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If x and y are integers greater than 1 and x>y, what are the values of x and y? 1) x+y=13 2) xy=22

==> In the original condition, there are 2 variables (x,y) 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), you get x=11 and y=2, 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). For con 1), from (x,y)=(11,2),(10,3), it is not unique and not sufficient. For con 2), you only get (x,y)=(2,11), hence it is unique.

Therefore, the answer is B, not C. Answer: B
_________________

==> In the original condition, there are 4 variables (w,p,s,t) and in order to match the number of variables to the number of equations, there must be 4 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), you get (w,s,p,t)=(1,1,1,1) yes, but (w,s,p,t)=(3,-1,-4,-1) no, hence it is not sufficient.

Therefore, the answer is E. Answer: E
_________________

If n is the product of 3 consecutive integers, which of the following must be true?

I. a multiple of 2 II. a multiple of 3 III. a multiple of 4

A. I only B. II only C. III only D. I and II E. II and III

==> If n is the product of 3 consecutive integers, it is always even and has 3, so it is always a multiple of 6. Thus, I and II is correct and for III, since n=1*2*3=6 is not a multiple of 4, hence it is incorrect.

1) The sum of any two prices of these 3 products is $8,000 2) At least one of them is 4,000

==> In the original condition, there are 3 variables, and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), the price of each 3 products becomes $4,000, hence it is unique and sufficient. This is an inequality 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 price of each 3 products always becomes $4,000, hence it is unique and sufficient. For con 2), it is unknown, hence it is not sufficient.

Therefore, the answer is A. Answer: A
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If the sum of the annual salaries of n persons is $x and the monthly salary per person is $y, what is the value of n in terms of x and y?

A. $x/12y B. $12x/y C. $12xy D. $12y/x E. $xy/12

==> Since the monthly salary per person is $y, the annual salary per person becomes $12y and the total sum of the annual salaries of n number of people becomes $12ny. Since it is $x, from $12ny=$x, you get n=x/12y.

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

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08 Apr 2017, 22:26

MathRevolution wrote:

This is a probability question. Each digit of 3-digit codes are formed from 0, 2, 4, 5, and 6. Each digit of the codes cannot be repeated. If the codes are divisible by 5, how many possible codes are there? A. 9 B. 12 C. 20 D. 21 E. 24 Answer: D

Since the codes need to be divided by 5, the units digit cannot be 0. Then we got 3*3=9. If the units digit is 0, we get 4*3=12. Then, 9+12=21. The answer is D.

Hi,

If we're talking about codes, then I guess we can surely have 0 at the front of the 3 digits. It would still be a 3 DIGIT number, however the value would be lesser. The value of the numbers formed shouldn't be considered in cases such as passwords or codes etc., right ?

==> In the original condition, there are 2 variables(a,b). In order to match with the number of equations, 2 equations are needed as well. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. Through 1) & 2), a=b=odd is derived, which is yes and sufficient. However, this is an integer question, one of the key questions, and apply the mistake type 4(A). In case of 1), (a,b)=(1,1) yes, (2,2) no, which is not sufficient. In case of 2), (a,b)=(odd,odd), which is yes and sufficient. Hence, the answer is B, not C.

==> If you modify the original condition and the question, is a^2b^3>0? becomes is b>0?, and If ab>0 becomes a>0?. Then, you get con 1) = con 2), and , the answer is D. Answer: D
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When n and k are positive integers, what is the greatest common divisor of n+k and n?

1) n=2 2) k=1

==> In the original condition, there are 2 variables, 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), you get n+k=2+1=3 and n=2, and GCD(3,2)=1, hence it is unique and sufficient. Therefore, 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), k is unknown hence it is not sufficient. For con 2), if k=1, n+k(=n+1) and n becomes 2 consecutive integers, so always GCD=1, hence it is unique and sufficient. Therefore, the answer is B, not C. Answer: B
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==> If you modify the original condition and the question, you get \(x^2>y^2\)??, or \(x^2-y^2\)?0?, or (x-y)(x+y)>0?. There are 2 variables (x,y) 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), you get x+y>2 and x-y>0, hence yes, it is always sufficient.

Therefore, the answer is C. Answer: C
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If two times x is 5 greater than three times y, what is the value of y, in terms of x?

A. y=2x-5 B. y=6x-5 C. y=(x/2)-5 D. y=(x/3)-5 E. y=(2x-5)/3

==> According to the ivy approach, is:”=”, greater than:”+”, hence you get 2x=5+3y. Thus, from 3y=5-2x, y=(2x-5)/3, the answer is E. Answer: E
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1) Two of them are odd 2) x, y, and z are different integers

==> In the original condition, there are 3 variables (a,b,d) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), (x,y,z)=(1,2,3) yes, but (x,y,z)=(2,3,5)no, hence it is not sufficient.

==> 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 2), n=7, 14, hence not unique and not sufficient. For con 2), n=7, 11, hence not unique and not sufficient. By solving con 1) and con 2), you get n=7, hence it is unique and sufficient.

==> If you modify the original condition and the question and check the question again, from a-b=int?, int-b=int?, you get b=int-int=int?. Since there is 2 variables (a,b), 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), you get b=0.37a=0.37(100int)=37int=int, hence it is always yes and sufficient. Therefore, the answer is C. Answer: C
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If the average (arithmetic mean) of set A is 10,000 and the average (arithmetic mean) of set B is 10,000, what is the range of set A and set B combined?

1) The range of set A is 6,000 2) The range of set B is 3,000

==> If you modify the original condition and the question, since there are 2 sets, set 1’s range=set 1’s Max-set 1’s min, and set 2’s range=set 2’s Max-set 2’s min. Thus, there are 6 variables and 2 equations, and in order to match the number of variables to the number of equations, there must be 4 more equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), the max and the min when combined is unknown, hence it is not sufficient.

Therefore, the answer is E. Answer: E
_________________

A store currently charges the same price per pound of salad. If the current price per pound were to be increased by $0.2, 0.5 pound smaller salad could be bought for $9. What is the current price of salad per pound?

A. $1.6 B. $1.7 C. $1.72 D. $1.8 E. $1.84

==> If you set the price of the salad per pound as $p, for n pounds, you get np=(n-0.5)(p+0.2)=9. From np=np+0.2n-0.5p-0.1, if you substitute 0.2n=0.5p+0.1, and n=2.5p+0.5, you get p=1.8.

==> In the original condition, there are 4 variables and in order to match the number of variables to the number of equations, there must be 4 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), from a=1, b=1,c=1,d=1 and a=2, b=1/2, c=1, d=2, it is not unique and not sufficient.

Therefore, the answer is E. Answer: E
_________________

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