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MathRevolution
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 31 Mar 2019, 18:37
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[GMAT math practice question]

The diagram below contains four right triangles with legs a and b. What is the area of the larger square?

Attachment:
3.29.png

1) a = 12
2) b = 9
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.

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

If we assume \(c\) is the length of the hypotenuse of the right triangle, we have \(c^2 = a^2 + b^2\) and \(c^2\) is the area the larger square.
We need the values of both \(a\) and \(b\). Thus, conditions 1) & 2) are sufficient, when applied together, but neither condition is sufficient on its own.

Therefore, C is the answer.
Answer: C
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 01 Apr 2019, 02:52
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[GMAT math practice question]

(absolute value) Is \(x<y<z\) ?

\(1) |x+1|<y<z+1\)
\(2) |x-1|<y<z-1\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 01 Apr 2019, 16:26
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[GMAT math practice question]

(number properties) If \(x, y\) are integers, is \((x-y)(x+y)(x^2+y^2)\) an odd number?

1) \(x\) is an odd number
2) \(x-y\) is an odd number
Show more
fskilnik,
Sir, is it possible to solve this question by rotations style?
Thanks__
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 18 Jan 2022, 01:18
Originally posted by MathRevolution on 01 Apr 2019, 21:12.
Last edited by MathRevolution on 18 Jan 2022, 01:18, edited 1 time in total.
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Sandeepanisha
(integer) [x] is the greatest integer less than or equal to x, is x-[x]>0?

1) x is positive
2) x is not integer
Show more

[x] is the integer part of x.
If x = n + h where n is an integer and 0 ≤ h < 1, then [x] = n.
For example, if x = 1.2 = 1+0.2, then [x] = 1.

Thus x - [x] = n + h - n = h is the decimal part of x.
x - [x] > 0 means h > 0 and x is not an integer.
Thus condition 2) is sufficient.

Condition 1)
If x = 1.2, then x - [x] = 1.2 - 1 = 0.2 > 0 and the answer is 'yes'.
If x = 1, then x - [x] = 1 - 1 = 0 and answer is 'no'.
Since we don't have a unique answer, condition 1) is not sufficient.

Therefore, the answer is B.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 01 Apr 2019, 21:19
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Sandeepanisha
(ratio) All of the households used a total of x watts for 24 hours and one household used y watts per hour. What is the total number of all the households, in terms of x and y?

A. x/y B. 24x/y C. x/24y D. 24xy E. 24/xy
Show more

Let n be the number of households.
Then we have 24y*n = x, which is the total waats they use.
Thus n = x/(24y).

Therefore, then answer is C.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 02 Apr 2019, 07:49
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[GMAT math practice question]

(absolute values) If \(|2x|>|3y|\), is \(x >y\)?

\(1) x>0\)
\(2) y>0\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 02 Apr 2019, 13:19
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MathRevolution
[GMAT math practice question]

(number properties) If \(x, y\) are integers, is \((x-y)(x+y)(x^2+y^2)\) an odd number?

1) \(x\) is an odd number
2) \(x-y\) is an odd number
fskilnik,
Sir, is it possible to solve this question by rotations style?
Thanks__
Show more

Hi, AsadAbu .

Thank you for your interest in my opinions, but (by contract) I must limit myself to post questions/solutions (and some brief explanations about our solutions, when asked).

I am not here to judge or compare GMATH´s method to other experts/companies approaches.

Thank you for your understanding.

Regards and success in your studies,
Fabio.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 02 Apr 2019, 14:10
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AsadAbu
MathRevolution
[GMAT math practice question]

(number properties) If \(x, y\) are integers, is \((x-y)(x+y)(x^2+y^2)\) an odd number?

1) \(x\) is an odd number
2) \(x-y\) is an odd number
fskilnik,
Sir, is it possible to solve this question by rotations style?
Thanks__

Hi, AsadAbu .

Thank you for your interest in my opinions, but (by contract) I must limit myself to post questions/solutions (and some brief explanations about our solutions, when asked).

I am not here to judge or compare GMATH´s method to other experts/companies approaches.

Thank you for your understanding.

Regards and success in your studies,
Fabio.
Show more
Yep, I get it.
Thanks__
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 18 Oct 2021, 02:48
Originally posted by MathRevolution on 03 Apr 2019, 04:14.
Last edited by MathRevolution on 18 Oct 2021, 02:48, edited 1 time in total.
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[GMAT math practice question]

(absolute value) Is \(x<y<z\) ?

\(1) |x+1|<y<z+1\)
\(2) |x-1|<y<z-1\)
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.

Since we have \(3\) variables (\(x, y\) and \(z\)) and \(0\) equations, E is most likely to be 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)
By condition 1), \(x < y\) since \(x < x + 1 ≤ | x + 1 | < y\).
By condition 2), \(y < z\) since \(y < z – 1 < z.\)
Therefore, \(x < y < z\).
Thus, both conditions 1) & 2) together are sufficient.

Since this question is an absolute value 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)
If \(x = 1, y = 3\), and \(z = 5,\) then the answer is ‘yes’.
If \(x = 1, y = 3,\) and \(z = 2.9\), then the answer is ‘no’ since z < y.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Condition 2)
If \(x = 1, y = 3,\) and \(z = 5\), then the answer is ‘yes’.
If \(x = 3.1, y = 3,\) and \(z = 5\), then the answer is ‘no’ since \(x > y\).
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

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.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 03 Apr 2019, 04:15
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[GMAT math practice question]

\(m\) and \(n\) are positive integers. Are \(m\) and \(n\) consecutive integers?

\(1) m^2+n^2 = 5\)
\(2) m-n = 1\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 18 Oct 2021, 02:49
Originally posted by MathRevolution on 04 Apr 2019, 00:32.
Last edited by MathRevolution on 18 Oct 2021, 02:49, edited 1 time in total.
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MathRevolution
[GMAT math practice question]

(absolute values) If \(|2x|>|3y|\), is \(x >y\)?

\(1) x>0\)
\(2) y>0\)
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.

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

From condition 1), we have \(3x > 2x = |2x| > |3y| ≥ 3y\) since \(|x| = x.\) So, \(x > y\) and the answer is ‘yes’.
Thus, condition 1) is sufficient.

Condition 2)
If \(x = 10\), and \(y = 1\), then \(x > y\) and the answer is ‘yes’.
If \(x = -10\), and \(y = 1,\) then \(x < y\) and the answer is ‘no’.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Therefore, A is the answer.
Answer: A
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 04 Apr 2019, 00:33
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[GMAT math practice question]

(number properties) \(m\) and \(n\) are integers. Is \(m + n\) an odd number?

\(1) m – n = 2\)
\(2) m^2n^2 = 225\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 26 Dec 2021, 02:44
Originally posted by MathRevolution on 05 Apr 2019, 01:41.
Last edited by MathRevolution on 26 Dec 2021, 02:44, edited 1 time in total.
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[GMAT math practice question]

\(m\) and \(n\) are positive integers. Are \(m\) and \(n\) consecutive integers?

\(1) m^2+n^2 = 5\)
\(2) m-n = 1\)
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.

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

Condition 1)
The only positive integers satisfying \(m^2+n^2 = 5\) are \(m = 1\) and \(n = 2\), or \(m=2\) and \(n = 1.\)
These are consecutive integers, so condition 1) is sufficient.

Condition 2)
Since the difference between \(m\) and \(n\) is \(1\), they are consecutive integers. Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 05 Apr 2019, 01:41
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[GMAT math practice question]

(inequality) Is \(x < 0\)?

\(1) x^3 + 1 < 0\)
\(2) x^3 + x + 1 < 0\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 26 Dec 2021, 02:43
Originally posted by MathRevolution on 07 Apr 2019, 18:38.
Last edited by MathRevolution on 26 Dec 2021, 02:43, edited 1 time in total.
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[GMAT math practice question]

(number properties) \(m\) and \(n\) are integers. Is \(m + n\) an odd number?

\(1) m – n = 2\)
\(2) m^2n^2 = 225\)
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.

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

Condition 2)
Since \(m^2n^2 = 225\) is an odd number, both \(m\) and \(n\) must be odd numbers, and \(m + n\) is an even number.
Thus, the answer is ‘no’, and condition 2) is sufficient by CMT (Common Mistake Type) 1.

Condition 1)
Since \(m – n = 2\), both \(m\) and \(n\) are odd numbers or even numbers.
Since \(m\) and \(n\) have the same parity, \(m + n\) is an even number.
Thus, the answer is ‘no’, and condition 1) is sufficient by CMT (Common Mistake Type) 1.

Therefore, D is the answer.
Answer: D
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 18 Jan 2022, 01:19
Originally posted by MathRevolution on 07 Apr 2019, 18:39.
Last edited by MathRevolution on 18 Jan 2022, 01:19, edited 1 time in total.
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[GMAT math practice question]

(inequality) Is \(x < 0\)?

\(1) x^3 + 1 < 0\)
\(2) x^3 + x + 1 < 0\)
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.

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)
\(x^3 + 1 < 0\)
\(=> (x+1)(x^2-x+1) < 0\)
\(=> x + 1 < 0\) since \(x^2-x+1 > 0\)
\(=> x < -1 < 0\)
Thus, condition 1) is sufficient, and the answer is ‘yes’.

Condition 2)
\(x^3 + x + 1 < 0\)
\(=> x^3 + x < -1\)
\(=> x(x^2 + 1) < -1\)
\(=> x < \frac{-1}{(x^2 + 1)}\) since \(x^2 + 1 > 0\)
\(=> x <\frac{-1}{(x^2 + 1)} < 0\) since \(x^2 + 1 > 0\)
Thus, condition 2) is sufficient, and the answer is ‘yes’.

Therefore, D is the answer.
Answer: D
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 08 Apr 2019, 02:02
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[GMAT math practice question]

(statistics) If the median and average (arithmetic mean) of a set of 4 different numbers are both 10, what is the smallest number?

1) The range of the 4 numbers is 10
2) The sum of the smallest and the largest numbers is 20
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 09 Apr 2019, 00:10
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[GMAT math practice question]

(statistics) \(x, y\) and \(z\) are different integers. Is their average equal to their median?

1) Their range is \(11\).
2) Their median is \(11\).
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 22 Sep 2021, 02:10
Originally posted by MathRevolution on 10 Apr 2019, 00:43.
Last edited by MathRevolution on 22 Sep 2021, 02:10, edited 1 time in total.
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[GMAT math practice question]

(statistics) If the median and average (arithmetic mean) of a set of 4 different numbers are both 10, what is the smallest number?

1) The range of the 4 numbers is 10
2) The sum of the smallest and the largest numbers is 20
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.

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

Let \(a, b, c\) and \(d\) be the \(4\) numbers, and suppose \(a < b < c < d.\)

Then \(\frac{( a + b + c + d )}{4} = 10\) and \(\frac{( b + c )}{2} = 10.\)

Since \(b + c = 20\) and \(a + b + c + d = 40\), we must have \(a + d = 20.\)

Condition 1)

Since \(d – a = 10\) by condition 1), we can figure out the values of \(a\) and \(d\). Thus, condition 1) is sufficient.

Condition 2)

\(a + d = 20\) can be deduced from the original condition as shown above.

So, condition 2) provides no additional information.

If \(a = 1, b = 9, c = 11\) and \(d = 19\), then the smallest number is \(1\).

If \(a = 2, b = 9, c =11\) and \(d = 18\), then the smallest number is \(2\).

Condition 2) is not sufficient since it does not yield a unique answer.

Therefore, A is the answer.
Answer: A
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 10 Apr 2019, 00:44
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[GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(m^2-n^2\) divisible by \(4\)?

1) \(m^2+n^2\) has remainder \(2\) when it is divided by \(4\)

2) \(m*n\) is an odd integer
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