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# Math Revolution DS Expert - Ask Me Anything about GMAT DS

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

(function) If the symbol $$#$$ represents one of addition, subtraction, multiplication, or division, what is the value of $$(2 # 1)$$?

1) 2 # 2 = 1

2) (–1/2) # (-1) = $$\frac{1}{2}$$
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
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GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(number properties) We define ‘a mod n’ to be the remainder when a is divided by n. What is the value of ‘a mod 12’?

1) a mod 3=1
2) a mod 4=a mod 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.

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

Condition 1)
The numbers satisfying condition 1) are $$1, 4, 7, 10, 13, 16, 19, 22, …$$ .

Their remainders, when they are divided by $$12$$, are $$1, 4, 7$$ and $$10.$$

Condition 1) is not sufficient since it doesn’t yield a unique answer.

Condition 2)
The numbers satisfying condition 2) are $$0, 1, 4, 5, 8, 9, 12, 13, 16, 17, …$$ .

Their remainders, when they are divided by $$12$$, are $$0, 1, 4, 5, 8$$ and $$9$$.

Condition 2) is not sufficient, since it doesn’t yield a unique answer.

Conditions 1) & 2)
The numbers satisfying conditions 1) & 2) are $$1, 4, 13, 16, … .$$

Their remainders, when they are divided by $$12$$, are $$0$$ and $$1.$$

Both conditions together are not sufficient, since they don’t yield a unique answer.

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 09 Jun 2019, 18:20.
Last edited by MathRevolution on 23 Aug 2021, 02:37, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(function) If the symbol $$#$$ represents one of addition, subtraction, multiplication, or division, what is the value of $$(2 # 1)$$?

1) 2 # 2 = 1

2) (–1/2) # (-1) = $$\frac{1}{2}$$

=>

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.

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

Condition 1)
$$#$$ is the division operation since $$\frac{2}{2} = 1.$$

So, $$2#1 = \frac{2}{1} = 2.$$

Condition 1) is sufficient since it yields a unique answer.

Condition 2)
$$#$$ could be the multiplication, subtraction or the division operation
since $$(-\frac{1}{2}) * (-1) = \frac{1}{2}, (-\frac{1}{2})-(-1) = (\frac{1}{2})$$ and (-$$\frac{1}{2})/(-1) = \frac{1}{2}.$$

Since $$2 * 1 = 2$$ and $$\frac{2}{1} = 2$$, but $$2-1 = 1$$, condition 2) does not yield a unique value for $$2#1$$.

Condition 2) is not sufficient since it doesn’t yield a unique answer.

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 09 Jun 2019, 18:22.
Last edited by MathRevolution on 29 Sep 2021, 01:25, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

(inequality) $$0 < a < b < c$$. Is $$a < 3$$?

$$1) \frac{1}{c} > \frac{1}{3}$$

$$2) \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$$
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

(inequality) Is $$x^3-x^2+x-1 > 0?$$

$$1) x^5 > x^2$$

$$2) x^3 + x > x^2 + 1$$
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(inequality) $$0 < a < b < c$$. Is $$a < 3$$?

$$1) \frac{1}{c} > \frac{1}{3}$$

$$2) \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$$

=>

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.

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

We have $$\frac{1}{a} > \frac{1}{b} > \frac{1}{c}$$, since we are given that $$0 < a < b < c.$$

Condition 1) implies that $$c < 3$$. Therefore $$a < 3$$, and Condition 1) is sufficient.

Condition 2)
Since $$\frac{1}{a} > \frac{1}{b} > \frac{1}{c} > 0$$, and $$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$$, we must have $$\frac{1}{a} + \frac{1}{a} + \frac{1}{a} = \frac{3}{a} > 1$$. Therefore, $$a < 3$$, and the answer is ‘yes’.
Condition 2) is sufficient since it yields a unique answer.

This question is a CMT4(B) question: condition 1) is easy to work with and condition 2) is difficult to work with. For CMT4(B) questions, D is most likely to be the answer.

Originally posted by MathRevolution on 12 Jun 2019, 01:26.
Last edited by MathRevolution on 23 Aug 2021, 02:38, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

(number properties) If $$x$$ and $$y$$ are positive integers, are $$x$$ and $$y$$ consecutive?

$$1) x+y=3$$

$$2) xy=2$$
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(inequality) Is $$x^3-x^2+x-1 > 0?$$

$$1) x^5 > x^2$$

$$2) x^3 + x > x^2 + 1$$

=>

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.

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

In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient.

$$x^3-x^2+x-1 > 0$$

$$=> x^2(x-1) + (x-1) > 0$$

$$=> (x^2+1)(x-1) > 0$$

$$=> (x-1) > 0$$, since $$x^2+1 > 0$$

$$=> x>1$$

The question asks if $$x > 1.$$

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)
$$x^5 > x^2$$

$$=> x^5 - x^2 > 0$$

$$=> x^2(x^3 – 1) > 0$$

$$=> x^2(x-1)(x^2+x+1) > 0$$

$$=> x – 1 > 0$$ since $$x^2+x+1 >0,$$ and $$x^2 > 0$$ if $$x ≠ 0$$
$$x > 1$$
This condition is equivalent to the question. Therefore, condition 1) is sufficient.

Condition 2)
$$x^3 + x > x^2 + 1$$

$$=> x^3 - x^2 + x – 1 > 0$$

$$=> x^2(x-1)+ (x-1) > 0$$

$$=> (x^2+1)(x-1) > 0$$

$$=> (x-1) > 0$$, since $$x^2+1 > 0$$

$$=> x > 1$$

This condition is equivalent to the question. Therefore, condition 2) is sufficient.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

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.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

(number properties) If p and q are prime numbers, what is the number of the different factors of p^2q^3?

1) pq=143
2) p and q are different
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(number properties) If $$x$$ and $$y$$ are positive integers, are $$x$$ and $$y$$ consecutive?

$$1) x+y=3$$

$$2) xy=2$$

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.

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 x and y are positive integers, condition 1) tells us that either x = 1 and y = 2, or x = 2 and y= 1. Thus, x and y are consecutive integers.

Since x and y are positive integers, condition 2 tells us that either x = 1 and y = 2, or x = 2 and y= 1. Thus, x and y are consecutive integers.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

(function) At how many points does the parabola y=f(x)=ax^2+bx+c (a≠0) intersect the x-axis?

1) x=f(y) intersects the y-axis at two points.
2) y=f(x-1) intersects the x-axis at two points.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(number properties) If p and q are prime numbers, what is the number of the different factors of p^2q^3?

1) pq=143
2) p and q are different

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. We should simplify conditions if necessary.

Since p and q are prime numbers, condition 1) tells us that p = 11 and q = 13, or p = 13 and q = 11. Therefore, since p and q are different prime numbers, the number of different factors of p^2q^3 is (2+1)(3+1) = 12. Condition 1) is sufficient since it yields a unique solution.

Condition 2)
Since condition 2) tells us that p and q are different prime numbers, the number of factors of p^2q^3 is (2+1)(3+1) = 12.
Condition 2) is sufficient since it yields a unique solution.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

Originally posted by MathRevolution on 16 Jun 2019, 22:55.
Last edited by MathRevolution on 07 Mar 2021, 04:05, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(function) At how many points does the parabola y=f(x)=ax^2+bx+c (a≠0) intersect the x-axis?

1) x=f(y) intersects the y-axis at two points.
2) y=f(x-1) intersects the x-axis at two points.

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. We should simplify conditions if necessary.

Condition 1)
Condition 1) is equivalent to the statement that y=f(x) intersects the x-axis at two points, simply by switching the roles of x and y. This means that y=f(x) intersects the x-axis at two points.
Condition 1) is sufficient since it yields a unique solution.

Condition 2)
The graph of y = f(x-1) is the same as the graph of f(x), moved to the right by one unit. This horizontal movement does not change the number of roots of y. Therefore, y = f(x) also has two roots.
Condition 2) is sufficient since it yields a unique solution.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

(inequality) Is x<0?

1) x^3+1<0
2) x^3+2x^2+x+2=0
Intern
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Concentration: Finance, Real Estate
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WE:Analyst (Investment Banking)
MathRevolution wrote:

Hello, I am Max Lee, Founder and Lead Math Tutor at Math Revolution.

My other discussions you may be interested in:

Thank you all - good luck on the GMAT and look forward to seeing you in the DS forum!
- Max Lee.

Hi,

Do you have a matrix with variables and equations? i.e. if there are 2 variables and 2 equations you can solve the equation etc

Best
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
[GMAT math practice question]

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

1) x>0
2) y>0
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17062 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
[GMAT math practice question]

(inequality) Is x<0?

1) x^3+1<0
2) x^3+2x^2+x+2=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.

Since we have 1 variable (n) 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
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
Thus, since the solution set of the question, ‘x<0’, includes that of condition 1), ‘x<-1’, condition 1) is sufficient.

Condition 2)
x^3+2x^2+x+2=0
⇔ x^2(x+2)+(x+2)=0
⇔ (x^2+1)(x+2)=0
⇔ x+2=0 since x^2+1 > 0
⇔ x = -2
Thus, x < 0 and condition 2) is sufficient.