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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 09 Jul 2021, 00:34
Originally posted by MathRevolution on 08 Mar 2020, 20:04.
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[GMAT math practice question]

(Algebra) What is \((a-b)^2\)?

1) \(|a| = 4, |b| = 3\)

2) \(\frac{b}{a} < 0 \)
Show more

=>

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 (\(p\) and \(q\)) 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)

Since \(|a| = 4\), and \(|b| = 3,\) we have \(a = ±4\), and \(b = ±3\) from condition 1) and ab < 0 from condition 2).
Then we have \(a^2 = 16, b^2 = 9 \)and \(ab = -12.\)

Thus \((a - b)^2 = a^2 - 2ab + b^2 = 16 – 2(-12) + 9 = 49.\)

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.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 09 Mar 2020, 09:31
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[GMAT math practice question]

(Statistics) A company has \(2\) departments, department \(A\) has \(5\) employees, and department \(B\) has \(6\) employees. All employees of the company did some “push-ups”. What is the standard deviation of these \(11\) employees?

1) The average and the standard deviation of \(A\) are \(7\) and \(1\), respectively.
2) The average and the standard deviation of \(B\) are \(7\) and \(3\), respectively.
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[GMAT math practice question]

(Statistics) What is the average of x1, x2, …, x10?

1) The average of x1, x2, …, x8 is 5.
2) x9 = 9-x10.
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[GMAT math practice question]

(Statistics) What is the average of x1, x2, …, x10?

1) The average of x1, x2, …, x8 is 5.
2) x9 = 9-x10.
Show more


From statement 1:

x1 + x2 + x3 + ... + x8 = 5 * 8 = 40

However, there is no information about x9 and x10 - Insufficient

From statement 2:

x9 = 9 - x10

=> x9 + x10 = 9

However, there is no information about x1, x2, ... x8 - Insufficient

Combining both statements:

Adding both equations:

x1 + x2 + ... + x8 + x9 + x10 = 40 + 10 = 50

=> Mean = 50/10 = 5 - Sufficient

Answer C
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 04 Mar 2021, 03:24
Originally posted by MathRevolution on 12 Mar 2020, 01:22.
Last edited by MathRevolution on 04 Mar 2021, 03:24, edited 1 time in total.
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[GMAT math practice question]

(Statistics) A company has \(2\) departments, department \(A\) has \(5\) employees, and department \(B\) has \(6\) employees. All employees of the company did some “push-ups”. What is the standard deviation of these \(11\) employees?

1) The average and the standard deviation of \(A\) are \(7\) and \(1\), respectively.
2) The average and the standard deviation of \(B\) are \(7\) and \(3\), respectively.
Show more

=>

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 the standard deviations of two sets, we have 2 variables 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)
Assume A1, A2, … , A5 are the “push-up” numbers of the employees in department A and B1, B2, … , B6 are the “push-up” numbers of the employees in department B.
The combined average of departments A and B is
\(\frac{( 5*7 + 6*7 ) }{ 11} = 11*\frac{7}{11} = \frac{77}{11} = 7.\)

The variances of A and B are squares of the standard deviations of A and B, respectively.
The variance of A is { (A1-7)^2 + … + (A5-7)^2 } / 5 = 1 and we have { (A1-7)^2 + … + (A5-7)^2 = 5.
The variance of B is { (B1-7)^2 + … + (B6-7)^2 } / 6 = 1 and we have { (B1-7)^2 + … + (B6-7)^2 = 6.

The combined variance of sets A and B is
{ (A1-7)^2 + … + (A5-7)^2 + (B1-7)^2 + … + (B6-7)^2 } / 11
\(= \frac{{ 5 + 6 } }{ 11} = \frac{11}{11} = 1\).
The standard deviation of the sets A and B is the square root of the combined variance equal to 1.

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

Since this question is a statistics 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)
Since we don’t have any information about department B, it is not sufficient, obviously.

Condition 2)
Since we don’t have any information about department A, it is not sufficient, obviously.

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.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 12 Mar 2020, 01:23
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[GMAT math practice question]

(Algebra) What is the value of \(a^3 + a^2b + ab^2 + b^3\)?

1) \(a + b = 2\sqrt{2}, ab = 1\)

2) \(a = \sqrt{2}+1 \)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 04 Mar 2021, 03:25
Originally posted by MathRevolution on 12 Mar 2020, 01:24.
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[GMAT math practice question]

(Statistics) What is the average of x1, x2, …, x10?

1) The average of x1, x2, …, x8 is 5.
2) x9 = 9-x10.
Show more

=>

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.

Condition 1) tells us that ( x1 + x2 + … + x8 ) / 8 = 5 or x1 + x2 + … + x8 = 40.
Condition 2) tells us that x9 + x10 = 9.
Thus, when we consider both conditions together, we have ( x1 + x2 + … + x8 + x9 + x10 ) / 10 = (40 + 9) / 10 = 49/10 = 4.9.

Therefore, C is the answer.
Answer: C
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 12 Mar 2020, 01:26
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[GMAT math practice question]

(Statistics) What is the standard deviation of a1, a2, a3, …, a100?

1) The minimum of (x - a1)^2 + (x - a2)^2 + (x - a3)^2+…+(x - a100)^2 is 16.

2) The average of a1, a2, a3, …, a100 is 0.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 09 Jan 2022, 03:23
Originally posted by MathRevolution on 13 Mar 2020, 02:53.
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[GMAT math practice question]

(Algebra) What is the value of \(a^3 + a^2b + ab^2 + b^3\)?

1) \(a + b = 2\sqrt{2}, ab = 1\)

2) \(a = \sqrt{2}+1 \)
Show more

=>

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 have
\(a^3 + a^2b + ab^2 + b^3\)

\(= a^3 + 3a^2b + 3ab^2 + b^3 - (2a^2b + 2ab^2)\)

\(= (a + b)^3 – (2a^2b + 2ab^2)\)

\(= (a + b)^3 – 2ab(a + b)\)

Then we have \(a^3 + a^2b + ab^2 + b^3 = (a+b)^3 – 2ab(a + b) = (2\sqrt{2})^3 – 2*1*( 2\sqrt{2}) = 16\sqrt{2} - 4\sqrt{2} = 12\sqrt{2}\) from condition 1).

Thus, condition 1) is sufficient. since condition 1) has \(2\) equations

Condition 2)
Since we don’t have any information about b, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 13 Mar 2020, 02:54
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[GMAT math practice question]

(Number Properties) \(A, B,\) and \(C\) are positive integers. We have \(A^2 + 2B^2 = C^2.\) What is the value of \(A\)?

1) \(A, B,\) and \(C\) are less than or equal to \(10.\)

2) \(B\) is a multiple of \(2\), and \(C\) is a multiple of \(3\).
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 30 Apr 2021, 02:56
Originally posted by MathRevolution on 16 Mar 2020, 04:00.
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[GMAT math practice question]

(Statistics) What is the standard deviation of a1, a2, a3, …, a100?

1) The minimum of (x - a1)^2 + (x - a2)^2 + (x - a3)^2+…+(x - a100)^2 is 16.

2) The average of a1, a2, a3, …, a100 is 0.
Show more

=>

Forget conventional ways of solving math questions. F or 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.

The expression (x - a1)^2 + (x - a2)^2 + (x - a3)^2+…+(x - a100)^2 has a minimum when x is the average of a1, a2, …, a100 from condition 1).
The standard deviation of a1, a2, …, a100 is the square root of {(x - a1)^2 + (x - a2)^2 + (x - a3)^2+…+(x - a100)^2} / 100 where x is the average.
Thus, their standard deviation is √(16/100) = 4/10.

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

Condition 2)
Since we don’t know their distribution, condition 2) does not yield a unique solution, and it is not sufficient.

Therefore, A is the answer.
Answer: A
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 30 Apr 2021, 02:57
Originally posted by MathRevolution on 16 Mar 2020, 04:02.
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[GMAT math practice question]

(Number Properties) \(A, B,\) and \(C\) are positive integers. We have \(A^2 + 2B^2 = C^2.\) What is the value of \(A\)?

1) \(A, B,\) and \(C\) are less than or equal to \(10.\)

2) \(B\) is a multiple of \(2\), and \(C\) is a multiple of \(3\).
Show more

=>

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 \(1\) equation, 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)

Since we have \(A^2 + 2B^2 = C^2\), we have \(2B^2 = C^2 – A^2 = (C+A)(C-A)\), which is an even number. Then both \(C + A\) and \(C – A\) are even numbers as well.

\(2B^2\) is a multiple of \(4\), and \(B\) is an even number.

Case 1: Assume \(B = 2.\)

We have \((C + A)(C - A) = 2(2)^2 = 8.\)

Consider \(C + A = 4\) and \(C - A = 2.\)

Then we have \(C = 3\) and \(A = 1.\)

\((A, B, C) = (1, 2, 3)\) is a solution.

Case 2: Assume \(B = 4.\)

We have \((C + A)(C - A) = 2(4)^2 = 32.\)

Consider \(C + A = 16\) and \(C - A = 2.\)

Then we have \(C = 9\) and \(A = 7.\)

\((A, B, C) = (7, 4, 9)\) is a solution.

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

Therefore, E is the answer.
Answer: E

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.
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[GMAT math practice question]

(Number Properties) If \(\sqrt{980xy}\) is a positive integer, what is the value of \(xy\)?

1) \(x\) and \(y\) are positive integers

2) \(x ≥ y\)
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[GMAT math practice question]

(Algebra) What is the value of \(xy\)?

1) \(x\) is the decimal part of \((2-\sqrt{3})^{2020}\)

2) \(y = (2+\sqrt{3})^{2020}\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 09 Jan 2022, 03:24
Originally posted by MathRevolution on 18 Mar 2020, 03:48.
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[GMAT math practice question]

(Number Properties) If \(\sqrt{980xy}\) is a positive integer, what is the value of \(xy\)?

1) \(x\) and \(y\) are positive integers

2) \(x ≥ y\)
Show more

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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)
We have \(980 = 2^25^17^2.\)

\(X = 5, y = 2 \)and \(x = 20, y = 2 \)are possible solutions.
Then we have \(xy = 10\) and \(40.\)
Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

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.
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[GMAT math practice question]

(Algebra) What is the value of \(y^{x^2}/ y^{2\sqrt{3}x-5}\)?

1) \(x = \sqrt{3} + \sqrt{2}\)

2) \(y = \sqrt{2} - 1\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 22 Jan 2021, 03:53
Originally posted by MathRevolution on 19 Mar 2020, 03:38.
Last edited by MathRevolution on 22 Jan 2021, 03:53, edited 1 time in total.
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[GMAT math practice question]

(Algebra) What is the value of \(xy\)?

1) \(x\) is the decimal part of \((2-\sqrt{3})^{2020}\)

2) \(y = (2+\sqrt{3})^{2020}\)
Show more

=>

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)

Since \(2-\sqrt{3}\) is less than \(1\), the decimal part of \((2-\sqrt{3})^{2020}\) is \((2-\sqrt{3})^{2020}\) itself.
Then we have \(xy = (2-\sqrt{3})^{2020}(2+\sqrt{3})^{2020} = (4-3)^{2020} = 1.\)

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.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 19 Mar 2020, 03:38
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[GMAT math practice question]

(Algebra) What is \(a^3b + a^2b^2 + ab^3\)?

1) \(a – b = 3\)

2) \(ab = 3\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 22 Jan 2021, 03:54
Originally posted by MathRevolution on 22 Mar 2020, 20:01.
Last edited by MathRevolution on 22 Jan 2021, 03:54, edited 1 time in total.
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[GMAT math practice question]

(Algebra) What is the value of \(y^{x^2}/ y^{2\sqrt{3}x-5}\)?

1) \(x = \sqrt{3} + \sqrt{2}\)

2) \(y = \sqrt{2} - 1\)
Show more

=>

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.

The question asks the value of \(y^{{x^2}-2\sqrt{3}x+5}\), since we have \(y^{x^2}/ y^{2\sqrt{3}x-5} = y^{{x^2}-2\sqrt{3}x+5}.\)

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)
Since we have \(x = √3 + √2\), we have \(x - √3 = √2.\)
Then we have \(x^2 - 2√3x + 3 = 2\) or \(x^2 - 2√3x = -1\) by squaring.
Thus we have \(x^2 - 2√3x + 5 = 4\) by adding \(5\) to both sides.

Then we have \(y^{{x^2}-2\sqrt{3}x+5}= (√2 - 1)^4\), which a unique solution.

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.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 22 Mar 2020, 20:02
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[GMAT math practice question]

(Algebra) What is \(\frac{a}{ab+a+1} + \frac{b}{bc+b+1} + \frac{c}{ca+c+1}\)?

1) \(abc = 1\)

2) \(a, b,\) and \(c\) are integers
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