Y.

We are asked to determine whether the median thickness of the 50 books is less than 20 millimeters.

You must know that to find out the median of a dataset, the elements of the dataset must be arranged in an ascending or in a descending order.

Let's assume that that all the 50 books are arranged as per the ascending order of their thickness. All 25 books of bookshelf X would be on the left-hand side, arranged as per the increasing order of the thickness of books, and all 25 books of bookshelf Y would be on the right-hand side, arranged as per the increasing order of the thickness of books. Thus, in this ordered arrangement of the 50 books, the thickest book of bookshelf X (25th book in order) would be immediately left of the thinnest book of bookshelf Y (26th in order).

You must know that:

(Median value of a dataset) = (Value of the middlemost element)
When the number of elements in the dataset is even, the median is equal to the average of the values of the two middlemost elements.

Thus:

(the median thickness of 50 books)=(Average of the thickness of 25th book and the thickness of 26th book in the ordered arrangement)
We know that the 26th book is the 1st book on bookshelf Y.

So, to get the value of median thickness of 50 books, we must know that value of the thickness of the thickest book of bookshelf X and of the thinnest book of bookshelf Y.

Note: In the above analysis, we arranged the books on the two shelves in ascending order of their thickness. If you chose to arrange them in descending order of thickness instead, that is fine too. The analysis remains the same.

Statement 1:

The thickness of the thinnest book on shelf X = 2 millimeters

This information is of no use to us as we want the thickness of the 25th and the 26th book to calculate the median. - Insufficient

Statement 2:

(Thickness of the thinnest book on shelf Y) = (Thickness of the 26th book in ascending order of thickness) = 20-millimeters
Though we do not know the thickness of the 25th book, we can make a deduction about the median. The question does not ask the value of the median; it asks whether the median thickness of the 50 books is less than 20 millimeters. This is a "Yes/No" type of question.

Since (the thickness of 26th book) = 20 millimeters, and we're given that even the thickest book on bookshelf X is thinner than the thinnest book on bookshelf Y, we can write: (the thickness of 25th book) < 20 millimeters.

Say (the thickness of 25th book)=19.99 millimeters. Thus, Median
=19.99 + 20 / 2 < 20 millimeters. The answer is Yes. - Sufficient

We are given that the box has balls of three different colors - red, blue and green, and the number of balls of each color is at least one in count. Thus, the minimum number of balls in the box = 3.

Let's understand what the question asks.

When one ball is drawn,

Is "(Probability of drawing a red ball) = (Probability of drawing a blue ball) ≠ (Probability of drawing a green ball)"

Say, the probability of drawing a red ball = p(r); the probability of drawing a blue ball = p(b); and the probability of drawing a green ball = p(g).

The question asks,

Is p(r) = p(b) ≠ p(g)?

So, the question boils down to:

"Does the box has the number of red color balls equal to the number of blue color balls but NOT equal to the number of green color balls?"

Statement 1:

There are 5 balls in the box.

Let's distribute them in three color balls such that we have at least one ball of each color.

Scenario 1: Red color: 1 ball; Blue color: 1 ball; and Green color: 3 balls.

We have the number of red color balls equal to the number of blue color balls, and NOT equal to the number of green color balls; the answer is Yes.

Scenario 2: Red color: 2 ball; Blue color: 1 ball; and Green color: 2 balls.

We have the number of red color balls NOT equal to the number of blue color balls, but equal to the number of green color balls; the answer is No.

No unique answer. Insufficient.

Note: Other scenarios are possible too but we do not need to consider them all because from just two scenarios, we can already see that Statement 1 is not sufficient for a unique answer.

Statement 2:

Only with this information, we can decide that the probability that the drawn ball is green is NOT equal to the probability that the drawn ball is blue; however, we have no clue about the number of red balls; number of red balls may or may not be equal to number of blue balls. Insufficient.

Statement 1 & 2:

Both the scenarios discussed in Statement 1 are applicable here too. Insufficient.

Had Statement 2 been, "The number of green color balls is greater than the number of blue balls and greater than the number of red balls," Scenario 2 would not have been applicable here, thus the answer would then be C.

We are given that f(n) = (a)^6/n, where a is a constant.

We have to find out the value of f(1).

Statement 1:

Given that f(2) = 64
Thus, f(2) = (a)^6/2 = a³ = 64
⇒ a = (64)^1/3 = 4
Thus, f(1) = (a)^6/1 = a⁶ = 4⁶. - Sufficient

Statement 2:

Given that f(3) = 16
Thus, f(3) = (a)^6/3 = a² = 16
⇒ a = (16)^1/2 = ±4
Thus, f(1) = (a)^6/1 = a⁶ = (±4)⁶ = 4⁶. - Sufficient

In all of my classes and tutoring sessions, I emphasize how important it is to “spot the con” and to critically analyze your decision-making process when working through GMAT problems. This frequently missed question is a wonderful example of what happens when you don’t remain critical. In statement (1), you are given a piece of information that the test writers purposefully want you to determine is insufficient. You look at statement (1), glance at statement (2), and immediately realize that x and t could be positive or negative in statement (1) alone, making it insufficient. People feel good about themselves for identifying this fact and quickly pick (C), since adding statement (2) seems to guarantee that x and t are positive 2 and positive 3, respectively. 

Anytime the test writers can create a scenario in which you have a dopamine response and feel good about finding a trap, you are likely to stop being critical. The positive/negative issues present in this question are a shiny penny—so many people pick (C) because they only focus on the positive/negative ambiguity in statement (1), and statement (2) guarantees they are positive. However, when taken together, all that statements (1) and (2) tell you is that the ratio of x:t must be 2:3 and x and t must be positive. This still leaves an infinite number of possibilities for the two values: 2 and 3, 4 and 6, 6 and 9, 8 and 12, etc. Since the value for x cannot be determined, the correct answer is (E).

If both statements together still result in an infinite number of possibilities for the value of x, why do a majority of high-performing students still pick (C), thinking x must be 2? Because they don’t understand the con and they let their guard down! Just because you find one “con” in a question (in this example, the positive/negative issue), does not mean there aren’t others still present! 

This problem highlights how important it is to read carefully and to look for potential interpretation errors in GMAT math questions. It also shows how it is often easier to manipulate the question stems to match the statements in data sufficiency questions than to change the statements to match the questions (what you naturally want to do). Here is the incredibly well-made “con” in this question:
 A majority of high performing students do not properly interpret how to determine the cost—the instructions say $0.75 for the first 3 minutes NOT $0.75 per minute for the first three minutes. However, most people carelessly calculate the charge as if it were per minute. If you do that improper interpretation, then the question stem seems to be asking this in terms of cost: a 15-minute call would be 3 x ($0.75) + 12 ($0.20) or $2.25 + $2.40 = $4.65, so the question would be “Did the phone call cost more than $4.65?” Statement (1) would give you a definitive “No” to the question (cost would always be less than $4.65) and thus be sufficient. Statement (2) would allow for the cost to be both below and above $4.65, so the “Maybe” answer would make it insufficient. With the improper interpretation, you seem to have done everything correct when picking (A). But the correct answer is (B)!
The proper interpretation:
 The first three minutes in total cost $0.75 and each minute after the first three costs $0.20 per minute. A 15-minute call would cost $0.75 + 12 ($0.20) or $3.15. So, after changing the question to ask about cost (in order to match the statements) it becomes: Did the call cost more than $3.15?
 Now you see that statement (1) gives a maybe answer since it allows for both a yes and a no answer to the question. Statement (2), however, guarantees that the cost will always be greater than $3.15, so it is sufficient, yielding the correct answer of (B).

From the question, we know that both X and Y are distinct integers and their product is 30.
30 can be obtained as a product of two distinct integers in the following ways.

Values that satisfy X × Y = 30

Evaluate Statement (1) ALONE: X is an odd integer
From this statement, we know that the value of X is odd.
Therefore, X can be one of the following values: 1, -1, 3, -3, 5, -5.
So, using information in statement 1 we will not be able to deduce a UNIQUE value for X.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.

Evaluate Statement (2) ALONE: X > Y
From this statement, we know that the value of X > Y.
From the combinations listed in the table above, X can take more than one value. Here are two possibilities: X could be 10 and Y could be 3. Or X could be 30 and Y could be 1.
Hence, using information in statement 2, we will not be able to find a UNIQUE value for X.

Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.

Evaluate Statements (1) & (2) Together: X is an odd integer and X > Y
Values of X and Y that satisfy both the conditions are

More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using information provided in the two statements together, the given data is NOT sufficient.

Statements TOGETHER are NOT SUFFICIENT. Choice E is the answer.

Standard deviation = √Mean of squares of the numbers−square of mean of the numbers

Evaluating Statement (1) ALONE: The sum of p, q, r, and s is 24.
From the information in statement 1 we can find the mean of the four numbers to be 6 and the square of the mean of the numbers to be 36.
We need additional information to find the SD.
This statement does not provide any information about the mean of the squares of the numbers.

Statement 1 alone is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.

Evaluating Statement (2) ALONE: The sum of the squares of p, q, r, and s is 224.
Hence, the mean of the squares of the numbers is 56.
However, this statement does not provide any information about the square of the mean of the numbers.

Statement 2 alone is NOT sufficient.
Eliminate choice B. Choices narrow down to C and E.

Evaluating the statements together.
From statement 1 we know that the square of the means is 36.
From statement 2 we know that the mean of the squares is 56.
Using the formula,
Standard deviation = √Mean of squares of the numbers−square of mean of the numbers,
we can find the SD of the 4 numbers.

Statements together are sufficient. Choice C is the answer.