Overview of GMAT Math Question Types and Patterns on the GMAT : Quantitative Questions

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

07 Jul 2021, 02:55

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(number properties) If $k, m$ and $n$ are positive integers, what is the value of $kmn$?

$1) k^4mn = 240$

$2) m = 3$

=>

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)
If $k = 2, m = 3$ and $n = 5,$ then $kmn = 30.$

If $k = 1, m = 3$ and $n = 80$, then $kmn = 240.$

Conditions 1) & 2) together are not sufficient, when applied together, since they don’t yield a unique solution.

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.

B

rohanjt96

Intern

Joined: 29 May 2021

Posts: 1

Own Kudos [?]: 0 [0]

Given Kudos: 1

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

07 Jul 2021, 04:20

MathRevolution wrote:

[GMAT math practice question]

(Algebra) Thomas went to a grocery store and bought some fruit with $$25$. The prices of the fruit are $$5, $1$, and $$0.50$ for each watermelon, pear, and apple, respectively. How many apples did he buy?

1) He bought $10$ pieces of fruit, and he didn’t get any change back.

2) He had at least one of each fruit.

Therefore, C is the answer.
Answer: C

Hello!
Can't we solve this with just the 1st condition?

The way I thought about it was:
Thomas has to buy 4 watermelons for $20.
If he buys 3 watermelons for $15, he'd need to buy 10 pears to make the total $25. If so, he would have 3 + 10 = 13 fruits which will fail the first part. (total of 10 fruits)

Since he buys 4 watermelons for $20, he has $5 and 6 fruits remaining.
This can only be made with 4 pears & 2 apples. (4x $1 + 2x $0.5)

And since this gives us a unique solution, condition 1 on it's own is sufficient.

So, answer A) should be correct.

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

09 Jul 2021, 00:32

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(Inequalities) What is the value of $y$? ($[x]$ denotes the greatest integer less than or equal to $x$.)

1) $y = 2[x] + 3$

2) $y = 3[x - 2] + 5$

=>

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)

Assume we have $n = [x].$

Since we have $y = 2n + 3$ and $y = 3(n - 2) + 5$ since we have $[x - 2] = [x] - 2.$

Then, substituting the first equation into the second equation we have
$2n + 3 = 3(n – 2) + 5$

$2n + 3 = 3n - 6 + 5$

$2n +3 = 3n - 1$

$-n = -4$

$n = 4$

Then:
y = 2n + 3
y = 2(4) + 3
y = 11.

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)
$x = 1, y = 5$ and $x = 2, y = 7$ are solutions.

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

Condition 2)
$x = 1, y = 2$ and$ x = 2, y = 5$ are solutions.

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

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

11 Jul 2021, 02:55

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(function) For which value of $x$ will $y=ax^2+20x+b$ have a minimum in the $xy$-plane?

$1) b=10$

$2) a=2$

=>

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, and then recheck the numbers of variables and equations.

We can modify the original condition and question as follows:

If $a > 0$, the function will have a minimum at $x = \frac{(-20)}{(2a)} = \frac{(-10)}{a}.$

If $a < 0$, the function has no minimum. So, to answer the question, we need to find the value of $a.$

Thus, condition 2) is sufficient.

Note: condition 1) cannot be sufficient as it provides no information about the value of $a.$

Therefore, the answer is B.
Answer: B

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

13 Jul 2021, 00:26

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(function) $f(x)$ is a function. What is the value of $f(2006)$?

$1) f(11)=11$

$2) f(x+3)=\frac{(f(x)-1)}{(f(x)+1)}$

=>

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.

Since we have many variables to determine a function 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)

Since we have $f(x+3) = \frac{(f(x)-1)}{(f(x)+1)}$ and $f(11)=11$, we have $f(14)=\frac{(f(11)-1)}{(f(11)+1)}=\frac{10}{12}=\frac{5}{6}$ when we substitute $11$ for $x.$

We have $f(17) = \frac{(f(14)-1)}{(f(14)+1)} = ((\frac{5}{6})-1)/(\frac{5}{6})+1) = (-(\frac{1}{6}))/(\frac{11}{6}) = \frac{-1}{11}$ when we substitute $14$ for $x.$

We have $f(20) = \frac{(f(17)-1)}{(f(17)+1)} = (-(\frac{1}{11})-1)/(-(\frac{1}{11})+1) = (-(\frac{12}{11}))/(\frac{10}{11}) = \frac{-12}{10} = \frac{-6}{5}$, when we substitute $17$ for $x.$

We have $f(23) = \frac{(f(20)-1)}{(f(20)+1)} = (-(\frac{6}{5})-1)/(-(\frac{6}{5})+1) = (-(\frac{11}{5}))/(-(\frac{1}{5}))=11$, when we substitute $20$ for $x.$

Then we have the following patterns.
$f(11) = f(23) = f(35) = … = f(12k-1) = 11$

$f(14) = f(26) = f(38) = … = f(12k+2) = \frac{5}{6}$

$f(17) = f(29) = f(41) = … = f(12k+5) = \frac{-1}{11}$

$f(20) = f(32) = f(44) = … = f(12k+8) = \frac{-6}{5}$

So, $f(2006) = f(12*167+2) = \frac{5}{6}.$
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 when the answer is A, B, C, or D.

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

15 Jul 2021, 03:42

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(number properties) What is the value of $\frac{2a}{(a+1)}+\frac{2b}{(b+1)}$?

1) $a, b$ are integers

2) $ab=1$

=>

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 $\frac{2a}{(a+1)} + 2b(b+1) = (2a*(b+1) + \frac{2b(a+1))}{(a+1)(b+1)} = \frac{(2ab + 2a + 2ab + 2b)}{(ab+a+b+1)} = \frac{(4ab + 2a + 2b)}{(ab+a+b+1)},$ the question asks the value of $\frac{(4ab + 2a + 2b)}{(ab+a+b+1).}$

Condition 1) is obviously not sufficient as it tells us nothing about the values of $a$ and $b.$

Condition 2):
If $ab = 1$, then $\frac{(4ab + 2a + 2b)}{(ab+a+b+1)} = \frac{(2a+2b+4)}{(a+b+2)} = \frac{2(a+b+2)}{(a+b+2)} = 2.$ Condition 2) is sufficient.

Therefore, the answer is B.
Answer: B

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

17 Jul 2021, 03:21

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(absolute value) What is the value of $x$?

$1) |x+y|=|x-y|$

$2) |y| > y$

=>

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 $2$ variables ($x$ and $y$) and $0$ equations, C 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)

$|x+y|=|x-y|$

$=> |x+y|^2=|x-y|^2$

$=> (x+y)^2=(x-y)^2$

$=> x^2+2xy+y^2=x^2-2xy+y^2$

$=> 4xy = 0$

$=> xy = 0$

$=> x = 0$or $y = 0$

Condition 1) is equivalent to $x = 0$ or $y = 0$. Condition 1) is not sufficient.

Condition 2) is equivalent to $y < 0$. It follows from condition 2) that $x = 0$ since $y$ can’t be zero.

Both conditions 1) & 2) together are sufficient since they yield a unique solution.

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.

However, as we have seen above, neither condition 1) nor condition 2) is sufficient on its own.

Therefore, C is the answer.
Answer: C

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

20 Jul 2021, 02:58

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(number properties) Is $3$ a factor of $x$?

1) $x-3$ is divisible by $6$
2) $x+3$ is divisible by $6$

=>

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.

To solve remainder questions, plugging in numbers is recommended.

Condition 1)
If we plug in x = 9, then x – 3 = 6 is divisible by 6 and x is a multiple of 3. Condition 1) is sufficient.

Condition 2)
If we plug in x = 9, then x + 3 = 12 is divisible by 6 and x is a multiple of 3. Condition 2) is sufficient.

Therefore, the answer is D.
Answer: D

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

23 Jul 2021, 03:19

Expert Reply

MathRevolution wrote:

[Math Revolution GMAT math practice question]

(inequality) If $x$ and $y$ are positive, is $x>y$?

$1) 2x>3y$
$2) -5x<-7y$

=>

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.

Since $x$ and $y$ are positive, condition 1) tells us that $3x > 2x > 3y$ or $x > y$.
Thus, condition 1) is sufficient.

Condition 2)
$-5x < -7y$
$=> 5x > 7y$
This implies that $7x > 5x > 7y$ or $x > y$, since $x$ and $y$ are positive.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

25 Jul 2021, 03:02

Expert Reply

MathRevolution wrote:

[Math Revolution GMAT math practice question]

(number properties) If $m$ and $n$ are positive integers, is $m + n$ an odd number?

1) $\frac{m}{n}$ is an even number
2) $m$ or $n$ is an even number

=>

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 $2$ variables ($m$ and $n$) and $0$ equations, C 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)
Since $\frac{m}{n}$ is even, $\frac{m}{n} = 2k$ and $m = (2k)n$ for some positive integer $k$.
If $m = 2$ and $n = 1$, then $m + n = 3$, is an odd integer and the answer is ‘yes’.
If $m = 4$ and $n = 2$, then $m + n = 6$ is an even integer and the answer is ‘no’.
Since we do not obtain a unique answer, conditions 1) & 2) are not sufficient when considered together.

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.

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

28 Jul 2021, 00:44

Expert Reply

MathRevolution wrote:

[Math Revolution GMAT math practice question]

(number property) $[x]$ is the greatest integer less than or equal to $x$. $<x>$ is the least integer greater than or equal to $x$. What is the value of $x$?

$1) [x] = 2$
$2) <x> = 2$

=>

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.

$[x]$ is analyzed as follows.
If $n ≤ x < n + 1$ for some integer $n$, then $[x] = n.$
$<x>$ is analyzed as follows.
If $n – 1 < x ≤ n$ for some integer $n$, then $<x> = n.$

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)
$[x] = 2$
$=> 2 ≤ x < 3$
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Condition 2)
$<x> = 2$
$=> 1 < x ≤ 2$
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Conditions 1) & 2)
Only $x = 2$ satisfies both conditions.
Since the answer is unique, both conditions together 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.

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

30 Jul 2021, 03:23

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(number properties) $a$ and $b$ are positive integers. What is the remainder when $b$ is divided by $4$?

1) if $a$ is divided by $4,$ the remainder is $3$

2) if $a^2+b$ is divided by $4$, the remainder is $1$

=>

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.

Since we have $2$ variables ($a$ and $b$) and $0$ equations, C 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)
Condition 1) tells us that $a$ has remainder $3$, when it is divided by $4$. So, $a^2$ has remainder $1$, when it is divided by $4.$

Condition 2) tells us that $a^2+b$ has remainder $1$ when it is divided by $4$. Since $a^2$ has remainder $1$ when it is divided by $4, b$ has remainder $0$ when it is divided by $4.$

Thus, both conditions together 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)
Since there is no information about $b$ in condition 1), it is not sufficient.

Condition 2)
If $a = 1$ and $b = 4$, then $b$ has remainder $0$ when it is divided by $4.$

If $a = 4$ and $b = 1,$ then $b$ has remainder $1$ when it is divided by $4.$

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

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.

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

01 Aug 2021, 03:00

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(algebra) What is the value of $\frac{x}{(x+y)} + \frac{y}{(x-y)}$?

$1) (x+y):y = 3:1$

$2) x + y = 8$

=>

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 $\frac{x}{(x+y)} + \frac{y}{(x-y)}$ is equivalent to $\frac{(x^2+y^2)}{(x^2-y^2)}$ for the following reason
$\frac{x}{(x+y)} + \frac{y}{(x-y)}$

$=> \frac{x(x-y)}{(x+y)(x-y)} + \frac{y(x+y)}{(x+y)(x-y)}$

$=> \frac{(x^2-xy+xy+y^2)}{(x^2-y^2)}$

$=> \frac{(x^2+y^2)}{(x2-y^2)}$

$=> \frac{(x^2}{y^2+1)}/\frac{(x^2}{y^2-1)}$ by dividing the top and bottom by $y^2$

$=> [(\frac{x}{y})^2+1)/[(\frac{x}{y})^2-1]$

When a question asks for a ratio, 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. This tells us that A is most likely to be the answer to this question.

Condition 1)
The condition $(x+y):y = 3:1$ is equivalent to $x = 2y$ since $x + y = 3y$ from $(x+y):y = 3:1.$

Then $\frac{(x^2+y^2)}{(x^2-y^2)} = \frac{((2y)^2+y^2)}{((2y)^2-y^2)} = \frac{(4y^2+y^2)}{(4y^2-y^2)} = \frac{5y^2}{3y^2} = \frac{5}{3}.$

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

Condition 2)
If $x = 5$ and $y = 3$, then we have $\frac{x}{(x+y)} + \frac{y}{(x-y)} = \frac{5}{8} + \frac{3}{2} = \frac{5}{8} + \frac{12}{8} = \frac{17}{8}.$

If $x = 6$ and $y = 2$, then we have $\frac{x}{(x+y)} + \frac{y}{(x-y)} = \frac{6}{8} + \frac{2}{4} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4}.$

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

Therefore, A is the answer.
Answer: A

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

04 Aug 2021, 02:51

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(statistics) Is the average (arithmetic mean) of $x, y,$ and $z$ equal to their median?

1) $y$ is the average (arithmetic mean) of $x, y,$ and $z$
2) $z = 2y - x$

=>

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 data are symmetric, then the average and the median of the data are the same.

Condition 1):
If $y$ is the mean of $x, y$ and $z$, then $x, y, z$ are symmetric. To see this note that $\frac{( x + y + z )}{3} = y$ implies that $y = \frac{( x + z )}{2}$. So, $2y = x + z$ and $y – x = z – y,$ which means that $x, y, z$ are symmetric.
Condition 1) is sufficient.

Condition 2):
$z = 2y – x$ is equivalent to $y – x = z – y$, which is equivalent to condition 1).
Condition 2) is sufficient.

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, D is the answer.
Answer: D

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

07 Aug 2021, 02:59

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(inequality) $x$ is a positive number. Is $x > 1$?

$1) √x > x$

$2) x^3 - x < 0$

=>

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.

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

Condition 1)
$√x > x$

$=> x > x^2$ by squaring

$=> x^2 – x < 0$

$=> x(x-1) < 0$

$=> 0 < x < 1$

Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
$x^3 - x < 0$

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

$=> (x+1)x(x-1) < 0$

$=> x<-1$ or $0 < x < 1$

$=> 0 < x < 1$ since $x$ is positive.

Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

09 Aug 2021, 03:05

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(inequality) If $x, y$ and $z$ are integers with $x<y<z$, is $z>4$?

$1) x+y+z=12$

$2) x<4$

=>

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), since $x + y + z = 12$, their average is $4$
.
The maximum of three numbers is greater than or equal to their average. Thus, $z ≥ 4$.

Indeed, we must have $z > 4$ since $x, y$ and $z$ are different for the following reasons.

If $z = 4$, then $x + y = 8$. But $x < y < z (= 4)$, so this is impossible.

If $z ≤ 4$, then $x < y < z ≤ 4$, and we must have $x < 4$ and $y < 4$.

This implies that $x + y + z < 4 + 4 + 4 = 12$ and $x + y + z ≠ 12$ , which contradicts condition 1).

Thus, $z > 4$.

Condition 1) is sufficient.

Condition 2)
If $x = 3, y = 4$ and $z = 5$, then $z > 4$ and the answer is ‘yes’.

If $x = 1, y = 2$ and $z = 3$, then $z < 4$ and the answer is ‘no’.

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

Therefore, A is the answer.
Answer: A

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10161

Own Kudos [?]: 16598 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

Send PM

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

11 Aug 2021, 02:54

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(Algebra) Abigail and Bella have some money. How much did Abigail have at the beginning?

1) The ratio of the amount of Abigail’s money to Bella’s is $5:3$.

2) Abigail gives $$300$ to Bella, and then Bella gives Abigail $\frac{3}{5}$ of the amount that Bella has. After that Abigail has $5$ times as much money as Bella.

=>

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.

Assume that $a$ and $b$ are the amounts of money Abigail and Bella have, respectively.

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) together give us:
We have $a:b = 5:3$ or $b = (\frac{3}{5})a$ from condition 1).

From condition 2) we have $(a - 300) + (b + 300)·(\frac{3}{5}) = (b + 300)(\frac{2}{5})·5$. Substituting $b = (\frac{3}{5)}a$ gives us $(a - 300) + ((\frac{3}{5})a + 300)·(\frac{3}{5}) = 2((\frac{3}{5})a + 300).$

Then we have $a – 300 + (\frac{9}{25})a + 180 = (\frac{6}{5})a + 600 or a + (\frac{9}{25})a – (\frac{6}{5})a = 720.$

Thus, we have $a = 4500.$

The answer is unique, and conditions 1) and 2) together are sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.

Both conditions 1) & 2) together are sufficient.

Therefore, C is the correct 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.

gmatclubot

Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

11 Aug 2021, 02:54