The Ultimate Q51 Guide [Expert Level]

[GMAT math practice question]

Triangle ABC is a right triangle with ∠C = 90. What is the length of AB?

1) The area of ABC is 35.
2) The length of the base is 4 less than twice of the height.

=>



Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since a triangle has three variables and we have 1 equation from a right angle, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)



Then we have (1/2)(x)(2x - 4) = 35 or x^2 - 2x - 35 = 0
We have (x + 5)(x - 7) = 0 by factoring, and x = 7 since x > 0.
Thus, BC = 2*7 – 4 = 14 – 4 = 10.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

[GMAT math practice question]

(Algebra) What is x^2 + y^2?

1) x + y = 2√3
2) √3x - √2y=5

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 2 variables (x and y) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

When we subtract √3 times the equation of condition 1) from the equation of condition 2), we have
√3x - √2y - √3(x + y) = 5 - √3(2√3)
√3x - √2y - √3x - √3y = 5 – 6
√2y - √3y = -1
√3y - √2y = 1
(√3 + √2)y = 1
y = 1/(√3 + √2)
y = √3 - √2.

Then we have
x + y = 2√3
x = 2√3 – y
x = 2√3 - (√3 - √2)
x = 2√3 - √3 + √2
x = √3 + √2.

x^2 + y^2 = (x + y)^2 – 2xy
= (√3 + √2 + √3 - √2)^2 – 2(√3 + √2)(√3 -√2)
= (2√3)^2 – 2(3 - √6 + √6 - 2)
= 4(3) - 2(1)
= 12 – 2
= 0

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

[GMAT math practice question]

(algebra) If x^2 - 4x + 1 = 0, what is x^2 + 1/x^2?

A. 14
B. 16
C. 18
D. 20
E. 22

=>

x^2 - 4x + 1 = 0
x – 4 + 1/x = 0 (dividing both sides by x)
x + 1/x = 4 (adding 4 to both sides)
(x+1/x)^2 = 16 (squaring both sides)
x^2 +2x(1/x) + 1/x^2 = 16 (foiling the left side)
x^2 + 1/x^2 + 2 = 16 (simplifying)
x^2 + 1/x^2 = 14 (subtracting 2 from both sides)

Therefore, A is the answer.
Answer: A

[GMAT math practice question]

(Function) f(x) and g(x) are functions. What is the value f(3) + g(3)?

1) f(x + g(y)) = ax + y + 1 where a is a constant.
2) f(0) = -2, g(0) = 1.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have 3 variables (x, y, and a) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
When we substitute 0 for y, we have f(x + g(0)) = f(x+1) = ax + 1.
Then, we have f(0) = f((-1) + 1) = a(-1) + 1 = 1 – a = -2 or a = 3.
f(3) = f(2+1) = 3*2+1 = 7.
We have f(x + g(y) – 1 + 1) = 3(x + g(y) - 1) + 1 = 3x + 3g(y) - 2 = 3x + y + 1 or 3g(y) = y – 3.
Then g(y) = y/3 + 1 and g(3) = 2.
Thus f(3) + g(3) = 7 + 2 = 9.

Since both conditions together yield a unique solution, they are sufficient.
Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

Why cant we use 30-60-90 triangle method, A is clearly divided in the ratio of 2:1 ?

√
[GMAT math practice question]

(Number Properties) What is the solution of (x, y)’s satisfying √500 = √x +√y and x < y?

1) x and y are positive integers.
2) x = 5t^2 with 0 < t < 5.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 1 variable (n) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Condition 1)
x = 5 = 5*1^2, y = 5*9^2 = 405 and x = 5*2^2, y = 5*8^2 = 320 are possible solutions.

Condition 2)
x = 5 = 5*1^2, y = 5*9^2 = 405 and x = 5*2^2, y = 5*8^2 = 320 are possible solutions.

Conditions 1) & 2)

x = 5 = 5*1^2, y = 5*9^2 = 405 and x = 5*2^2, y = 5*8^2 = 320 are possible solutions.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.

[GMAT math practice question]

(Statistics) The standard deviation of x1, x2, …, x5 is 2√2. What is the standard deviation of √2x1, √2x2, …, √2x5?

A. 0
B. 1
C. 2
D. 3
E. 4

=>

Remind the property that S(aX+b) = |a|S(X) where S(X) is the standard deviation of set X and X is a data set.

S(√2x1, √2x2, …, √2x5) = √2S(x1,x2,x3,x4,x5) =√2*(2√2) = 4.

Therefore, E is the answer.
Answer: E

[GMAT math practice question]

(Number Properties) a, b, and c are 3 different unit numbers. What is the 3-digit number abc?

1) The 5-digit number ababc is a multiple of 12.
2) The 2-digit number ab is equal to c^2.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 3 variables (a, b, and c) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Since the 5-digit number ababc is a multiple of 12, it is a multiple of both 3 and 4. It means we have a + b + a + b + c = 2a + 2b + c, which is a multiple of 3, and 10b + c is a multiple of 4 since we can check the multiplicity of 3 with the sum of all digits and the multiplicity of 4 with the last two digits.

Since the 2-digit number ab is equal to c^2, we have 10a + b = c^2.
Then, the possible solutions of (a, b, c) are (1, 6, 4), (4, 9, 7), (6, 4, 8), (8, 1, 9) from condition 2) since a, b, and c are different and a is not equal to 0.

When we apply condition 1), we get a = 1, b = 6 and c = 4. This is because a + b + a + b + c = multiple of 3, and in this case 1 + 6 + 1 + 6 + 4 = 18, which is a multiple of 3.

Since both conditions together yield a unique solution, they are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
a = 1, b = 3, c = 2 and a = 7, b = 3, c = 2 are possible solutions.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
A = 1, b = 6, c = 4. and a = 4, b = 9, c = 7 are possible solutions from the above reasoning.

Since condition 2) does not yield a unique solution, it is not sufficient.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

[GMAT math practice question]

(Inequalities) What is the summation of the maximum and the minimum values of 6x - 37?

1) x satisfies 2 < √3(x-4) ≤ 5.
2) x is an integer.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 1 variable (x) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Condition 1)

2 < √3(x-4) ≤ 5
=> 4 < 3(x - 4) ≤ 25 (squaring)
=> 4/3 < x - 4 ≤ 25/3 (dividing by 3)
=> 16/3 < x ≤ 37/3 (adding 4)

Then even though x has a maximum value, x doesn’t have a minimum value.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)

Since condition 2) does not yield a unique solution; obviously, it is not sufficient.

Conditions 1) & 2)

Since we have 16/3 < x ≤ 37/3 from condition 1), the possible values of x are 6, 7, 8, …, 12.
Then the maximum and minimum values of x are 6 and 12, respectively.
Thus, their sum is 6 + 12 = 18.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C


If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.

[GMAT math practice question]

(Number Properties) x is a 3-digit positive integer. What is the value of x?

1) x is a multiple of 9 and √3x is an integer.
2) x is less than 200.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have a three-digit integer, we have 3 variables, and E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Since √3x is an integer, we have 3x = k^2 for some integer k.
Then k must be a multiple of 3, and we have k = 3n for some integer as well since 3 is a prime number.
Thus, we have 3x = k^2 = (3n)^2 = 9n^2 or x = 3n^2.
Since x is a 3-digit integer less than 200, we have 100 ≤ x = 3n^2 < 200 or 33.3 ≤ n^2 < 66.7 (dividing all terms by 3).
Then we have 34 ≤ n^2 ≤ 66 (because the answer is an integer according to the original condition) and squares between 34 and 66, inclusive are 36, 49, and 64.
The possible values of x are 3*36 = 108, 3*49 = 147 and 3*64 = 192.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

[GMAT math practice question]

(Algebra) What is the value of x^5 + y^5?

1) x + y = 3.
2) xy = 2.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have 2 variables (x and y) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

We have x = 1, y = 2 or x = 2, y = 1.
Then we have x^5 + y^5 = 33 for both cases.
Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

[GMAT math practice question]

(Algebra) x and y are positive integers satisfying 0 < x - √3y < 1 and b is the decimal portion of (x + √3y)3. What is the value of (x - √3y)3 in terms of b?

A. b
B. -b
C. 1 + b
D. 1 - b
E. 3b

=>

Assume a is the decimal portion of (x - √3y)^3.
Since the integer portion of (x - √3y)^3 is 0, we have a = (x - √3y)^3.
If c is the integer portion of (x + √3y)^3, we have (x + √3y)^3 = c + b.
Then, we have (x - √3y)^3 + (x + √3y)^3 = 2(x^3 + 9xy^2) = a + c + b.
a + b = 2(x^3 + 9xy^2) - c
Since x, y, and c are positive integers, a + b is an integer.
Since we have 0 < a < 1 and 0 ≤ b < 1, we have 0 < a + b < 2.
Thus a + b = 1.
(x - √3y)^3 = a = 1 - b.

Therefore, D is the answer.
Answer: D

[GMAT math practice question]

(Algebra) x, y, and z are real numbers. What is the value of y/x?

1) x and y are positive numbers.
2) x/y=2y/x-z=2x+y/z.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 3 variables (x, y, and z) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

We have x^2 - zx = 2y^2 when we cross multiply x/y=2y/x-z.

We have 2xy + y^2 = zx when we cross multiply x/y=2x+y/z.

When we subtract the second equation from the first equation, we have
x^2 – zx – (2xy + y^2) = 2y^2 – zx
x^2 – zx – 2xy – y^2 = 2y^2 – zx (multiplying -1 through the bracket)
x^2 – zx – 2xy – y^2 – 2y^2 + zx = 0 (moving all terms to the left side of the equation)
x^2 - 2xy - 3y^2 = 0 (gathering like terms)
(x - 3y)(x + y) = 0 (factoring)
Since x > 0 and y > 0 from condition 1), we have x + y ≠ 0 and x = 3y.
Thus y/x = y/3y = 1/3.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

[GMAT math practice question]

(Number Properties) x in an integer. Is x a perfect square?

1) x is one greater than the product of 4 consecutive positive integers.
2) x is the sum of five consecutive odd numbers.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have 1 variable (x) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Condition 1)

Assume x = k(k + 1)(k + 2)(k + 3) + 1.
Then x = (k^2 + 3k)(k^2 + 3k + 2) + 1 = A(A + 2) + 1 = A^2 + 2A + 1 = (A + 1)2 for A = k^2 + 3k for an integer k.

Thus, x is a perfect integer, and the answer is ‘yes’.

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)

If x = 1 + 3 + 5 + 7 + 9 = 25, then x is a perfect integer and the answer is ‘yes’.
If x = 3 + 5 + 7 + 9 + 11 = 35, then x is not a perfect integer and the answer is ‘no’.

Since condition 2) does not yield a unique solution, it is not sufficient.

Therefore, A is the answer.
Answer: A

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.

[GMAT math practice question]

(Number Properties) Is 111…11 – 222…22 a perfect square, where 111…11 and 222…22 are n and m digit numbers, respectively?


1) n = 2m.
2) m = 5.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

111…11 – 222…22 = 999…99 / 9 – 2(999…99/9) = (10^n - 1)/9 – 2(10^m - 1) / 9
= [(10^n - 1) - 2(10^m - 1)] / 9
= [(10^n – 1 + 2*10^m + 2)] / 9
= [(10^2m – 2*10^m + 1)] / 9
= (10^m – 1)^2 / 9
= [(10^m – 1) / 3]^2, if n = 2m from condition 1).

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)

Since we don’t have any information about n, condition 2) does not yield a unique solution, and it is not sufficient.

Therefore, A is the answer.
Answer: A

Since both conditions together are trivial, C is not an answer. If one condition includes a ratio and the other condition just gives a number, the condition, including the ratio is most likely to be sufficient by Tip 4. This tells us that A is most likely to be the answer to this question.

[GMAT math practice question]

(Number Properties) x^3 + y^3 = A(x + y), x^2 + y^2 = B, where x and y are positive integers. What is the value of xy?
1) A - B = 36.
2) B = 97.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

We can simplify the equation x^3 + y^3 = A(x + y) found in the original equation as follows:
x^3 + y^3 = A(x + y)
=> (x + y)(x^2 – xy + y^2) = A(x + y) (factoring using the sum of cubes)
=> [(x + y)(x^2 – xy + y^2)] / (x + y) = A (dividing both sides by (x + y))
=> (x^2 – xy + y^2) = A (simplifying)

Since xy = x^2+xy+y^2 – (x^2+y^2) = (x^3+y^3)/(x+y) – (x^2+y^2) = A – B = 36, condition 1) is sufficient.

Condition 2)
Since x^2 + y^2 = 97, the possible pairs of (x, y) are (4, 9) and (9, 4).
If x = 4, y = 9, then we have xy = 36.
If x = 9, y = 4, then we have xy = 36.

Since condition 2) yields a unique solution, it is sufficient.

Therefore, D is the answer.
Answer: D

This question is a CMT 4(B) question: condition 1) is easy to work with, and condition 2) is difficult to work with. For CMT 4(B) questions, D is most likely the answer, since this question is an integer question.

Sir I am getting value of XY as -36 through first statement.
If you can explain whether negative sign is not considered in here or where I am lacking with in your given steps. That will be grateful. Thank You.

Posted from my mobile device