mathewhe/aqua_rat huggingface dataset:
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds b in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
(A) 25%
(B) 35%
(C) 45%
(D) 70%
(E) 80%
Rationale: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out b: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Answer: (B) 35%
Question: The sum of the even numbers between 1 and n is 81*82, where n is an odd number, then n=?
(A) 163
(B) 171
(C) 177
(D) 185
(E) 193
Rationale: Let n-1 = 2a.
2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 81*82
Then a = 81 and n = 163.
The answer is A.
Answer: (A) 163
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3659
(A) 3659
(B) 9654
(C) 5945
(D) 7963
(E) 8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3659. Hence, it is the odd one.
The answer is 3659.
ANSWER:A
Answer: (A) 3659
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 75
(D) 90
(E) 86
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Answer: Option D
Hence, total number of notes = 3x = 90.
Answer: (D) 90
Question: John covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
(A) 10 Kmph
(B) 15 Kmph
(C) 17 Kmph
(D) 18 Kmph
(E) 19 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
B)
Answer: (B) 15 Kmph
Question: What is the ratio Q of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 3/5
(E) 2
Rationale: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5.= Q
Answer = D
Answer: (D) 3/5
Question: The number of cars present at a particular time was measured at 2,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 15% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
(A) 1,159
(B) 1,394
(C) 1,860
(D) 2,460
(E) 2,829
Rationale: The question states that all these 2,999 locations were measured twice, once on each day.
It also breaks the 2,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 2999
But, for the second day count, W = 1.15 T
i.e. for Second day count, T + 1.15T = 2999
i.e. 2.15 T = 2999
i.e. T = 1394
B
Answer: (B) 1,394
Question: If p/q = 6/7 , then 2p+q= ?
(A) 12
(B) 14
(C) 13
(D) 15
(E) 19
Rationale: let p=6, q=7 then 2*6+7=19
so 2p+q=19.
ANSWER:E
Answer: (E) 19
Question: The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?
(A) 17.5 km/hr
(B) 27.5 km/hr
(C) 67.5 km/hr
(D) 87.5 km/hr
(E) 77.5 km/hr
Rationale: Explanation:
Let the speeds of two trains be 7X and 8X km/hr.
8x = {\color{Blue} \frac{400}{4}}
=> x= 12.5 km/hrX=4004=>X=12.5Km/hr
So speed of first train is 12.5*7 = 87.5 km/hr
Answer: D
Answer: (D) 87.5 km/hr
Question: The difference between the squares of two consecutive numbers is 37. Find the numbers.
(A) 38 and 19.
(B) 28 and 19.
(C) 18 and 19.
(D) 18 and 29.
(E) None
Rationale: Solution:
If the difference between the squares of two consecutive numbers is x, then the numbers are (x-1)/2 and (x+1)/2
(37-1)/2 and (37+1)/2
36/2 and 38/2
Therefore the required answer = 18 and 19.
Answer C
Answer: (C) 18 and 19.
Question: If 4 people are selected from a group of 6 married couples, what is the probability that none of them would be married to each other?
(A) 1/33
(B) 2/33
(C) 1/3
(D) 16/33 probability
(E) 11/12
Rationale: Each couple can send only one "representative" to the committee. We can choose 4 couples (as there should be 4 members) to send only one "representatives" to the committee in C46C64 # of ways.
But these 4 chosen couples can send two persons (either husband or wife): 2∗2∗2∗2=242∗2∗2∗2=24.
So # of ways to choose 4 people out 6 married couples so that none of them would be married to each other is: C46∗24C64∗24.
Total # of ways to choose 4 people out of 12 is C412C124.
P=C46∗24C412=1633P=C64∗24C124=1633
Answer: D.
Answer: (D) 16/33 probability
Question: If in a race of 70m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
(A) 20m
(B) 16m
(C) 14m
(D) 10m
(E) 15m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (70 * 5) / 25 = 14m
Hence, A beats B by 14m.
ANSWER C
Answer: (C) 14m
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 10
(B) 9
(C) 11
(D) 12
(E) 15
Rationale: 4/12 + x/15 = 1
x = 10
ANSWER A
Answer: (A) 10
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 80 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of family?
(A) 3/7years
(B) B)31
(C) C)30
(D) D)33
(E) E)35
Rationale: Required average
= (80 x 2 + 35 x 2 + 6 x 3 )/(2 + 2 + 3)
= (160 + 70 + 18)/7
= 248/7
= 35 3/7years.
Answer is A
Answer: (A) 3/7years
Question: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 4, when a # b = 100?
(A) 5
(B) 9
(C) 10
(D) 13
(E) 17
Rationale: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 4 = 10/2 + 4 = 9.
The correct answer is B.
Answer: (B) 9
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $131 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: $131 = 25*$5 + 2*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 25, 22, 19, 16,...,1 for a total of 9 combinations.
The answer is D.
Answer: (D) 9
Question: The length of the bridge, which a train 135 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 76 m
(B) 178 m
(C) 240 m
(D) 187 m
(E) 176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (135 + x)/30 = 25/2
=> 2(135 + x)= 750 => x = 240 m.
Answer: C
Answer: (C) 240 m
Question: What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81?
(A) 1020600
(B) 1020593
(C) 56693
(D) 28343
(E) 18900
Rationale: 14 = 2 * 7
25 = 5 * 5
36 = 2 * 2 * 3 * 3
81 = 3 * 3 * 3 * 3
So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C.
Answer: (C) 56693
Question: A car traveled the first quarter of a certain distance at one-seventh the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
(A) 1/22
(B) 1/25
(C) 1/26
(D) 1/27
(E) 1/28
Rationale: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be one-seventh, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 1 3/7 km/h for the remaining quarters.
He'll take 1 hour to do the first quarter and then 7 hours for the second quarter, 7 hours for the third and 7 hours for the fourth. On total he will take 22 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/22. Answer A.
Answer: (A) 1/22
Question: A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 150 m
(B) 200 m
(C) 350 m
(D) 400 m
(E) None
Rationale: Sol.
Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x metres.
Then, x + 300 / 39 = 50/3 ⇔ 3(x + 300) = 1950 ⇔ x = 350m.
Answer C
Answer: (C) 350 m
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
(A) 24 years
(B) 66 years
(C) 77 years
(D) 55 years
(E) 16 years
Rationale: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
Answer: A
Answer: (A) 24 years
Question: Paulson spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. Find the percentage increase in his savings?
(A) 20%
(B) 25%
(C) 50%
(D) 75%
(E) 60%
Rationale: Let original income = $100
expenditure = $75
savings = $25
new income = $120
new expenditure = $110/100 * 75 = $165/2
New savings = 120 - 165/2 = $75/2
Increase in savings = 75/2 - 25 = $25/2
Increase % = 25/2 * 1/25 * 100 = 50%
Answer is C
Answer: (C) 50%
Question: if p/q=3/4
then3p+4q=?
(A) 25/4
(B) 25/2
(C) 20/4
(D) 35/4
(E) 25/3
Rationale: 3p+4q=?
Divided by q,
3(p/q)+4=x
3*(3/4)+4=25/4
ANSWER:A
Answer: (A) 25/4
Question: If 0.6 : x :: 5 : 8, then x is equal to:
(A) A)0.96
(B) B)1.2
(C) C)1.25
(D) D)1.3
(E) E)0.8
Rationale: (x * 5) = (0.6 * 8)
x = 4.8/5
x = 0.96
Answer = A
Answer: (A) A)0.96
Question: x = y - (40/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
(A) decrease
(B) stay the same
(C) increase four fold
(D) double
(E) Triples
Rationale: Alternate approach
Plug in some values of y > 0
Let y = 10
So, x = y - (40/y)
Or, x = 10 - (40/10) =6
Let y = 20
So, x = y - (40/y)
Or, x = 20 - (40/20) =18
So, x increases from 6 to 18
Hence the number increases 3 times, thus the correct answer will be (E)
Answer: (E) Triples
Question: What is the least number should be added to 929, so the sum of the number is completely divisible by 30?
(A) 1
(B) 2
(C) 5
(D) 6
(E) 8
Rationale: (929 / 30) gives remainder 29
29 + 1 = 30, So we need to add 1
Answer : A
Answer: (A) 1
Question: The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: Let q = 10% then l = 100/11 %
let b = 100 then a = 110
after increasing a by l and decreasing b yq we get c= 108
therefore c<a
C it is answer
Answer: (C) III only
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 30,000, A receives:
(A) s. 12,000
(B) s. 12,200
(C) s. 12,400
(D) s. 12,600
(E) s. 12,800
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (30000 x 21/50) = Rs. 12,600.
D
Answer: (D) s. 12,600
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 5 sec
(E) 4 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer: B
Answer: (B) 6 sec
Question: Find the principle on a certain sum of money at 8% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 939.6
(B) 928.8
(C) 927.78
(D) 926.82
(E) 902.1
Rationale: 1120 = P [1 + (8*12/5)/100]
P=939.60
Answer: A
Answer: (A) 939.6
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
(A) 65
(B) 48
(C) 37
(D) 23
(E) 12
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer:B
Answer: (B) 48
Question: If the S.P of Rs. 12 results in a 40% discount on the list price, What S.P would result in a 10% discount on the list price?
(A) s. 16
(B) s. 17
(C) s. 18
(D) s. 19
(E) s. 20
Rationale: Let the list price be Rs. X,
60/100*x = 12, x = 12*100/60 = 20
Required S.P = 90% of Rs. 20
= 90*20/100
=18
ANSWER:C
Answer: (C) s. 18
Question: Find the missing value : 8597 - ? = 7429 - 4358
(A) 5526
(B) 5426
(C) 5326
(D) 5226
(E) None of them
Rationale: Let 8597 - x = 7429 - 4358.
Then, x = (8597 + 4358) - 7429 = 12955 - 7429 = 5526.
Answer is A.
Answer: (A) 5526
Question: What is the sum of all digits for the number 10^27 - 48?
(A) 212
(B) 222
(C) 232
(D) 242
(E) 252
Rationale: 10^27 is a 28-digit number: 1 followed by 27 zeros.
10^27 - 48 is a 27-digit number: 25 9's and 52 at the end.
The sum of the digits is 25*9+5+2=232.
The answer is C.
Answer: (C) 232
Question: If x and y are different prime numbers less than ten, what must be true about the sum of x and y?
(A) the sum is even
(B) the sum is odd
(C) the sum is less than ten
(D) the sum is greater than ten
(E) the sum is less than 13
Rationale: This has to be solved by checking for each option:
Prime numbers less that 10 = 2, 3, 5, 7
A. the sum is even
May or may not be true. x = 3, y, = 5 -> True.
x = 2, y = 3 - True
B. the sum is odd
May or may not be true. x = 3, y, = 5 -> False.
x = 2, y = 3 - True
C. the sum is less than ten
May or may not be true x= 5, y = 7, Sum = 12
x = 2, y = 3. Sum = 5
D. the sum is greater than ten
May or may not be true x= 5, y = 7, Sum = 12
x = 2, y = 3. Sum = 5
E. the sum is less than 13
This will always be true.
Maximum sum = 7 + 5 = 12.
This is always less than 13.
Correct Option: E
Answer: (E) the sum is less than 13
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 180%
(B) 190%
(C) 100%
(D) 170%
(E) 900%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
Answer: (C) 100%
Question: A group of 5 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?
(A) x/70
(B) x/35
(C) 3x/40
(D) 3x/10
(E) 3x/7
Rationale: cost of boat per day = x
cost per person =x/5
if three more persons afre there, cost =x/8
difference = x/5-x/8
=3x/40
Ans C
Answer: (C) 3x/40
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 38 minutes, then the slower pipe alone will be able to fill the tank in
(A) 144 mins
(B) 140 mins
(C) 136 mins
(D) 152 minw
(E) None of these
Rationale: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/38
=>4/x=1/38
x=38∗4=152mins
Option D
Answer: (D) 152 minw
Question: A walks at 10 kmph and 3 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
(A) 100km
(B) 150km
(C) 60km
(D) 120km
(E) 200km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 3 hours.
x/10 - x/20 = 3
x = 60 km
Answer is C
Answer: (C) 60km
Question: If x is an integer and (x)(x^4)(x^3) is positive, which of the following could be negative?
(A) x^4
(B) (x)(x^3)
(C) (x)(x)
(D) x + x^11
(E) 3x^2
Rationale: A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^11 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)
Answer D.
Answer: (D) x + x^11
Question: Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 4 days. In what time Suma can do it alone?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 17
Rationale: Renu’s one day’s work = 1/6
Suma’s one day’s work = 1/4 - 1/6 = 1/12
Suma can do it alone in 12 days.
ANSWER:B
Answer: (B) 12
Question: 2y - 3x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?
(A) 2
(B) 1
(C) 0
(D) -2
(E) 3
Rationale: Plug in the answer choices in the equation from the question stem.
A) y = 2 >>> 4-3x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - 3x = 2x >>> Same, POE
C) y = 0 >>> -3x = 0 >>> x can not equal 0
D) y = -2 >>> -4 - 3x = -4x >>> Holds true for x = 4, no need to check E. This is the answer.
Answer D
Answer: (D) -2
Question: Five kilograms of oranges contained 95% of water. If the next day the concentration of water decreased by 5%, what was the new weight of the oranges, in kilograms?
(A) 30
(B) 25
(C) 15
(D)  10
(E)  5
Rationale: Five kilograms of oranges contained 95% of water. If the next day the concentration of water decreased by 5%, what was the new weight of the oranges, in kilograms?
(A) 30
(B) 25
(C) 15
(D) 10
(E) 5
If B is the answer, then the question means that the concentration of water the newt day became 90%.
Out of 5 kilograms 95%, or 4.75 kilograms was water and 0.25 kilograms was non-water.
The next day, after some water evaporated, oranges became 90% water and 10% of non-water, so the next day 0.25 kilograms of non-water composed 10% of oranges, which means that the new weight of the oranges was x*0.10=0.25 --> x=25 kilograms.
Answer: B.
Answer: (B) 25
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $50,000?
(A) $48,720
(B) $40,000.
(C) $38,976.
(D) $39,679.
(E) $36,796.
Rationale: 50,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option A fulfills the condition and hence is the answer
Answer: (A) $48,720
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability W that at least one will be orange?
(A) W=7/10
(B) W=3/5
(C) W=2/5
(D) W=3/10
(E) 1/10
Rationale: Method 1
Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue)*P(Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Answer: (A) W=7/10
Question: The perimeter of an isosceles right triangle is 14+14 sq rt 2. What is the length of the hypotenuse of the triangle?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9.899
Rationale: side of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 = 14 + 14 Sqrt2 or,
a. ( 2+ sqrt2) =14(1 + sqrt2), a= 14*(1+sqrt2)/2+sqrt2 =14*2.414/3.414 = then hypotenuse = 9.899
E
Answer: (E) 9.899
Question: In a kickball competition of 8 teams, how many possible matches can each team play with each other?
(A)  9
(B)  16
(C)  24
(D)  28
(E)  54
Rationale: 8C2 = 28
Option D
Answer: (D)  28
Question: If k is the sum of the digits of integer m, and m=11n, where n is an integer, which of the following must be true?
(A) k is a multiple of 6
(B) The sum of the digits of k is divisible by 3
(C) m is a multiple of 10k
(D) k is divisible by 2
(E) k is a multiple of 8
Rationale: m= 11n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =11,22,33,44 or -11 ,-22 ,-33 ,-44 then k 2,4,6,8 or -(1+1) , -(2+2) , -(3+3) ,-(4+4) .
ans D
Answer: (D) k is divisible by 2
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 8%. What was its profit on the items sold in February?
(A) 27.5%
(B) 30%
(C) 35%
(D) 37.5%
(E) 38%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.92*150x = 138x
Hence total profit = 38%
Option E
Answer: (E) 38%
Question: Of the 5 numbers, whose average is 120, the first is one-fourth of the sum of the last 4. The first number is?
(A) 83
(B) 80
(C) 50
(D) 120
(E) 60
Rationale: Total of 5 numbers = 5 * 120 = 600
Let total of last 4 numbers = x
1st number = x/4
x+ x/4 = 600
5x = 2400 => x =480
1st number = 480/ 4 = 120
Answer :D
Answer: (D) 120
Question: Which one of the following is equal to 17?
(A) 3 - 4 * 5 + 6
(B) 3 *4 + 5 / 6
(C) 3 + 4 * 5 - 6
(D) 3/ 4 + 5 - 6
(E) 3 * 4/ 5 + 6
Rationale: In the table below, each of the five expressions is evaluated using the correct order of operations.
Expression Value
(A) 3 - 4 x 5 + 6= 3 - 20 + 6 = -17 + 6 = -11
(B) 3 x 4 + 5 + 6=12 + 5 / 6 = 12 + 5/6 = 12 5/6
(C) 3 + 4 x5- 6= 3 + 20 - 6 = 23- 6 = 17
(D) 3 / 4 + 5 * 6=3/4 + 5 - 6 = 5 3/4 - 6 = 23/4- 24/4 = -1/4
(E) 3x 4 /5 + 6 =12 5 + 6 = 12/5 + 6 = 2 2/5 + 6 = 8 2/5
The only expression that is equal to 17 is 3 + 4 * 5 - 6, or (C).
correct answer C
Answer: (C) 3 + 4 * 5 - 6