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Is the standard deviation of set A greater than that of set B?

1) The median of set A is greater than that of set B 2) The average (arithmetic mean) of set A is greater than that of set B

==> In the original condition, more than 90% of the questions related to the the relationship between median, mean, and standard deviation have E as the answer.

The answer of this question is also E. Answer: E
_________________

1) When n is divided by 3, the remainder is 1 2) When n+1 is divided by 4, the remainder is 2

==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you can directly substitute. Therefore, for con 1), from n=3p+1=1,4,…, the remainder when divided by 4 becomes 1=4(0)+1, which makes remainder=1, and from 4=4(1)+0, you get remainder=0, hence it is not unique and not sufficient. For con 2), from n+1=4q+2 and n=4q+1, the remainder when divided by 4 always becomes 1, hence it is unique and sufficient.

Therefore, the answer is B. Answer: B
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==> If you modify the original condition and the question, you get 3x>x-6?, 2x>-6?, x>-3?. There is 1 variable (x) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from x>-4, the range of the question doesn’t include the range of the condition, hence it is not sufficient. For con 2), from x>0, the range of the question includes the range of the condition, hence it is sufficient.

Therefore, the answer is B. Answer: B
_________________

When x is divided by 7, the remainder is 3. When x3 is divided by 7, what is the remainder?

A. 2 B. 3 C. 4 D. 5 E. 6

==> For remainder questions, it is important to use direct substitutions. From X=7p+3=3,10,17,…., if you substitute x=3, from x^3=3^3=27=7(3)+6, you get a remainder of 6.

Therefore, the answer is E. Answer: E
_________________

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

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30 Jul 2017, 20:41

MathRevolution wrote:

When x+y is integer, is y an integer?

1) x is an integer. 2) x+2y is an integer.

==> In the original condition, there are 2 variables (x,y) and 1 equation (x+y=integer). In order to match the number of variables to the number of equations, there must be 1 more equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from x=integer and x+y=integer, integer+y=integer, you get y=integer, which is yes and sufficient. For con 2), from x+2y=x+y+y=integer, integer+y=integer, you get y=integer, which is also yes and sufficient.

Therefore, the answer is D. Answer: D

st 2. x+2y is an integer- y can be 0.5, 2.5, 1 or 2 etc so st 2 is not sufficient

1) The units digit of n^2 is 4 2) The units digit of n^3 is 8

==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), you get n=~2, ~8, hence it is not unique and not sufficient. For con 2), you only get n=~2, hence it is unique and sufficient.

Therefore, the answer is B. Answer: B
_________________

==> In the original condition, there are 2 variables (m,n) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from con 1), you get 9^n=(3^2)^n=3^{2n}=3^m, which becomes 2n=m. In order for con 2) to satisfy as well, you only get m=n=0, hence it is unique and sufficient. The answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), the way to satisfy 9^n=(3^2)^n=3^{2n}=3^m to 2n=m is not unique and not sufficient. For con 2), from 2^n=5^m, you get 2^n=even and 5^m=odd, so even≠odd. Only m=n=0 satisfies this, hence it is unique and sufficient.

Therefore, the answer is B, not C. Answer: B
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If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. 3/5 B. 4/5 C. 3/7 D. 4/7 E. 3/8

==> Probability=Want/Total. Total=since the number of ways when throwing the coins each becomes head or tail 2 times, you get 2*2*2*2=16. Want=if it lands on head 2 times, it lands on tail 2 times, so you get 4!/2!2!=6. Thus, the probability=6/16=3/8.

The percent of employees participated in A program is 80% of the total employees. What is the total number of employees in the company?

1) 168 employees participated in this program. 2) 42 employees did not participate in this program.

==> If you modify the original condition and the question and set the number of people who participated in the program as a and number of people who did not participate in the program as b, from a=80%(a+b), there are 2 variables and 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from 168=80%(a+b) and a+b=168/80%=210, it is unique and sufficient. For con 2), from 42=20%(a+b) and a+b=42/20%=210, it is unique and sufficient.

Therefore, the answer is D. Answer: D
_________________

=>Condition 1) If x = y = 12, then the median of them is 12. If x < y, then the median of them 12, since x < 12 < y. If x > y, then the median of them 12, since y < 12 < x. This is sufficient.

Condition 2) Since we don’t know x, we don’t identify their median. This is not sufficient.

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