mathewhe/aqua_rat huggingface dataset:
Question: Of the 250 employees at company X, 80 are full-time, and 175 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
(A) 25
(B) 30
(C) 50
(D) 80
(E) 100
Rationale: 250 employees
80 are full-time
175 have worked at company X for at least a year
20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
250-80=170 employees not full time
170-20= 150 employees not full time who worked over a year
175 employees have worked at company X for at least a year-150 employees not full time who worked over a year = 25 full-time employees of company X have worked at the company for at least a year
ans A
Answer: (A) 25
Question: There are 3 red shoes & 7 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
(A) 1/13
(B) 1/14
(C) 1/12
(D) 1/15
(E) 1/16
Rationale: taking 2 red shoe the probablity is 3C2
from 10 shoes probablity of taking 2 red shoe is 3C2/10C2=1/15
ANSWER:D
Answer: (D) 1/15
Question: A car was driving at 80 Km/h for 40 minutes, and then at 60 Km/h for another 40 minutes. What was its average speed?
(A) 113.33.
(B) 103.33
(C) 93.33
(D) 83.33
(E) 73.33
Rationale: driving at 80 Km/h for 40 minutes ,distance covered = 80*2/3=53.33 km
driving at 90 km/h for 40 minutes ,distance covered = 90*2/3=60 km
average speed = total distance/total time = 113.33/1 = 113.33 km/h
Answer: 113.33 km/h
Answer: (A) 113.33.
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 22
(B) 88
(C) 16
(D) 83
(E) 82
Rationale: 10 * 15 + 36 – 26 = 160/10 = 16
Answer: C
Answer: (C) 16
Question: How many total number of ways in which c distinct objects can be put into two different boxes is
(A) n2
(B) 2c
(C) 2n
(D) 3n
(E) None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the c objects. So, the total number of ways is
2 × 2 ×.....× 2 (c times ) = 2c
Answer B
Answer: (B) 2c
Question: In a party every person shakes hands with every other person. If there were a total of 153 handshakes in the party then what is the number of persons present in the party ?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Explanation :
Let the number of persons be n
âˆ´ total handshakes = nC2 = 153
n(n-1)/2 = 153 âˆ´ n = 18
Answer : Option D
Answer: (D) 18
Question: Find the value of X: 3x^2-6x+3 = 0
(A) -1
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: (B) 1
Question: In an election between two candidates first candidate got 50% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
(A) 5600 votes
(B) 5800 votes
(C) 5900 votes
(D) 5980 votes
(E) 5990 votes
Rationale: Total = 100 %,
First person got 50%
second person got remaining 50 % of votes.
than 50 % = 2800
50% = 50Ã—56 = 2800
100% =100Ã—56 =5600 votes
A
Answer: (A) 5600 votes
Question: What is the units digit of the expression 14^7−20^4?
(A)  8
(B)  3
(C)  4
(D)  6
(E)  0
Rationale: I think answer on this one should be A too. Since we know that 14^7>20^4, as Will said one should always check if the number is positive.
Answer: (A)  8
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 22% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 12.8%
(C) 15%
(D) 22%
(E) 30%
Rationale: Answer is B.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 10%+0,22X
id est X = 12,8%
Answer: (B) 12.8%
Question: A man purchases 2 watches for $ 540. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 260 and $ 300
(B) $216 and $ 324
(C) $224 and $336
(D) $560 and $560
(E) $224 and $ 350
Rationale: x + y = 540 --- (1)
1.15x + 0.9y = 540 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*108)/(3*108) = 216/324
Answer: B
Answer: (B) $216 and $ 324
Question: A box contains four gold coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
(A) 2/5
(B) 3/5
(C) 4/5
(D) 1/5
(E) 3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = 4/5
Option C
Answer: (C) 4/5
Question: The lowest number which should be added to 1277 so that the sum is exactly divisible by 3, 2, 5, 4 and 7 is:
(A) 303
(B) 403
(C) 203
(D) 453
(E) 203
Rationale: L.C.M. of 5, 6, 4 and 3 = 420.
On dividing 1277 by 420, the remainder is 17.
Number to be added = (420 - 17) = 403. Answer: Option 'B'
Answer: (B) 403
Question: A 10 kg dry mixture is composed of 40 % sugar and rest salt. How much sugar (in kg) must be added to this mixture so that salt and sugar are in same proportion?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: Total mass of the mixture is 10 kg out of which sugar is 40 %, means the mass of the sugar is 4 kg and the rest is salt, this means the salt content is 6 kg.
Suppose x kg of sugar is added so as to equalise the proportion of salt and sugar in the mixture.
After adding x kg sugar, the sugar content becomes (4 + x) kg and the salt content is the same 6 kg.
Now in the new mixture we desire the salt and sugar content to be same, this means we want their masses to be same.
This means ( 4 + x ) = 6
Solving we get x = 2.
Ans A
Answer: (A) 2
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) Rs.3944
(B) Rs.3918
(C) Rs.3928
(D) Rs.3929
(E) Rs.3289
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58
= Rs.3944.
Answer: A
Answer: (A) Rs.3944
Question: A physics class has 25 students, two of whom are Alex and Justin. Three students are chosen
uniformly at random for a lab demonstration. What is the probability that at least one of Alex
and Justin is chosen?
(A) 0.3
(B) 0.25
(C) 0.19
(D) 0.23
(E) 0.2
Rationale: We first calculate the probability that neither Alex nor Justin is chosen. The number
of ways to choose 3 people in the class is
􀀀25
3
. If neither Alex nor Justin can be chosen, there are
23 students that can be chosen and hence
􀀀23
3
ways to choose them. Therefore, the probability
that neither Alex nor Justin is chosen is
􀀀23
3
􀀀25
3
(=
23*22*21
3!
25*24*23
)=
23 *22 * 21/25 * 24 *23=
22 * 21/25 *24=
77/100,
so the probability that at least one of them is chosen is
1 -
77/100=
23/100=0.23
correct answer D
Answer: (D) 0.23
Question: On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The first box contains $3, the second $300, and the third $3000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. Mention the probability that a contestant will win more than $3000?
(A) 1/6
(B) 1/8
(C) 1/7
(D) 1/3
(E) 1/2
Rationale: Let's call the boxes that contain $3, $300, and $3000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $3000. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $3000, not more than $3000. The only configuration that leads to winning more than $1000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $3000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6
Answer = A
Answer: (A) 1/6
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 1/48
(B) 5/16
(C) 11/12
(D) 11/16
(E) 23/48
Rationale: Event(1): Probability of getting head in a flip of coin = 1/2
Event(2): Probability of getting 6 in a roll of dice = 1/6
Event(3): Probability of getting spade in a pack of card = 1/4
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*5/6*3/4 +1/2*1/6*3/4 +1/2*5/6*1/4
=15/48 + 3/48 +5/48
=23/48
Answer :E
Answer: (E) 23/48
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 6 hours
(B) 8 hours
(C) 3 hours
(D) 9 hours
(E) 1 hours
Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
Answer: C
Answer: (C) 3 hours
Question: A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 5 hours longer than the first half, how many hours did it take the runner to run the second half?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+5
T1 = 5 and so T2 = 10.
The answer is C.
Answer: (C) 10
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 34
(B) 42
(C) 48
(D) 49
(E) 53
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
Question: If 7687 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
(A) 27 books
(B) 1 book
(C) 28 books
(D) 0 books
(E) 8 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 7687.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 7687 =28 and 27 is divisible by 9.
Hence, we need to remove 1 to this number for it to be divisible by 9
Correct Option:B
Answer: (B) 1 book
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for 4 years and that for 12 years.
(A) 2:3
(B) 2:5
(C) 1:3
(D) 2:3
(E) None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗4/100) /(P∗R∗12/100)]
=4PR /12PR=1:3
Option C
Answer: (C) 1:3
Question: A, B and C start swimming in a pool simultaneously from the same end. To complete 10 laps, A takes 10 minutes, B takes 8 minutes and C takes 4 minutes. What is the ratio of speeds A:B:C?
(A) 3:4:5
(B) 12:15:20
(C) 5:4:3
(D) 4:5:10
(E) 12:15:25
Rationale: The slowest one is A, then comes B and the fastest one is C. So, the the ratio of speeds A:B:C must be in ascending order. Eliminate options C, D, and E.
A's speed (distance)/(time) = 10/10 = 1 lap per minute = 4laps in 4 minute;
B's speed (distance)/(time) = 10/8 = 5/4 lap per minute = 5 laps in 4 minutes;
C's speed (distance)/(time) = 10/4 = 5/2 lap per minute = 10 laps in 4 minutes/
Therefore, the the ratio of speeds A:B:C is 4: 5:10.
Answer: D.
Answer: (D) 4:5:10
Question: When n is divided by 15, the remainder is 6. When n is divided by 12, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: N = 159 q + 6
N = 12 z + 6
Equating
15 Q + 6 = 12z+6
12z=15q
12z/15 = q
since q is an integer Z must be divisible by 15.
Hence C
Answer: (C) 15
Question: During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 15 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
(A) 80%
(B) 100%
(C) 116.7%
(D) 120%
(E) 160%
Rationale: Kim purchased 20 gallons of gas. She paid for 15 + 0.9*5 = 19.5 gallons, so the overall discount she got was 0.5/20 = 0.025.
Isabella purchased 25 gallons of gas. She paid for 15 + 0.9*10 = 24 gallons, so the overall discount she got was 1/25 = 0.04.
4/2.5*100 = 160%
Answer: E.
Answer: (E) 160%
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What will be its population for 2years hence?
(A) 200000
(B) 215600
(C) 194582
(D) 194481
(E) 215460
Rationale: population after 2years = 176400*(1+ 5/100)^2 = 194481
Answer is D
Answer: (D) 194481
Question: In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?
(A) 1:0
(B) 1:3
(C) 1:9
(D) 1:6
(E) 1:5
Rationale: Explanation:
33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3
Answer: B) 1:3
Answer: (B) 1:3
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits T of the larger integer?
(A) T=2
(B) T=5
(C) T=8
(D) 10
(E) 11
Rationale: Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: (A) T=2
Question: On dividing a number by 7, we get 3 as quotient and 0 as remainder. On dividing the same number by 3, what will be the remainder?
(A) 1
(B) 2
(C) 3
(D) 0
(E) 4
Rationale: Number = 7 * 3 + 0 = 21
3) 21 (7
21
--------
0
Required number = 0.
ANSWER:D
Answer: (D) 0
Question: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
(A) 173 m
(B) 200 m
(C) 273 m
(D) 300 m
(E) None of these
Rationale: xplanation:
Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, <ACB = 30º and <ADB = 45º.
AB/AC=tan30
Answer: C
Answer: (C) 273 m
Question: If 12 men and 16 boys can do a piece of work in 7 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
(A) 1:4
(B) 1:2
(C) 1:3
(D) 2:1
(E) 4:1
Rationale: 12M + 16B ----- 7 days
13M + 24B ------- 4 days
84M + 112B = 52M + 96B
32M = 16B => 2M = B
M: B = 1:2
ANSWER:B
Answer: (B) 1:2
Question: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true?
(A) -5/2
(B) -3/2
(C) -1/2
(D) 1/4
(E) 1/2
Rationale: z^+z-3/4=(z+1/2)^2-1
It>0 is not true means it has to be less or equal to 0.
(z+1/2)^2-1<=0
(z+1/2)^2<=1
-1<=z+1/2<=1
-3/2<=z<=1/2
The minimum value of z is thus -3/2.
ANSWER:B
Answer: (B) -3/2
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ?
(A) x-2
(B) x-4
(C) x+4
(D) x-3
(E) x-1
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 36 more than 10x+y
10x+y+36=10y+x
10x-x+36=10y-y
9x+36=9y
x+4=y
OR
y=x+4
Answer : C
Answer: (C) x+4
Question: How many odd numbers between 10 and 900 are the squares of integers?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
13 numbers.
Answer: B.
Answer: (B) 13
Question: Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.
(A) 1
(B) 6
(C) 4
(D) 2
(E) 8
Rationale: C
Four
three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer: (C) 4
Question: For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.
(A) 15
(B) 36
(C) 33
(D) 27
(E) 29
Rationale: f(x) = -3(x - 10)(x - 4) = -3x2 + 42x - 120 : expand and obtain a quadratic function
h = -b/2a = -42/-6 = 7 : h is the value of x for which f has a maximum value
f(h) = f(7) = 27 : maximum value of f.
Answer: (D) 27
Question: The true discount on a bill of Rs.8640 is Rs.1440.The banker's discount is
(A) 1428
(B) 1528
(C) 1628
(D) 1728
(E) None of these
Rationale: Solution
P.W	= Rs.(8640 - 1440)
= Rs. 720
S.I on Rs. 8640	=Rs.(1440/7200 x 8640)
= Rs. 1728.
Answer D
Answer: (D) 1728
Question: How many possible different bus routes are available in a metro city ? Suppose the bus route numbers consist of a natural number less than 100, followed by one of the letters U,V,W,X,Y and Z.
(A) 500
(B) 550
(C) 564
(D) 594
(E) None of these
Rationale: The number can be any one of the natural numbers from 1 to 99. There are 99 choices for the number. The letter can be chosen in 6 ways. Number of possible bus routes are 99*6= 594
Answer D
Answer: (D) 594
Question: A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $64, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
(A) 48
(B) 52
(C) 54
(D) 58
(E) 56
Rationale: LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =64 OR 1/7T + 1T =64 THEREFORE T= 64*7/8 = 56
E
Answer: (E) 56
Question: Two pipe A and B fill a tank in 6 hours and 8 hours respectively.and C empty that tank in 12 hour.if all three pipe open together in empty tank then how much time it take to fill the tank?
(A) 19/3
(B) 23/2
(C) 24/5
(D) 18
(E) 16
Rationale: all three pipe resultant fill tank in 1 hour=[1/6+1/8-1/12]=5/24
total time taken to fill tank=24/5 hour
answer C
Answer: (C) 24/5
Question: In a certain corporation, there are 300 male employees and 150 female employees. It is known that 30% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
(A) 2/3
(B) 3/5
(C) 3/10
(D) 8/15
(E) 11/30
Rationale: P(female) = 150/450 = 1/3
P(male with advanced degree) = 0.3*300/450 = 90/450 = 1/5
The sum of the probabilities is 8/15
The answer is D.
Answer: (D) 8/15
Question: If the average of ten numbers is 60, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 60
(A) I
(B) II
(C) III
(D) I&II
(E) all three options
Rationale: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.
IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.
E
Answer: (E) all three options
Question: Car T and Car Y traveled the same 80-mile route. If Car T took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car T, how many hours did it take Car Y to travel the route?
(A)  2/3
(B)  1
(C)  4/3
(D)  8/5
(E)  3
Rationale: The speed of car T is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: (C)  4/3
Question: If a4 +(1/a4)=119 then a power 3-(1/a3)
(A) 22
(B) 36
(C) 27
(D) 18
(E) 19
Rationale: Explanation:
Given that a4+1a4=119a4+1a4=119 , adding 2 on both sides, we get : (a2+1a2)2=121(a2+1a2)2=121
⇒a2+1a2=11⇒a2+1a2=11
Again, by subtracting 2 on both sides, we have, ⇒(a−1a)2=9⇒(a−1a)2=9
⇒a−1a=3⇒a−1a=3
Now, ⇒a3−1a3⇒a3−1a3 = (a−1a)(a2+1a2+1)(a−1a)(a2+1a2+1) = 12×3 = 36
Answer:B
Answer: (B) 36
Question: What is the greatest prime factor of 4^17 - 2^29?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 31
Rationale: I'm happy to help with this.
We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*17) = 2^34
That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)
So, 4^17 - 2^29 = 2^34 - 2^29 = 2^(29 + 5) - 2^29 = (2^29)*(2*6) - 2^29 = (2^6 - 1) *(2^29)
= (32 - 1)*(2^29) = 31*(2^29)
The prime factors of 31 are 31, so the largest prime factor is 31, answer choice D.
Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/
Does all that make sense? Please let me know if you have any further questions.
Mike
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
E
Answer: (E) 31