mathewhe/aqua_rat huggingface dataset:
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 7th year?
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
7th year : 6-7 (age), we take age =6
Thus for the 5th year = 50,
6th year = 50 -5 = 45
7th year = 45-6 = 39
The correct answer is D.
Answer: (D) 39
Question: The sum of the numbers is 98. If the ratio between the first and the second be 2:3 and that between the second and third be 5:8, then find the second number?
(A) 24
(B) 30
(C) 36
(D) 42
(E) 50
Rationale: Given ratios
2 : 3
5 : 8
10:15:24
The second number = 98/(10+15+24) * 15 = 30
Answer is B
Answer: (B) 30
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.9 kmph
(B) 62.5 kmph
(C) 10.5 kmph
(D) 12.5 kmph
(E) 16.5 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Answer: (D) 12.5 kmph
Question: Out of 9 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
(A) 15/23
(B) 21/28
(C) 31/38
(D) 37/42
(E) 43/56
Rationale: P(no graduates) = 5C3 / 9C3 = 5/42
P(at least one graduate) = 1- 5/42 = 37/42
The answer is D.
Answer: (D) 37/42
Question: On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 22%
(E) 30%
Rationale: suppose there are X motorists.
10% of them exceeded the speed limit and received the ticket, i.e. X/10.
Again, suppose total no. of motorists who exceeded the speed limit are Y.
20% of Y exceeded the speed limit but didn't received the ticket, i.e. Y/5.
it means 4Y/5 received the ticket.
hence, 4Y/5 = X/10
or Y/X=1/8
or Y/X * 100= 1/8 * 100= 12.5%
ANSWER:B
Answer: (B) 12.5%
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 210 the Other is
(A) 330
(B) 300
(C) 270
(D) 250
(E) 350
Rationale: The other number
= L.C.M * H.C.F/given number
= 2310*30/210 = 330
Answer is A.
Answer: (A) 330
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: What Is The Next Number
12 13 15 17 111 113 117 ?
(A) 154
(B) 119
(C) 129
(D) 428
(E) 224
Rationale: 119.
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
Answer : B
Answer: (B) 119
Question: If A can complete a work in 36 days and B can do the same work in 42days. If A after doing 6 days, leaves the work, find in how many days B will do the remaining work ?
(A) 35 days
(B) 15 days
(C) 30 days
(D) 25 days
(E) 27 days
Rationale: Explanation:
A’s one day work =1/36
6 day work = 6*1/36 = 1/6
Remaining work = 1-1/6=5/6
B completes the work in 5/6*42 = 35 days
Answer: Option A
Answer: (A) 35 days
Question: There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?
(A) 95
(B) 103
(C) 111
(D) 119
(E) 127
Rationale: The total number of ways to select 4 books is 9C4 = 126
The number of ways which do not include any paperbacks is 6C4 = 15
The number of combinations with at least one paperback is 126-15 = 111
The answer is C.
Answer: (C) 111
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
(A) 18
(B) 15
(C) 16
(D) 19
(E) 11
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.Answer:B
Answer: (B) 15
Question: Express a speed of 42 kmph in meters per second?
(A) 10 mps
(B) 18 mps
(C) 19 mps
(D) 17 mps
(E) 12 mps
Rationale: 42 * 5/18
= 12 mps
Answer:E
Answer: (E) 12 mps
Question: How many 3 digit positive integers W exist that when divided by 7 leave a remainder of 5?
(A) 128
(B) 142
(C) 143
(D) 141
(E) 129
Rationale: Minimum three digit number is 100 and maximum three digit number is 999.
The first three digit number that leaves remainder 5 when divided by 7 is 103.
14 * 7 = 98 +5 = 103
The second three digit number that leaves remainder 5 when divided by 7 is 110.
15 * 7 = 105 +5 =110
The third three digit number that leaves remainder 5 when divided by 7 is 117
and so on
The last three digit number that leaves remainder 5 when divided by 7 is 999
142 * 7 = 994 + 5 = 999
Therefore, we identify the sequence
103,110,117.....999
use the formula of last term
Last term = first term + (n - 1) * common difference
you will get the answer 129 that is definitely E.
Answer: (E) 129
Question: With respect to the division whose percent of total income exceeded its percent of total expenses by the greatest amount among the four divisions, by approximately what amount did the division's income exceed its own expenses ?
Division A :. 38%
Division B : 12%
Division C : 30%
Division D : 20%
(A) $ 69,000
(B) $ 90,000
(C) $ 150,000
(D) $ 185,000
(E) $ 240,000
Rationale: Division A's percent of total income exceeded its percent of total expenses by 38%-35%=3%;
Division B's percent of total income did not exceeded its percent of total expenses, 12%-26%=-14%;
Division C's percent of total income exceeded its percent of total expenses by 20%-14%=6%;
Division D's percent of total income exceeded its percent of total expenses by 30%-25%=5%;
Since division C's difference is the greatest then we should calculate the amount of this difference in $: 0.20*1,560,000-0.14*495,000=~240,000.
Answer: E.
Answer: (E) $ 240,000
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
(A) 33
(B) 389
(C) 40
(D) 38
(E) 22
Rationale: Explanation:
Let the required number of days be x.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
{\color{Blue} \left.\begin{matrix} Cows & 1:40\\ Bags& 40:1 \end{matrix}\right\}:: 40:x}
{\color{Blue} \therefore }1 x 40 x x = 40 x 1 x 40
{\color{Blue} \Rightarrow } x = 40.
Answer: C) 40
Answer: (C) 40
Question: On the coordinate plane , points M and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?
(A)  (1.5,1)
(B)  (2,-5)
(C)  (0,0)
(D)  (1,1.5)
(E)  (2,2)
Rationale: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.
One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).
Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that MQ is the diameter of the circle.
There can be a case when MQ is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.
If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D
Answer: (D)  (1,1.5)
Question: How many multiples of 4 are there between 1 and 100, inclusive?
(A) 25
(B) 22
(C) 23
(D) 30
(E) 36
Rationale: 25
multiples of 4 between 1 and 100 inclusive.
from 4 * 1 upto 4 *25, (1,2,3,4,...,25). Hence, 25 multiples !
correct option is A
Answer: (A) 25
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 3/41
(B) 2/45
(C) 9/42
(D) 5/46
(E) 5/47
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: (C) 9/42
Question: 3,7,12,18,25..............9th terms
(A) 43
(B) 53
(C) 63
(D) 65
(E) 78
Rationale: 3+4=7
7+5=12
12+6=18
18+7=25
25+8=33
33+9=42
42+10=52
52+11=63
ANSWER:C
Answer: (C) 63
Question: If taxi fares were $1.00 for the first 1/5 mile and $0.45 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was
(A) $1.56
(B) $2.40
(C) $3.80
(D) $4.20
(E) $7.30
Rationale: In 3 miles , initial 1/5 mile charge is $1
rest of the distance = 3 - (1/5) = 14/5
rest of the distance charge = 14(0.45) = $6.3 (as the charge is 0.45 for every 1/5 mile)
=> total charge for 3 miles = 1+6.3 = 7.3
Answer is E.
Answer: (E) $7.30
Question: If A:B = 1/2: 1/4 B:C = 1/2:1/4 then A:B:C?
(A) 12:24:36
(B) 1:2:3
(C) 4:14:24
(D) 12:8:16
(E) 16:8:4
Rationale: A:B = 1/2:1/4 = 4:2
B:C = 1/2:1/4 = 4:2
--------------------
A:B:C = 16:8:4
Answer: E
Answer: (E) 16:8:4
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 39 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 28 4â„7 years
(B) 31 5â„7 years
(C) 32 6â„7 years
(D) 27 1â„2 years
(E) None of these
Rationale: Required average = (67Ã—2+39Ã—2+6Ã—3/2+2+3)
=230/7
= 32 6â„7 years
Answer C
Answer: (C) 32 6â„7 years
Question: 66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
(A) 44 m
(B) 84 m.
(C) 89 m
(D) 83 m
(E) 42 m
Rationale: Let the length of the wire be h.
Radius =1/2 mm=	1/20	cm.	Then,
= 22/7 x	1/20	x 1/20 x h = 66.
h =	66 x 20 x 20 x 7/22	= 8400 cm = 84 m.
Answer: B
Answer: (B) 84 m.
Question: A manufacturing plant produces 2 products (bolts and screws). 3% of all products are defective. If the ratio of products made is 3:2, respectively, and the percentage of bolts defective 5%, what percentage of screws are defective?
(A) 1/3%
(B) 3%
(C) 5%
(D) 5/2%
(E) 5/3%
Rationale: Let B and S be number bolts and screws, respectively, and d represent defective.
B + S = total products.
B:S = 2:3
Bd/B = 5%
Sd/S = ?
[(2)(Bd/B) + (3)(Sd/S)]/(2 + 3) = 3%
[(2)(5%) + (3)(Sd/S)]/5 = 3%
Sd/S = 5/3%
Answer: E
Answer: (E) 5/3%
Question: Two vessels contains equal number of mixtures milk and water in the ratio 3:2 and 4:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
(A) 1:3
(B) 9:13
(C) 5:11
(D) 7:3
(E) 15:4
Rationale: The ratio of milk and water in the new vessel is = (3/5 + 4/5) : (2/5 + 1/5)
= 7/5 : 3/5 = 7:3
Answer is D
Answer: (D) 7:3
Question: If x/y = 8/7, Then (7x + 6y) / (7x â€“ 6y) = ?
(A) 11
(B) 8
(C) 9
(D) 7
(E) 6
Rationale: Answer
Dividing numerator as well as denominator by y, we get
Given Exp. = (7x + 6y) / (7x â€“ 6y) = (7x/y + 6) / (7x/y â€“ 6)
Since x/y = 8/7
this implies that
=[(7*8)/7 +6]/[(7*8)/7 -6)]
= (8 + 6) / (8 - 6)
= 7
Option: D
Answer: (D) 7
Question: An employer pays Rs.20 for each day a worker works and for feits Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280 . for how many days did the worker remain ideal?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: if he work for 20 days then he get =20*20=Rs.400
and left 40 days he will not work so for this employer feits Rs.120
now total earning of a worker =400-120=280
40 days he will be ideal
ANSWER:C
Answer: (C) 40
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 423
(B) 456
(C) 264
(D) 200
(E) 154
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1]
= 200.
Ans: D
Answer: (D) 200
Question: The product of x and y is a constant. If the value of x is increased by 20%, by what percentage must the value of y be decreased?
(A) 16.66%
(B) 33.33%
(C) 44.44%
(D) 55.55%
(E) 19.92%
Rationale: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.2x (120)
i.e. 120*New 'y' = 10000
i.e. New 'y' = 10000/120 = 83.33
i.e. y decreases from 100 to 83.33 i.e. Decrease of 16.66%
Answer: option A
Answer: (A) 16.66%
Question: If there are 200 questions in a 3 hr examination. Among these questions are 50 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
(A) 72 min
(B) 62 min
(C) 70 min
(D) 74 min
(E) 76 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
150x+50*2x=180
x=180/250
x=0.72
time taken for type A problem=50*2*0.72=72min
ANSWER:A
Answer: (A) 72 min
Question: Lily shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
(A) 0.8
(B) 0.75
(C) c) 8/9
(D) 5/7
(E) 6/8
Rationale: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?
In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!
Here's the working: Lily shop runs a sale on goldfish and platys.
13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2
2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3
8x + 12y = 4.6 [Multiply Equation 3 with 4]
5x = 1.0 [Equation 1 - Equation 2]
x = 0.2
3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]
y = 0.25
x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]
The whole thing must have taken me about 45 s :D
Answer: (D) 5/7
Question: If t is a positive integer and 10^t – 74 in decimal notation has digits whose sum is 440, what is the value of t?
(A) 40
(B) 44
(C) 45
(D) 46
(E) 50
Rationale: Answer E = 50
We have (10^t)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.
So we have 48 + 2 as an t = 50
Answer: (E) 50
Question: The weight of a glass of jar is 15% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?
(A) 1/5
(B) 1/3
(C) 2/5
(D) 9/17
(E) 9/23
Rationale: Let weight of jar filled with beans = 100 g
Weight of jar = 15 g
Weight of coffee beans = 85 g
Weight of jar and remaining beans = 60 g
Weight of remaining beans = 45 g
Fraction remaining = 45/85 = 9/17
Answer is D.
Answer: (D) 9/17
Question: 3*12+3*13+3*16+11 = ?
(A) 122
(B) 126
(C) 134
(D) 148
(E) 151
Rationale: 3*12+3*13+3*16+11 = 36 + 39 + 48 + 11 = 134
The answer is C.
Answer: (C) 134
Question: A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 8000.
(A) Rs. 2500
(B) Rs. 8500
(C) Rs. 7200
(D) Rs. 8000
(E) None of these
Rationale: Explanation:
A = 2B and B = 5C
=> A : B = 2 :1and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 8000] = Rs. 2500
Answer: Option A
Answer: (A) Rs. 2500
Question: if integer N has p factors ; how many factors will 4N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: Case 1:
Let N = 6 => 2 x 3 (prime factorization) => p = 4;
4N = 24 => no. of factors = 8; (p*2)
Case 2:
Let N = 9 => 3^2 (prime factorization) => p = 3;
4N = 36 => > no of factors = 9; (3p)
For different N different results are observed. So, shouldn't E be the right answer?
Answer: (E) Cannot be determined
Question: A batsman scored 130 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 53.85%
(B) 40%
(C) 60%
(D) 70%
(E) 80%
Rationale: Number of runs made by running = 130 - (3 x 4 + 8 x 6)
= 130 - (60)
= 70
Now, we need to calculate 70 is what percent of 130.
=> 70/130 x 100 = 53.85 %
ANSWER:A
Answer: (A) 53.85%
Question: Mary works in a restaurant a maximum of 70 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
(A) 600
(B) 620
(C) 660
(D) 320
(E) 400
Rationale: Mary receives $8(20)=$160 for the first 20 hours.
For the 50 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $50(20)=$500.
The total amount is $160+$500 = $660
Answer C 660.
Answer: (C) 660
Question: IN Common Wealth Games an athlete runs 200 meters in 36 seconds. Hisspeed is ?
(A) 25 km/hr
(B) 27 km/hr
(C) 30 km/hr
(D) 20 km/hr
(E) None of these
Rationale: Explanation :
(200/1000)/(36/3600)=20 km/hr
Answer : D
Answer: (D) 20 km/hr
Question: A train passes a platform in 25 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 75
(B) 25
(C) 26
(D) 23
(E) 22
Rationale: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 20
=> 300+L = 15×25 = 375
=> L = 375-300 = 75 meter
Answer is A.
Answer: (A) 75
Question: Calculate the percentage increase in the area of a square if each of its sides is increased by 15%?
(A) 32.25%
(B) 39.25%
(C) 36.25%
(D) 35.25%
(E) 31.25%
Rationale: Assume original length = 100m by 50m
original area = 100*50= 5000
15% increase on each side
l = 100 + 15 = 115
w = 50 + 7.5 = 57.5
new area = 115*57.5= 6612.5
increase in area = 6612.5 - 5000 = 1612.5
%increase =21%
Answer A
Answer: (A) 32.25%
Question: Laura has a deck of standard playing cards with 12 of the 60 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
(A) 1/4
(B) 1/5
(C) 5/26
(D) 12/42
(E) 13/42
Rationale: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.
If there is no replacement then how is the (P) that the 10th card is 12/60 ??
there are many cases here to be considered here if there is no replacement such as:
H- Denotes heart X-may be any diamond, spade or club.
1. HXXXXXXXXH
2. HHXXXXXXXH
3. HHHXXXXXXH
.
.
.
.
.
9. HHHHHHHHHH
10. XXXXXXXXXH
All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.
For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 12/60 = 1/6 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....
B
Answer: (B) 1/5
Question: How many pieces of 8.6 metres length cloth can be
cut out of a length of 455.8 metres cloth?
(A) 43
(B) 48
(C) 55
(D) 53
(E) 68
Rationale: Number of pieces =455.8 /8.6 = 53
Answer D
Answer: (D) 53
Question: In store A there are 30 pairs of pants for every 60 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
(A) 3:16.
(B) 2:3.
(C) 1:3.
(D) 3:4.
(E) 2:5.
Rationale: 1st statement : ratio of pants
Store A : Store B
30x : 60x
X:2X
Price :
4y:3y
Total revenue
4xy : 6xy
2:3
Answer is B
Answer: (B) 2:3.
Question: how many four digits numbers are formed such that the digits are in decreasing order
(A) 210
(B) 220
(C) 230
(D) 240
(E) 250
Rationale: START with 3 = 3_ _ _. You can fill in with digits 0,1,2. Hence 3C3 = 1
START with 4 = 4_ _ _. (0,1,2,3). hence 4C3= 4
START with 5, you have (0,1,2,3,4) to fill in the blanks behind 5, hence 5C3 = 10
START with 6, 6C3=20
7... = 7C3 = 35
8...=8C3 = 56
9...= 9C3 = 84
so ans=1+4+10+20+35+56+84=210
ANSWER:A
Answer: (A) 210
Question: A certain company’s profit in 1996 was 10 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
(A) 5%
(B) 18%
(C) 32%
(D) 35%
(E) 38%
Rationale: Profit in 1995 - 100
Profit in 1996 - 110
%increae Profit in 1997 in comparison to 1995 = 10 + 110*20%= 32
Correct Option : C
Answer: (C) 32%
Question: Best friends Sprite and Icey have are playing a game of marbles. They invite 1 of their friends to play with them. There are 36 marbles in the bag. If all 3 people are playing, how many marbles does each person get?
(A) 3
(B) 12
(C) 5
(D) 6
(E) 7
Rationale: Answer= B
36 / 3 = 12
Answer= B
Answer: (B) 12
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 50, the runs scored by B are?
A. 15 B. 18
(A) 12
(B) 18
(C) 99
(D) 77
(E) 24
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 50 = 12
Answer: A
Answer: (A) 12
Question: For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/17
(A) a) 12
(B) b) 6
(C) c) 10
(D) d) 17
(E) e) 32
Rationale: It seems that the accepted answer is wrong, according to WolframAlpha. The answer should be 27, which isn't even listed as a selectable answer.
D
Answer: (D) d) 17
Question: Find the largest 4 digit number which isexactly divisible by 88?
(A) 3454
(B) 4586
(C) 9944
(D) 10564
(E) 18664
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: (C) 9944
Question: After 6 games, team B had an average of 75 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?
(A) 5
(B) 4
(C) 7
(D) 3
(E) 8
Rationale: (6*75) + 47 +x >500
450+47+x > 500
497+x >500
=> x>3
Option D
Answer: (D) 3
Question: If the area of a circle is 81pi square feet, find its circumference.
(A) 8
(B) 28
(C) 18
(D) 48
(E) 38
Rationale: The area is given by pi × r × r. Hence
pi × r × r = 81 pi
r × r = 81 ; hence r = 81 feet
The circumference is given by
2 × pi × r = 2 × pi × 9 = 18 pi feet
correct answer C
Answer: (C) 18