mathewhe/aqua_rat huggingface dataset:
Question: Profit of one hospital is 320 percent of the cost. If the cost increases by 25 % but the SP is same, approximately what % of the SP is the profit?
(A) 40%
(B) 45%
(C) 50%
(D) 70%
(E) 75%
Rationale: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage = 295	x 100	%	=	1475	% = 70% (approximately).
420	21
D
Answer: (D) 70%
Question: (1000)7÷(10)20=?
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) None of these
Rationale: Explanation:
=(103)7/(10)20
=(10)21/(10)20=10(1)=10
Option A
Answer: (A) 10
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 8. What is the radius of circle O?
(A) –2/pi
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: pi*r^2 + 2r -2*pi*r = 8
Simplifying the equation: pi*r(r-2)+2r=8
Without much algebraic: We can Test the answers quickly, then 4 is the only possible answer that will eliminate pi from equation.
Answer is D
Answer: (D) 4
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
(A) 4/16
(B) 4/17
(C) 4/11
(D) 4/13
(E) 4/12
Rationale: P(SᴜK)
= P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK)
= 13/52 + 4/52 - 1/52
= 4/13
Answer:D
Answer: (D) 4/13
Question: There are 35 students in a hostel. If the no. of students increases by 5, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) s. 64.80
(B) s. 69.80
(C) s. 72.80
(D) s. 78.80
(E) s. 79.80
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 5) = x – 1
or, 35x + 42 = 40x – 40
or, x = 16.4
Thus the original expenditure of the mess = 35 x 16.4=574
Therefore x-1 = 15.4
hence 42 x 15.4 =646.80
646.80 - 574 = Rs. 72.80
C
Answer: (C) s. 72.80
Question: When the price of an article was reduced by 20% its sale increased by 80%. What was the net effect on the sale?
(A) 44% increase
(B) 44% decrease
(C) 60% increase
(D) 66% increase
(E) 66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 20%, the new price is 0.8p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.8p)(1.8n) = 1.44np, which is 1.44 times the old revenue, so is 44% greater.
ANSWER:A
Answer: (A) 44% increase
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
(A) 9
(B) 10
(C) 12
(D) 18
(E) 14
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: Option C
Answer: (C) 12
Question: A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton, how many kilos did he consume on the sixth hour?
(A) 38
(B) 43
(C) 50
(D) 53
(E) 62
Rationale: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 360/9 = 40, so the median is also 40, and that is the amount eaten in the 5th hour. We need to add 3 to find the total eaten in the next hour, so the answer is 43.
option B
Answer: (B) 43
Question: A, B and C have Rs.350 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
(A) A)200
(B) B)190
(C) C)180
(D) D)170
(E) E)160
Rationale: A+B+C = 350
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 350
----------------
C = 200
Answer:A
Answer: (A) A)200
Question: Xavier starts from P towards Q at a speed of 90 kmph and after every 12 mins increases his speed by 10 kmph. If the distance between P and Q is 51km, then how much time does he take to cover the distance?
(A) 30
(B) 32
(C) 30
(D) 36
(E) 40
Rationale: first 12min = 90 *12/60 =18km
2nd 12min = 100*12/60 =20km
3rd 12 min = 110*12/60 = 22 km
TOTAL time 12 *3 = 36 min
D
Answer: (D) 36
Question: The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 4 revolutions ? (use Ï€ = 22â„7)
(A) 35.2 m2
(B) 44 m2
(C) 48 m2
(D) 36 m2
(E) None of these
Rationale: Required area covered in 5 revolutions
= 4 Ã— 2Ï€rh = 4 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 2 = 35.2 m2
Answer A
Answer: (A) 35.2 m2
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is?
(A) 1/50
(B) 1/13
(C) 1/26
(D) 1/52
(E) 1/4
Rationale: Probability of a spade = 13/52 = 1/4
Probability of a jack = 4/52 = 1/13
Probability of both = P1*P2 = 1/(4*13) = 1/52
Answer is D.
Answer: (D) 1/52
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 17%
(B) 62%
(C) 12%
(D) 19%
(E) 22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: (C) 12%
Question: How many times are the hands of a clock at right angle in 2 days?
(A) 80
(B) 82
(C) 84
(D) 86
(E) 88
Rationale: In 1 day, they are at right angles 44 times.
In 2 days, they are at right angles 88 times. Answer: Option E
Answer: (E) 88
Question: The compound interest on Rs.2800 for 1 1/2years at 10% per annum is
(A) Rs.441.35
(B) Rs.436.75
(C) Rs.434
(D) Rs.420
(E) None
Rationale: Explanation:
Amount = Rs.[[2800×(1+10/100)](1+5/100)]
= Rs.[2800×11/100×21/20]= Rs.3234
C.I = Rs.(3234-2800)= Rs.434
Correct Option: C
Answer: (C) Rs.434
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 1/15
(B) 31/32
(C) 1/10
(D) 30/32
(E) 25/27
Rationale: Probability of getting least one tail at the coin tossed five times.
= There is not even a single tail.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER B
Answer: (B) 31/32
Question: The price of a car is marked at $11,000. If the car has successive discounts of 20%, 15% and 5%, then at what price does a customer buy the car?
(A) $6702
(B) $6924
(C) $7106
(D) $7348
(E) $7580
Rationale: 0.95*0.85*0.8*11000 = $7106
The answer is C.
Answer: (C) $7106
Question: Six students - 3 girls and 3 boys - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two girls and no two boys can sit next to one another?
(A) A)12
(B) B)36
(C) C)72
(D) D)240
(E) E)720
Rationale: in order not to have two girlss or two boys next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B).
Total ways = 2C1*3!*3!
=2*6*6
=72
Ans - C
Answer: (C) C)72
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $300, by what percent is the price to be reduced?
(A) 10%
(B) 15%
(C) 20%
(D) 60%
(E) 30%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $300
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (300)*100 / 500 = 60%
Answer: Option D
Answer: (D) 60%
Question: What is the smallest positive integer that can be multiplied by 432 to make it a perfect square?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: 432=2^4*3^2*3
Therefore the smallest integer to multiplied to 1008 to make it a perfect square is 3.
Answer B.
Answer: (B) 3
Question: Obra drove 120π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
(A) 6.67%
(B) 12.5%
(C) 18.75%
(D) 25%
(E) 33.3%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 120π/480π =25%
Hence, answer is D.
Answer: (D) 25%
Question: Difference of two numbers is 1650. If 7.5% of the number is 12.5% of the other number , find the number ?
(A) 2660, 1000
(B) 3660, 2000
(C) 3000, 4160
(D) 2490, 4150
(E) 2475, 4125
Rationale: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1650
5*y/3 –y =1650
2*y/3= 1650
y =[ (1650*3)/2] =2475.
One number = 2475, Second number =5*y/3 =4125.
Answer E.
Answer: (E) 2475, 4125
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 4-letter code words?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Method #1: Using the permutation formula
# of 6 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 6)! = 10*9*8*7*6*5
# of 4 letter code words:
nPr = 10! / (10 – 4)! = 10*9*8*7
# of 5 words / # of 4 words = (10*9*8*7*6*5)/(10*9*8*7) = 30
B
Answer: (B) 30
Question: A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 25% of the length of the race?
(A) 35%
(B) 48%
(C) 52%
(D) 42%
(E) 46%
Rationale: First calculate the distance, B has covered with his speed in the time, in which A reached 80% of the race.
Then Add the remaining distance as head start for B to win the race.
Its best to apply Ratios concept here.
Since A's speed is 15/13 of B, therefore, B's speed is 13/15 of A
Distance covered by B = speed x time = (13/15) x (0.75) = 0.65%
(Which means B would have covered 0.65 of the race length during the time in which A has covered 0.75 of the race length.
Therefore to win, B needs a headstart of (1 - 0.65 = ) 0.35 of the race length.
So the answer is A
Answer: (A) 35%
Question: There are X girls in a class, and their average height is P inches. In the same class, there are Y boys with an average height of Q inches. What is the average height of all the students in the class?
(A) (X + Y)/(M + N)
(B) (M + N)/(X + Y)
(C) (XM + YN)/(M + N)
(D) (XP + YQ)/(X + Y)
(E) MN/XY
Rationale: Total height = XP+YQ
No of students = X+Y
Avg = (XP+YQ)/(X+Y)
Answer is D
Answer: (D) (XP + YQ)/(X + Y)
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.2, 0.1, and 0.7 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
(A) 0.061
(B) 0.12
(C) 0.218
(D) 0.216
(E) 0.941
Rationale: The probability that eachdoesn'thit is: 0.8, 0.9, and 0.3. When we have multiple independent events, we multiply the probabilities:
.8*.9*.3 = 0.216.
Option: D
Answer: (D) 0.216
Question: A and B together have Sterling 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
(A) Sterling 460
(B) Sterling 484
(C) Sterling 550
(D) Sterling 664
(E) None
Rationale: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1210 x 2/5) = Sterling 484.
Answer: Option B
Answer: (B) Sterling 484
Question: What is the units digit of (63^4)(41^7)(99^9)?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: The units digit of 63^4 is the units digit of 3^4 which is 1.
The units digit of 41^7 is the units digit of 1^7 which is 1.
The units digit of 99^9 is the units digit of 9^9 which is 9.
Note the pattern: 9^1 = 9, 9^2 = 81, 9^3 = 729,...
The units digit alternates between 9 and 1.
The units digit of 1*1*9 is 9.
The answer is E.
Answer: (E) 9
Question: How many factors does 35^2 have?
(A) 2
(B) 8
(C) 24
(D) 25
(E) 26
Rationale: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*4 = 24
Answer C.
Answer: (C) 24
Question: If the cost price of 24 chocolates is equal to the selling price of 16 chocolates, the gain percent is :
(A) 24%
(B) 8%
(C) 50%
(D) 40%
(E) None of these
Rationale: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 16 chocolates = Rs. 16;
S.P. of 16 chocolates =Rs. 24.
.'. Gain% = 8*100/16 = 50%
Answer : C
Answer: (C) 50%
Question: Company C sells a line of 25 products with an average retail price of $1,400. If none of these products sells for less than $420, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
(A) 16000
(B) 11400
(C) 13200
(D) 15400
(E) 16800
Rationale: The average price of 25 products is $1,400 means that the total price of 25 products is 25*1,200=$35,000.
Next, since exactly 10 of the products sell for less than $1,000, then let's make these 10 items to be at $420 each (min possible).
Now, the remaining 14 items cannot be priced less than $1,000, thus the minimum possible price of each of these 14 items is $1,000.
Thus the minimum possible value of 24 products is 10*420+14*1,000=$18,200.
Therefore, the greatest possible selling price of the most expensive product is $35,000-$18,200=$16,800.
Answer: E
Answer: (E) 16800
Question: A volume of 11248 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
(A) 2812
(B) 8231
(C) 2734
(D) 4222
(E) 4254
Rationale: a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 11248l can be kept in (11248/4) hemispheres
ans.2812
ANSWER:A
Answer: (A) 2812
Question: A train 200m long passes a standing man in 15 seconds. What is the speed of the train?
(A) 30km/hr
(B) 36km/hr
(C) 48km/hr
(D) 50km/hr
(E) 32km/hr
Rationale: Speed of the train = 200/15* 18/5 = 48km/hr
Answer is C
Answer: (C) 48km/hr
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 5 shirts each of them then average number of shirt each of them now has
(A) 65
(B) 63
(C) 62
(D) 64
(E) 61
Rationale: Required average
= Old average + New average
= 60 + 5 = 65
answer :A
Answer: (A) 65
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2 : 1
(B) 1 : 2
(C) 1 : 1
(D) 4 : 3
(E) None of these
Rationale: Explanation :
5% of A + 4% of B = (2/3)(6% of A + 8% of B)
(5A/100) + (4B/100) = (2/3)((6A/100) + (8B/100))
⇒ 5A + 4B = (2/3)(6A + 8B)
⇒ 15A + 12B = 12A + 16B
⇒ 3A = 4B
⇒ A/B = 4/3
⇒ A:B = 4:3
Answer : Option D
Answer: (D) 4 : 3
Question: A tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A)  5.12%
(B)  6.12%
(C)  7.12%
(D)  8.12%
(E)  9.12%
Rationale: We start with 6,500 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 6,500 = 325 gallons of sodium chloride.
When 2,500 gallons of water evaporate we are left with 4,000 gallons of solution. From here we can determine what percent of the 4,000 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(325/4,000) x 100 = ?
0.0812 x 100 = ?
= 8.12%
Answer is D.
Answer: (D)  8.12%
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
(A) 399
(B) 266
(C) 150
(D) 277
(E) 281
Rationale: 1/2 * 15 * 20 = 150
Answer:C
Answer: (C) 150
Question: A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
(A) 15
(B) 66
(C) 77
(D) 8
(E) 54
Rationale: One days's work of A, B and C = 1/90 + 1/30 + 1/45
= (1 + 3 + 2)/90 = 1/15
A, B and C together can do the work in 15 days.
Answer: A
Answer: (A) 15
Question: A car has a 20-gallon fuel to travel 500 miles.At this rate, how many gallons of fuel are needed for a 1000 mile car ?
(A) 10
(B) 30
(C) 20
(D) 40
(E) 50
Rationale: Number of gallons of fuel per mile = 500 /20 = 25 gallons per mile
Number of gallons of fuel for a 1000 mile car = 1000/25 = 40
ANSWER:D
Answer: (D) 40
Question: What is the area of square field whose side of length 15 m?
(A) 225
(B) 662
(C) 772
(D) 882
(E) 21
Rationale: 15 * 15
= 225 sq m
Answer:A
Answer: (A) 225
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 1% p.a. in 3 years. What is the sum?
(A) 122762
(B) 132877
(C) 122882
(D) 133875
(E) 132887
Rationale: Principal = (100 * 4016.25) / (1 * 3)
= Rs.133875.
Answer:D
Answer: (D) 133875
Question: A man can buy a new house in 4 years with all of his earnings. But he spend the same amount in household expenses in 8 years and for savings in 12 years. How many time needed for buying the house?
(A) 12
(B) 20
(C) 30
(D) 15
(E) 24
Rationale: His savings in 1 year = 1/4 - (1/8+ 1/12) = 1/24
He can buy a new house in 24 years
ANSWER:E
Answer: (E) 24
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
(A) 1.44%
(B) 1.74%
(C) 1.94%
(D) 2.44%
(E) 1.47%
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 %
= 1.44%
Answer:A
Answer: (A) 1.44%
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 percent. Overall he make a.
(A) 228
(B) 288
(C) 27
(D) 200
(E) 280
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 11/100) = 8000 + 880
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 880 = Rs. 280
As this is positive, an overall profit of Rs. 280 was made.Answer:E
Answer: (E) 280
Question: Two cyclists are running on a circular track of 500m.They start from the same point A at the same time.If they meet for the first time at a point 100 m from A, which of the following could be the possible ratio of their speeds?
(A) 1:4
(B) 2:3
(C) 3:5
(D) 5:7
(E) 7:11
Rationale: well, the key aspect of this question is the distance mentioned, when they met for the first time, which is 100m away from the starting point. This distance between their first meeting can be less than 500 in only two circumstance.
1) if both are travelling in the same direction and one of them has been given a head start say by few meters.
2) or if both are travelling in the opposite direction.
now since they start their journey at the same time. hence option 1 is ruled out. hence they must be running in the opposite direction. hence answer should be 2:3.
Why?? here is a solution
As here time is constant, therefore, distance traveled will be directly proportional to the the respective velocities/speed of the two runners.(d1/d2=v1/v2)
now one of them has covered 100m, therefore other must have covered 400m, therefore ratio of their speeds/velocities will be 1:4
A
Answer: (A) 1:4
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
(A) 5:3
(B) 3:5
(C) 1:5
(D) 5:1
(E) None of them
Rationale: Let 40% of A = 2/3 B
Then, 40A/100= 2B/3
= 2A/5 = 2B/3
= A/B = (2/3) x (5/2)= 5/3
Therefore, A : B = 5 : 3.
Answer is A.
Answer: (A) 5:3
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 152
(B) 150
(C) 289
(D) 369
(E) 287
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:B
Answer: (B) 150
Question: The sum of two numbers is 65 and their product is 1050. What will be the sum of their reciprocals?
(A) (11/140)
(B) (11/210)
(C) (35/4)
(D) (75/8)
(E) None
Rationale: Solution
x+y=65 xy=1050 1/x+1/y=x+y/xy 65/1050 = (11/210).
Answer B
Answer: (B) (11/210)
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
(A) 5 km/hr
(B) 7 km/hr
(C) 9 km/hr
(D) 2 km/hr
(E) 1 km/hr
Rationale: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer:A
Answer: (A) 5 km/hr
Question: Find the third proportional to 2 and 8?
(A) 10
(B) 32
(C) 36
(D) 19
(E) 20
Rationale: Formula = Third proportional = (b × b)/a
A = 2 and B = 8
(8 x 8 )/ 2 = 64/2 = 32
B
Answer: (B) 32
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
(A) 54
(B) 432
(C) 864
(D) 2,916
(E) 148,824
Rationale: We have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*4C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A).
9C1*4C1*8C1*3C1=864.
Answer: C.
Answer: (C) 864
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
(A) 38
(B) 43
(C) 46
(D) 49
(E) 52
Rationale: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
C
Answer: (C) 46
Question: If a positive integer n, divided by 5 has a remainder 2, which of the following must be true
I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2
(A) None
(B) I only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: n can be written as :
n = 5k+2. Thus, taking k=0, we have n=2.
I.n=2,even.False
II.2+1=3, is a prime. False.
III.n+2 = 4,4 divided by 7 leaves a remainder of 4. False.
ANSWER:A
Answer: (A) None
Question: Buffalo gives 4 liter milk, cow gives (1/2) liter milk and goat gives 1/4 liter milk. you have to get 20 liter milk by 20 animals.what is the number of cows?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Assume number of respective animals are x,y,z.
x+y+z=20---(1) as the total number of animal has to be 20
Amt of milk will be 4x+(1/2)y+(1/4)z=20---(2)
Solving equation 1 and 2 we get
15x+y=60 ----(3)
Since buffalo gives 4litre and total milk is 20, x < 5
But from eq 3, x cannot be more than 4;
Further if x=1 or 2; y>20... Not possible, since total animal is 20
Thus, x=3, y=15, z=2
15cows
ANSWER:D
Answer: (D) 15
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
(A) 50 KM
(B) 60 KM
(C) 40 KM
(D) 55 KM
(E) 120 KM
Rationale: Let the actual distance travelled be x km.
Then,x/10	=(x + 20)/14
14x = 10x + 200
4x = 200
x = 50 km.
ANSWER A
Answer: (A) 50 KM
Question: The total weight of six nougat nuggets is 7 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
(A) 0.18 oz.
(B) 0.5 oz.
(C) 1.8 oz.
(D) 5 oz.
(E) 1.2 oz
Rationale: Average = Total/Number of items
= 7/6 = 1.2.
Hence, E
Answer: (E) 1.2 oz