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Math Revolution Approach (DS)

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Re: Math Revolution Approach (DS) [#permalink]

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New post 20 Oct 2017, 09:01
MathRevolution wrote:
What is the median of 5 numbers?

1) Each of the 3 numbers is 11
2) The 2 greatest numbers of them are 21 and 25


==> If you modify the original condition and the question, the median of 5 numbers become the third number.
In case of con 1), from 11,11,11,( ),( ) or ( ),11,11,11,( ) or ( ), ( ),11,11,11, it is always median=11, so it is unique and sufficient.

Therefore, the answer is A.
Answer: A


Safe to assume the numbers are integers?

Thank you.

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Re: Math Revolution Approach (DS) [#permalink]

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New post 22 Oct 2017, 20:16
[GMAT math practice question]

In the coordinate plane, a triangle ABC has 3 points A(-1,0), B(1,0), and C(m,n). What is the area of the triangle ABC?

1) m=2
2) n=2

=>
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.
The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.
We can consider AB as the base and the y-coordinate n of the point C as another point of the triangle, and |n| is its height.
Thus, its area is (1/2)*2*|n| = |n|.

Hence, only condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
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Re: Math Revolution Approach (DS) [#permalink]

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New post 22 Oct 2017, 20:18
[GMAT math practice question]

What is the value of x?

1) x^-2x=1
2) x^x=1

=>

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.
We have 1 variable and 0 equation. D is most likely to be the answer.

Condition 1)
Both x =1 and x = -1 satisfy condition 1).
Since the solution are not unique, this condition is not sufficient.

Condition 2)
Only x = 1 satisfies condition 2).
This is sufficient.
Note. 00 = 1 is not in the scope of GMAT exam.

Therefore, B is the answer.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E.


Answer: B
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Re: Math Revolution Approach (DS) [#permalink]

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New post 25 Oct 2017, 01:17
[GMAT math practice question]

If C=P(1+r/100)^n where C is the capital, P is the principal in 2001, and r is the compound interest rate after n years, by what percent did the capital increase from n years later to n+5 years later?

1) n=5
2) r=5



=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

The questions ask what the value of { P(1+r/100)^{n+5} } / { P(1+r/100)^n } is. However, { P(1+r/100)^{n+5} } / { P(1+r/100)^n } = (1+r/100)^5. It depends on r only.

Only condition 2) is sufficient.
Therefore, the answer is B.
Ans: B
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Re: Math Revolution Approach (DS) [#permalink]

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New post 25 Oct 2017, 23:45
[GMAT math practice question]

If n is positive integer, is 6 a factor of n?

1) 6 is a factor of n^2
2) 6 is a factor of 2n


=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 1 variable and 0 equation, D is most likely to be the answer. According to CMT4(B), if D is chosen as an answer too easily for key area questions, we should check the answer A or B. This question is about integers, which is one of the key question areas.

Condition 1)
n^2 = 2*3*k for an integer.
Since 2 and 3 are prime factors of n^2, 2 and 3 are prime factor of n.
Thus, 2*3 = 6 is a factor of n.
This is sufficient.

Condition 2)
We have two cases as follows.
n = 3 does not have 6 as a factor.
n = 12 has 6 as a factor.
This is not sufficient.

Therefore, the answer is A.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Thus, D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Answer: A
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Re: Math Revolution Approach (DS) [#permalink]

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New post 27 Oct 2017, 00:28
[GMAT math practice question]

If a is an integer, is a-b an integer?

1) 95 is a factor of a
2) b is 20 percent of a

=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Under the condition that a is an integer, if a – b is an integer, b is an integer. Thus, the question asks if b is an integer.

Since we have 2 variables and 0 equation, C is most likely to be the answer.
Condition 1) & 2)
b = 95 * (20/100) = 95 / 5 = 19.
Both conditions are sufficient.
Thus, C is the answer as expected.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both con 1) and con 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using con 1) and con 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.

Answer: C
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Re: Math Revolution Approach (DS) [#permalink]

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New post 29 Oct 2017, 17:02
[GMAT math practice question]

Is x>0?

1) x^3+x-1=0
2) x^3>1

=>
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.
Since we have 1 variable and 0 equation, D is most likely to be the answer.

Condition 1)
x^3+x-1=0
x^3+x = 1
x(x^2+1) = 1
x = 1/(x^2+1) > 0.
This is sufficient.

Condition 2)
x^3 > 1
x^3 – 1 > 0
( x – 1 )( x^2 + x + 1 ) > 0
x – 1 > 0, since x^2 + x + 1 > 0.
x > 1 > 0.
This is sufficient.

Therefore, D is the answer as expected.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Thus, D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E.


Answer: D
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Re: Math Revolution Approach (DS) [#permalink]

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New post 29 Oct 2017, 17:04
[GMAT math practice question]

If mn>0, is m^3n^4>0?

1) m>0
2) n>0

=>

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.
Since we have 2 variables and 1 equation, D is most likely to be the answer.
In an inequality question, an inequality in the original condition is counted as an equation.

The question m^3n^4>0? is equivalent to m > 0?, after dividing both sides by m^2n^4. Since mn>0, m>0 is equivalent to n>0 too.

Condition 1)
m > 0 is same as the question.
This is sufficient.

Condition 2)
We have m > 0 from mn > 0 and n > 0. It is same as the question.
This is sufficient too.
By tip 1), D is the answer, due to 1) = 2).
Therefore, D is the answer as expected.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Thus, D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E.

Answer: D
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Re: Math Revolution Approach (DS) [#permalink]

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New post 01 Nov 2017, 00:55
[GMAT math practice question]

If the average (arithmetic mean) exam score of Alice, Bob and Cindy is 80, what is their median score of the exam?

1) Alice’s score is 75.
2) Cindy’s score is 80.

=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

Assume A, B and C are exam scores of Alice, Bob and Cindy, respectively.
We have ( A + B + C ) / 3 = 80 or A + B + C = 240.
Since we have 3 variable and 1 equation, C is most likely to be the answer.

Conditions 1) and 2)
Since A = 75, C = 80 and A + B + C = 240, we have B = 85.
Then, the median is C = 80.
Since it is a statistics question, one of the key questions, according to CMT4(A), we should consider A or B if C is chosen too easily.

From the condition 1), A = 75, we can’t figure out the median.
From the condition 2), C = 80, we have A + B = 160.
If one of them is less than 80, the other one must be greater than 80 and C = 80 is the median.
Otherwise, A = B = C = 80 and the median is 80.
The condition 2) is sufficient.
Therefore, B is the answer.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Ans: B
_________________

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Math Revolution Approach (DS) [#permalink]

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New post 02 Nov 2017, 00:05
[GMAT math practice question]

xz < 0?

1) |x+y| = |x| + |y|
2) |y+z| = |y| + |z|

=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 3 variables and 0 equation, E is most likely to be the answer.

Conditions 1) & 2)

From the condition 1) and 2),
|x+y| = |x| + |y| is equivalent to xy ≥ 0 and |y+z| = |y| + |z| is equivalent to yz ≥ 0. Then we have xy^2z ≥ 0 or xz ≥ 0.

x = 1, y = 0, z = 1 implies xz = 1 > 0.
x = -1, y = 0, z = 1 implies xz = -1 < 0.

Both conditions together are not sufficient.

The answer is E.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Thus, E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously, there may be cases where the answer is A, B, C or D.
_________________

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Last edited by MathRevolution on 07 Nov 2017, 07:37, edited 1 time in total.

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Re: Math Revolution Approach (DS) [#permalink]

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New post 04 Nov 2017, 09:29
MathRevolution wrote:
Is (r^2)x>0?
1) r^5=1
2) x>0

ANS: There are two variables (r and x) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Hence, the correct answer is C.


Hello Sir

if we are given in question that product of (r raise to 2) * r, can we assume that (r raise to 2)the number will be positive. So we require only the symbol of x?

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Re: Math Revolution Approach (DS) [#permalink]

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New post 04 Nov 2017, 17:17
[GMAT math practice question]

1/x > 1/y?

1) x < y
2) xy > 0

=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

When we modify the question, we can multiply both sides of the inequality by x^2y^2, we have x(y^2)>x^2y? or xy(y-x)>0. Condition 1) states y – x > 0 and condition 2) states xy > 0.

Thus, C is the answer as expected.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.

Answer: C
_________________

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Re: Math Revolution Approach (DS) [#permalink]

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New post 05 Nov 2017, 17:22
[GMAT math practice question]

If x is a 5-digit integer, abc,de, is it divisible by 4?

1) d is an even number.
2) e is an even number.

=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

We can check the divisibility by 4 with the last two digits. The last two digit number is 10d + e. Since we have 2 variables and 0 equation, C is most likely to be the answer.
Condition 1) & 2)
d = 2, e = 4 ➔ 24 is divisible by 4.
d = 4, e = 4 ➔ 44 is not divisible by 4.
Therefore, E is the answer.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.

Answer: E
_________________

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Re: Math Revolution Approach (DS) [#permalink]

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New post 05 Nov 2017, 17:23
[GMAT math practice question]

If x and y are integers, is x-y an even number?

1) x+3y is even
2) (x-1)^2(y+1)^2 is even

=>

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution

Condition 1)
x – y = ( x + 3y ) - 4y is a difference of even integers, since x + 3y is even and 4y is even. This is sufficient.

Condition 2)
x = 3, y = 1 ➔ x – y = 2 is even.
x = 3, y = 2 ➔ x – y = 1 is odd.
This is not sufficient.
Therefore, the answer is A.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.
Answer: A
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Math Revolution Approach (DS) [#permalink]

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New post 06 Nov 2017, 22:50
ubaid1900 wrote:
MathRevolution wrote:
What is the median of 5 numbers?

1) Each of the 3 numbers is 11
2) The 2 greatest numbers of them are 21 and 25


==> If you modify the original condition and the question, the median of 5 numbers become the third number.
In case of con 1), from 11,11,11,( ),( ) or ( ),11,11,11,( ) or ( ), ( ),11,11,11, it is always median=11, so it is unique and sufficient.

Therefore, the answer is A.
Answer: A


Safe to assume the numbers are integers?

Thank you.


Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Since we have 5 variables and 0 equation, E is most likely to be the answer.

Condition 1) & 2)

We have 11, 11, 11, 21, 25.
The median is 11.

Since this question is Statistics, which is one of key questions, we should consider A or B by CMT 4(A).

Condition 1)
We have 3 cases which are 11 ≤ 11 ≤ 11 ≤ x ≤ y, x ≤ 11 ≤ 11 ≤ 11 ≤ y and x ≤ y ≤ 11 ≤ 11 ≤ 11.
Thus we have the median 11 for each of cases.
This is sufficient.

Condition 2)
We have x, y and z where x ≤ y ≤ z ≤ 21 ≤ 25.
Then we don't know what the value of median.
This is not sufficient.


Therefore, the answer is A.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
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Re: Math Revolution Approach (DS) [#permalink]

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New post 07 Nov 2017, 07:52
Adit07 wrote:
MathRevolution wrote:
Is (r^2)x>0?
1) r^5=1
2) x>0

ANS: There are two variables (r and x) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Hence, the correct answer is C.


Hello Sir

if we are given in question that product of (r raise to 2) * r, can we assume that (r raise to 2)the number will be positive. So we require only the symbol of x?



r^2 is not always positive. Actually, r^2 ≥ 0.

When we consider the condition 2) only, we have two following cases.
r = 1, x = 1 ⇒ (r^2)x = 1 > 0 : Yes
r = 0, x = 1 ⇒ (r^2)x = 0 : No

The condition 2) only is not sufficient.
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Re: Math Revolution Approach (DS) [#permalink]

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New post 08 Nov 2017, 23:43
[GMAT math practice question]

Is x > 0?

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


=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 1 variable and 0 equation, D is most likely to be the answer.

Conditions 1) x^3+x^2+x<0
x(x^2+x+1)<0 implies x < 0, since x^2+x+1 > 0.
The answer is no.
Since “no” is also an answer according to CMT (Common Mistake Time) 1, this is sufficient.

Condition 2) x^2<1
We have x2-1 < 0 and (x+1)(x-1) < 0.
Thus, you get -1 < x < 1 according to the “between” rule in inequalities.
This is not sufficient.

Therefore, A is the answer.


For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E.
Ans: A
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Re: Math Revolution Approach (DS) [#permalink]

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New post 08 Nov 2017, 23:59
[GMAT math practice question]

What is the remainder of x^2 + y^2, when it is divided by 4?
1) x and y are different prime numbers.
2) x – y = 2


=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 2 variables and 0 equation, C is most likely to be the answer.

Conditions 1) & 2)

Since x and y are different prime numbers and x – y = 2, both x and y are odd integers. x = 2a + 1 and y = 2b + 1 for some integers a and b. x^2 + y^2 = (2a+1)^2 + (2b+1)^2 = 4a^2 + 4a + 1 + 4b^2 + 4b + 1 = 4(a^2 + a + b^2 + b ) + 2.
Thus, its remainder is 2, when it is divided by 4.
Both condition 1) and 2) are sufficient.
The answer is C.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.
Answer: C
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Re: Math Revolution Approach (DS) [#permalink]

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New post 12 Nov 2017, 17:59
[GMAT math practice question]

P(A) and P(B) are the probabilities of independent events A and B, respectively. What is P(A)∙P(B)?

1) The probability that event A occurs but event B does not occur is 0.35.
2) The probability that event A occurs is 0.5.

=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 2 variables P(A) and P(B), and no equation, C is most likely to be the answer.

Since events A and B are independent, P(A∩B) = P(A) ∙P(B) and P(B) = P(A∩B) / P(A).

Condition 1) & 2)
Since P(only A) = 0.35 and P(A) = 0.5, we have P(A) ∙P(B) = P(A∩B) = 0.15.
Both conditions 1) and 2) together are sufficient.


Therefore, the answer is C as expected.


Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.
Answer: C
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Re: Math Revolution Approach (DS) [#permalink]

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New post 12 Nov 2017, 18:01
[GMAT math practice question]

If f(x+y) = f(x)f(y), what is the value of f(0)?

1) f(x) > 0
2) f(x) has integer values

=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

To find the value of f(x), we can plug in 0 for the variables x and y.
Then we have f(0+0) = f(0) ∙ f(0) or f(0) = {f(0)}^2
{f(0)}^2 - f(0) = 0
f(0) { f(0) – 1 } = 0
Then f(0) = 0 or f(0) = 1.
Then f(0) becomes an unknown variable and we have 1 variable. D is most likely to be the answer.
Condition 1)
Since f(0) > 0, we have f(0) = 1.
This is sufficient.

Condition 2)
Both 0 and 1 are integers, f(0) = 0 or f(0) = 1.
Thus, this is not sufficient.

Therefore, A is the answer.
Answer: A
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Re: Math Revolution Approach (DS)   [#permalink] 12 Nov 2017, 18:01

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