california

Ans: C Average = (11+99)/2 = 55

Ans: C 1. After simplifying 8w+4x+2y+z = 11 This is true only if w = 1, x = 0, y = 1 and z = 1. Then w+x+y+z = 3 - Suff. 1. After simplifying, 27w+9x+3y+z = 31 This is true only if w = 1, x = 0, y = 1 and z = 1. Then w+x+y+z = 3 - Suff.

Thanks Tatiana.

Hi Tatiana, Can you please post the link from which we can download PS1000? Thanks in advance, Cali

Ans: B What is OA?

Thank you guys! If you really like the solution, can you please add reputation points to my ID. I need three more points inorder to download or upload documents in this forum. I have already added reputation points to all of you. Thanks in advance for yor help. Cali.

Let 5n/18 = a and 3n/18 = b where a and b are integers. a-b = 5n/18 - 3n/18 = 2n/18 which is an integer because difference of two integers is always an integer. Let 2n/18 = c where c is an integer b-c = 3n/18 - 2n/18 = n/18, which is an integer for the same reason mentioned above. Ans: C

I agree with you Dynamo.I hope 800Bob provides good solution for this.

Let m and n be the first number in the series of X and Y consecutive integers respectively. a) x = 2 , y = 6. a = 2(2m+1)/2 and b = 6(2n+5)/2 We need to check if a = b for at least one set of integers for m and n 2(2m+1)/2 = 6(2n+5)/2 2m+1 = 6n+15 2m-6n = 14 m = 7+3n For every value of n>=1, m is an integer. We can have infinite number of series for x and y to satisfy option a. Ex: n = 2 and m = 13 Series of X consecutive integers = 13, 14 ( a = 13+14 = 27 ) Series of Y consecutive integers = 2,3,4,5,6,7 ( b = 27 ) If we repeat this process for all the options, we can find out that for options d, we can not have a series so that a = b. Hoping to see any other easier way of doing this.

(2 - Sqrt(5))x = -1 x = -1/(2-Sqrt(5)) => 1/(Sqrt(5)-2) Multiplying Numberator and denominator by (Sqrt(5)+2) x = (Sqrt(5)+2)/(5-4) => 2+Sqrt(5). Ans: A

Let me try... I think everybody agreed that the simplyfied question is Is xy/(x+y) > xy? 1. x = 2y => x/y = 2. This tells that x y and x and y are of the same sign, either +ve or -ve. In either case xy is a positive integer. As x and y are integers, x+y is an integer, either +ve or -ve. If xy is positive integer and x+y is an integer(+ve or -ve) then xy/(x+Y) can never be > xy as a positive integer1 divided by another integer2 > 1 can not be greater than the integer1. So xy/(x+Y) 2. x+y>0 gives nothing about the sign and values of x and y ---Insufficient. Ans: A

A for mee too.

Let the original price of the stereo be x x+0.06x = 530 => x = 500. Amount that could be saved = 500(0.06 - 0.05) = 5.00 Ans: D

You are right Lhomme. When each angle is greater than 110, then the polygon should have more than 5 sides. Answer shold be B

I think the Answer is E. Lhomme has already proved that 1 and 2 are sufficient by themself. Combining both the statements also gives different answers depending on the values of a and b. Ex: a = -1, b = 0 => |a| > |b| a = -1, b = -2 => |a|

First digit can be filled in 8 ways Second digit can be filled in 10 ways Third digit can be filled in 10 ways Fourth digit can be filled in 5 ways(Only odd digits) Total = 8x10x10x5 = 4000

7th term = a+6*2 = 9 => a = -3 Sum = 8(-3*2 + 7*2)/2 = 32

Let x be the ratio of a note to its lowr note Lower frequency = 440 Highest frequency = 440*x^12 = 880 => x = (2)^(1/12) Frequency of seventh note = 440*x^6 = 440*Sqrt(2) Ans: A

5050 + (5050 + 100*100) = 20,100 Ans: E

6/11 = 0.545454........ 25th decimal is 5 Ans: C

a6 = a1 + 5 a7 = a1 + 6 = a2 + 5 a8 = a1 + 7 = a3 + 5 a9 = a1 + 8 = a4 + 5 a10 = a1 + 9 = a5 + 5 a6+a7+a8+a9+a10 = a1+5 + a2+5 + a3+5 + a4+5 + a5+5 = (a1+a2+a3+a4+a5) + 25 = 560+25 = 585

Krovviddy, Your approch is correct, but each number repeats six times in each position. It will be 60*1111 = 66660.

Total = 9+8+7+6+5+4+3+2+1 = 45 Ans: D

Sum of each column is 4 times the number in the first cell Total sum = 4(1+2+3+4+5+6+7) = 4x28 = 112 Ans: B

560+25 = 585 Ans: A