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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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17 Jun 2017, 09:03
Can someone please explain how the answer to the following DS question is A?
There are five homes. If the median price of a home is $200,000, is the range of all prices greater than $80,000? 1) The average price of the five homes is $240,000. 2) Three of five homes have the same price.



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18 Jun 2017, 18:05
If x, y are integers, is x+y an odd number? 1) y=3x+5 2) y=2x3 ==> If you modify the original condition and the question, in order to get x+y=odd, you need to get (x,y)=(even,odd)or (odd,even). For con 1), you get (x,y)=(even,odd) or (odd, even), hence always yes and sufficient. Therefore, the answer is A. Answer: A
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19 Jun 2017, 18:05
What is the number of multiples of 6 from 35 to 69? A. 14 B. 16 C. 17 D. 20 E. 21 ==> 0 becomes the multiple of all integers. From 1~69, 11 of them are multiples of 6, from 1~35, 5 of them are multiples of 6, hence you get 11+5+1=17. The answer is C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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20 Jun 2017, 19:52
√75+2√3=? A. 3√3 B. 5√3 C. 7√3 D. 8√3 E. 9√3 ==> You get √75+2√3=√(5^2)3+2√3=5√3+2√3=7√3. The answer is C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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21 Jun 2017, 18:05
Is ab+cd>0? 1) ac+bd＞0 2) bc+ad＞0 ==> In the original condition, there are 4 variables (a, b, c, d), 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 a=2, b=3, c=1, d=2: yes BUT a=5,b=1,c=1,d=2:, hence it is not sufficient. Therefore, the answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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22 Jun 2017, 18:41
If x/100+x/1,000+x/10,000+x/100,000=111, what is the approximation of x? A. 11,100 B. 111,000 C. 1,111,000 D. 11,111,000 E. 111,111,000 ==> Since it is approximation, you get _. Then, only x/100=111 is left, and thus you get x=11,100. The answer is A.
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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25 Jun 2017, 18:22
If average (arithmetic mean) score of 9 students is 90, what is the median score? 1) The 5 smallest scores are 84, 83, 82, 81, and 80 2) The 4 largest scores are 89, 88, 86, and 85 ==> If you modify the original condition and the question, and list the 9 numbers in the ascending order, you get 5th=median. Thus, according to con 1), you get 5th=median=84. Therefore, the answer is A.
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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26 Jun 2017, 17:51
If x≠0, is x^2<x? 1) x<1 2) x>1 ==> If you modify the original condition and the question, from x^2<x?, x^2<x?, when you divide both sides by x, (Since x>0, the inequality sign doesn’t change after division) you get x<1?, and then 1<x<1?. The answer is C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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27 Jun 2017, 18:45
If n is the least common multiple of 18 and 60, which of the following can be the factor of n? I. 24 II. 36 III. 45 A. Ⅰonly B. Ⅱ only C. Ⅲ only D.Ⅰ& Ⅲ only E. Ⅱ&Ⅲ only ==> You get 18=2(3^2) 60=(2^2)(3)(5), and since the least common multiple is the maximum value of the index, and you get n=(2^2)(3^2)(5). Therefore, you get I. 24=(2^3)(3) (X) II. 36=(2^2)(32) (O) III. 45=(3^2)(5) (O) The answer is Ⅱ&Ⅲ, which is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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28 Jun 2017, 16:50
If p is the sum of all odd numbers greater than 0 but less than 50, and q is the sum of all even numbers greater than 0 but less than 50, what is the value of pq? A. 24 B. 0 C. 1 D. 24 E. 25 ==> Since p=1+3+….+47+49, from q=2+4+…+46+48, the difference between 3+5+…+47+49 (part of p) and q=2+4+..+46+48 is 1 each, so there are 24. Since there is also +1 at the front of p, you get 24+1=25. The answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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29 Jun 2017, 18:49
If set A={a,b,c,d,e}, what is the number of subsets that must include only 3 elements? A. 8 B. 10 C. 12 D. 15 E. 18 ==> You get 5C3=5C2=(5)(4)/2!=10. The answer is b. Answer: B
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02 Jul 2017, 18:06
When 2 dices are tossed, what is the probability that the 2 faced numbers have a difference of 3? A. 1/9 B. 2/9 C. 1/3 D. 4/9 E. 1/6 ==> Numerator:(6,3), (5,2), (4,1), (3,6), (2,5), (1,4). Denominator:6*6. Thus, you get 6/6*6=1/6. The answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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03 Jul 2017, 18:03
If f(2x+3)=6x, f(5)=? A. 6 B. 3 C. 2 D. 3 E. 6 ==> From 2x+3=5, you get x=1, and then you get f(5)=6(1)=6. The answer is A. Answer: A
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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04 Jul 2017, 14:28
MathRevolution wrote: This is one of the most challenging types of the question that looks like a journal. This is a PS question that you should be familiar with.
It is wellknown that the way to find out approximation value of a positive integer n’s square root is following; 1st approximation: select a positive integer "a" and n is divided by a. 2nd approximation: a positive integer n’s square root is the average (arithmetic mean) of a quotient and divisor. What is the approximation positive integer n’s square root, in terms of a and n? A. (a^2+n)/2a B. (a^2+n)/2 C. (a^2n)/2a D. (a^2+n)/a E. (a^2+2n)/a Answer: A N=aQ, (a+Q)/2=(a+n/a)/2=(a^2+n)/2a
This type of questions looks very simple, but it is rather challenging. You should not underestimate the difficulty levels of PS questions (by the way this is a statistics problem). MathRevolution , can you further expand on this problem? How did you reach the solution?



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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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06 Jul 2017, 18:26
If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars? A. 10,000(1+ )^10 B. 10,000(1+0.08)^5 C. 10,000(1+0.08) D. 10,000(10.08)^2 E. 10,000*1.08 ==> if it is invested at 8 percent annual interest and is compounded semiannually, From 10,000(1+8%(1/2))^2*5= 10,000(1+ )^10 the answer is A Answer: A
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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08 Jul 2017, 10:37
How is it D? can you please elaborate. Should it not be E? MathRevolution wrote: Even for the mistake type 4 questions, they are becoming more complicated unlike simple questions in the past. For a question like the below, 1)=2), which is no and sufficient. Therefore, D is the answer.
(ex 3) If n is positive integer, is 3n+n2+1 not divisible by 3? 1) n is not multiple of 2 2) n is not multiple of 3
Answer: D
That is, questions are evolving like highly challenging questions, in which the mistake type 4 and 1 are combined. So, we should keep up with the evolving questions. In particular, integer questions are numerously given and you should carefully approach the questions, which will lead you to hit 51.



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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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09 Jul 2017, 18:31
3 robots can finish the same task in 6hrs, 7hrs, and 8hrs.What is the greatest part of the task that can be finished by two of these robots together in 1 hour? A. 13/42 B. 11/42 C. 42/13 D. 42/11 E. 13/21 ==> Assuming that A, B, and C finishes their tasks in 6hrs, 7hrs, and 8 hrs each, the work rate of A and B are good, and each finished 1/6 and 1/7, so you get 1/6+1/7=13/42. The answer is A. Answer: A
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10 Jul 2017, 11:07
MathRevolutionWould you please share something so that I can learn how to spot Mistake Type/Trap Questions.?



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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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10 Jul 2017, 17:53
For x and y, what is the value of x? 1) (x3)(x+y)=0 2) (x3)(2x+y)=0 ==> 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=3, which is unique and sufficient. Therefore, the answer is C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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11 Jul 2017, 18:04
1cd=? 1) c+d=1 2) c=1d ==> In the original condition, there are 2 variables (c,d) 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 con 1) = con 2), so both of them becomes c+d=1, and 1cd=1(c+d)=1(1)=2, hence it is unique and sufficient. Therefore, the answer is D. Answer: D
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