Last visit was: 14 Jul 2024, 07:47 It is currently 14 Jul 2024, 07:47
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
   
Show Tags
Hide Tags
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
[GMAT math practice question]

(Algebra) For the positive numbers \(x\) and \(y\), what is the value of \(\frac{\sqrt{xy}}{(x+y)^3}\)?

1) \(\frac{1}{x }+ \frac{1}{y} = \frac{2}{\sqrt{xy} }\)

2) \(x + y = \sqrt{2}xy\)
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

(Algebra) What is the value of \(\frac{x}{y}\)?

1) \(5x(5 + 2\sqrt{5}) - 5\sqrt{5}y(3 - 2\sqrt{5})\) is a rational number.

2) \(x\) and \(y\) are rational numbers and \(xy ≠ 0.\)


=>

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)

\(5x(5 + 2\sqrt{5}) - 5\sqrt{5}y(3 - 2\sqrt{5}) \)

\(= 25x + 10√5x - 15√5y + 50y\) (multiplying through the brackets)

\(= 25x + 50y + 10√5x - 15√5y\) (rearranging the terms)

\(= 25(x + 2y) + 5√5(2x - 3y)\) (taking out common factors)

We must have \(2x – 3y = 0\) in order for \(5√5(2x-3y)\) to be zero (and therefore cancel out the square root or irrational number because condition \(1\) states that the answer is a rational number) when \(x\) and \(y\) are rational numbers.

Thus, we have \(2x = 3y\) or \(\frac{x}{y} = \frac{3}{2}\).

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.

Originally posted by MathRevolution on 27 Feb 2020, 02:12.
Last edited by MathRevolution on 04 Feb 2021, 03:58, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
[GMAT math practice question]

(Geometry) Triangle \(ABC\) is a right triangle with \(∠C = 90^o\). What is the length of \(AB\)?

Attachment:
2.27ds.png
2.27ds.png [ 3.58 KiB | Viewed 1014 times ]


1) The area of \(ABC\) is \(35.\)

2) The length of the base is \(4\) less than twice of the height.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

(Algebra) For the positive numbers \(x\) and \(y\), what is the value of \(\frac{\sqrt{xy}}{(x+y)^3}\)?

1) \(\frac{1}{x }+ \frac{1}{y} = \frac{2}{\sqrt{xy} }\)

2) \(x + y = \sqrt{2}xy\)


=>

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)

Since we have \(\frac{1}{x} + \frac{1}{y} = \frac{2}{√xy}\) from condition 1), we have
=> \(\frac{(y√xy) }{ (xy√xy)} + \frac{(x√xy) }{ (xy√xy)} = \frac{(2xy) }{ (xy√xy)}\) (getting a common denominator)

=> \(\frac{(y√xy + x√xy) }{ (xy√xy)} = \frac{(2xy) }{ (xy√xy) }\)(adding the fractions)

=>\(y√xy + x√xy = 2xy\) (multiplying both sides by \(xy√xy\))

=>\(√xy(y + x) = 2xy\) (taking out a common factor

=> \(y + x = \frac{2xy}{√xy}\) (dividing both sides by √xy

=> \(y + x = 2√xy\)

=>\( x + y = 2√xy\) is equivalent to \(x – 2√xy + y = 0\) which is equivalent to \((√x - √y)^2 = 0 \)

=> \(√x - √y = 0\) (squaring both sides)

=> \(√x = √y\) (subtracting \(√y\) from both sides

=> \(x = y\) (squaring both sides)

When we replace the variable \(y\) in the equation \(x + y = √2xy\) by \(x\), we have

=> \(x + x = √2x*x \)

=> \(2x = √2x^2 \)(simplifying)

=> \(√2x^2 – 2x = 0\) (subtracting \(2x\) from both sides)

=> \(√2x(x-√2) = 0\). (taking out a common factor

Then we have \(x = 0\) or \(x = √2.\)

We have \(x = y = √2\) since \(x\) and \(y\) are positive numbers.

\(\frac{\sqrt{xy}}{(x+y)^3} = \frac{\sqrt{√2√2}}{(√2+√2)^3} = \frac{\sqrt{2}}{(2√2)^3} = \frac{√2}{16√2} = \frac{1}{16}\)

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.

Originally posted by MathRevolution on 01 Mar 2020, 18:13.
Last edited by MathRevolution on 28 Apr 2021, 03:55, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
[GMAT math practice question]

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

1) \(A, B,\) and \(C\) are less than \(11.\)

2) \(A, B\), and \(C\) are integers.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

(Geometry) Triangle \(ABC\) is a right triangle with \(∠C = 90^o\). What is the length of \(AB\)?

Attachment:
The attachment 2.27ds.png is no longer available


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)

Attachment:
2.27(a).png
2.27(a).png [ 14.52 KiB | Viewed 996 times ]


Then we have\( (\frac{1}{2})(x)(2x - 4) = 35\) 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.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

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

1) \(A, B,\) and \(C\) are less than \(11.\)

2) \(A, B\), and \(C\) are integers.


=>


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 \(A^2 + 2B^2 = C^2 \), we have \(2B^2 = C^2 - A^2\) or \(2B^2 = (C + A)(C - A)\).

\(C^2 - A^2 = (C + A)(C - A)\) is an even number, both \(A\) and \(C\) must either odd numbers or even numbers.

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

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

Since we have \(0 < C^2 - A^2 = 2B^2 < 10^2\) or \(0 < C^2 - A^2 = 2B^2 < 100\), we have \(0 < B < √50\) and \(B = 2, 4 \)or \(6.\)
We have \(C + A > C – A.\)

Case 1: \(B = 2\)
Since we have \((C + A)(C - A) = 8\), we have \(C + A = 4\) and \(C – A = 2.\)
Then we have \(C = 3, A = 1\) and \(A + B + C = 1 + 2 + 3 = 6.\)

Case 2: \(B = 4\)
Since we have \((C + A)(C - A) = 32\), we have \(C + A = 16, C - A = 2\) or \(C + A = 8, C – A = 4.\)
If \(C + A = 16, C – A = 2\), then we have \(A = 7, C = 9\) and \(A + B + C = 7 + 4 + 9 = 20.\)

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.

Originally posted by MathRevolution on 01 Mar 2020, 18:39.
Last edited by MathRevolution on 22 Jun 2021, 03:22, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
[GMAT math practice question]

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

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

2) \(\sqrt{3}x - \sqrt{2}y=5 \\
\)
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
Expert Reply
[GMAT math practice question]

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

1) \(x^2 + 4x + 9\) is a perfect square of an integer.

2) \(x\) is an integer.
Director
Director
Joined: 14 Dec 2019
Posts: 829
Own Kudos [?]: 906 [0]
Given Kudos: 354
Location: Poland
Concentration: Entrepreneurship, Strategy
GMAT 1: 640 Q49 V27
GMAT 2: 660 Q49 V31
GMAT 3: 720 Q50 V38
GPA: 4
WE:Engineering (Consumer Electronics)
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
MathRevolution wrote:
[GMAT math practice question]

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

1) \(x^2 + 4x + 9\) is a perfect square of an integer.

2) \(x\) is an integer.


Taking i) and ii) together

\(x^2 + 4x + 9\) is a perfect square of an integer. Let that integer be 3 therefore square of it would be 9

Therefore \(x^2 + 4x + 9\) = 9 => x(x+4) = 0 => x=0 or x=-4

2 Values of x as integers - Insufficient

Answer - E
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

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

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

2) \(\sqrt{3}x - \sqrt{2}y=5 \\
\)


=>

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
\(√3x - √2y - √3(x + y) = 5 - √3(2√3)\)

\(√3x - √2y - √3x - √3y = 5 – 6\)

\(√2y - √3y = -1\)

\(√3y - √2y = 1\)

\((√3 + √2)y = 1 \)

\(y = \frac{1}{(√3 + √2)}\)

\(y = √3 - √2.\)

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.

Originally posted by MathRevolution on 04 Mar 2020, 01:20.
Last edited by MathRevolution on 01 Jun 2021, 01:36, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
Expert Reply
[GMAT math practice question]

(Statistics) \(A\) and \(B\) are subsets of positive integers. Are the standard deviations of \(A\) and \(B\) equal?

1) \(A\) is the set of all odd numbers between \(1\) and \(100\), inclusively.

2) \(B\) is the set of all even numbers between \(1\) and \(100\), inclusively.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

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

1) \(x^2 + 4x + 9\) is a perfect square of an integer.

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 to be the answer. So, we should consider each condition on its own first.

Condition 1)

\(x^2 + 4x + 9 = x^2 + 4x + 4 + 5 = (x + 2)^2 + 5 = k^2\) for some integer \(k.\)

Then we have
\(5 = k^2 - (x+2)^2 \)(subtracting \((x + 2)^2\) from both sides)

\(5 = (k + x + 2)(k – x – 2)\) (factoring using difference of squares).

If \(k + x + 2 = 5\) and \(k – x – 2 = 1\), then we have \(2x + 4 = ( k + x + 2 ) – ( k – x – 2 ) = 5 -1 = 4\) and \(x = 0.\)

If \(k + x + 2 = 1 \)and \(k – x – 2 = 5\), then we have \(2x + 4 = ( k + x + 2 ) – ( k – x – 2 ) = 1 - 5 = -4\) and \(x = -4.\)

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)

The reasoning in condition 1) can be applied to both conditions together too.

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.

Originally posted by MathRevolution on 05 Mar 2020, 03:21.
Last edited by MathRevolution on 25 Apr 2021, 02:59, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
[GMAT math practice question]

(Inequalities) When \(x\) is a real number, {\(x\)} denotes the integer part of \(\sqrt{x}\) and [\(x\)] the decimal part of \(\sqrt{x}\). What is the value of \(x\)?

1) \({x} = 2\)

2) \(0.3 < [x] < 0.5\)
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

(Statistics) \(A\) and \(B\) are subsets of positive integers. Are the standard deviations of \(A\) and \(B\) equal?

1) \(A\) is the set of all odd numbers between \(1\) and \(100\), inclusively.

2) \(B\) is the set of all even numbers between \(1\) and \(100\), inclusively.


=>

Since we have \(2\) variables \((A\) and \(B\)) 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)

\(B = { 2, 4, 6, … , 100 } = A + 1 = { 1, 3, 5, … , 99 } + 1.\)

Since set B is the shift of set \(A\) by \(1\), sets \(A\) and \(B\) have the same standard deviation.

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 condition 1) does not have any information regarding set \(B\), it is not sufficient obviously.

Condition 2)

Since condition 2) does not have any information regarding set \(A\), 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.

Originally posted by MathRevolution on 06 Mar 2020, 03:02.
Last edited by MathRevolution on 25 Apr 2021, 03:00, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
[GMAT math practice question]

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

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

2) \(\frac{b}{a} < 0 \)
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17014 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
1
Kudos
Expert Reply
MathRevolution wrote:
[GMAT math practice question]

(Inequalities) When \(x\) is a real number, {\(x\)} denotes the integer part of \(\sqrt{x}\) and [\(x\)] the decimal part of \(\sqrt{x}\). What is the value of \(x\)?

1) \({x} = 2\)

2) \(0.3 < [x] < 0.5\)


=>

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.

We have \(x = {x} + [x]\) since \({x}\) is the integer part of \(x\) and \([x]\) is the decimal part of \(x\).

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

Condition 1)
\({x} = 2 \)means we have \(2 ≤ x < 3.\)

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

Condition 2)

\(0.3 < [x] < 0.5\) means that we have \(0.3 < x < 0.5, 1.3 < x < 1.5, … .\)

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

Conditions 1) & 2)
Since \(0.3 < [x] < 0.5 \)and \({x} = 2,\) we have \(2.3 < {x} + [x] < 2.5. \)
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.

Originally posted by MathRevolution on 08 Mar 2020, 20:03.
Last edited by MathRevolution on 01 Jun 2021, 01:37, edited 1 time in total.
GMAT Club Bot
Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink]
   1  ...  40   41   42   43   44  ...  64   
Moderator:
Math Expert
94342 posts