mathewhe/aqua_rat huggingface dataset:
Question: X, Y and Z can do a work in 9 , 10 and 15 days respectively. They completed the work and got Rs.600. What is the total amount earned by X and Y?
(A) 476
(B) 356
(C) 456
(D) 466
(E) 450
Rationale: The ratio of their working rates = 1/9 : 1/10 : 1/15 = 10 : 9 : 6.
Since, they work together, the share of X
= 10/25 * 600 = Rs.240
the share of Y = 9/25 * 600 = Rs.216
total amount earned by X and Y = 240 + 216 = Rs.456
Answer: C
Answer: (C) 456
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $120, how much more remains to be paid?
(A) $880
(B) $990
(C) $1,000
(D) $1,100
(E) $1,080
Rationale: 10/100P = 120 >> p= 120*100/10 = 1200
1200 - 120 = 1080
ANSWER:E
Answer: (E) $1,080
Question: How many odd 4-digit positive integers R that are multiples of 5 can be formed without using the digit 3?
(A) 648
(B) 729
(C) 900
(D) 1296
(E) 3240
Rationale: I choose A.
Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)
Possible n° of 2nd digit: 9 (3 is excluded)
Possible n° of 3rd digit: 9 (3 is excluded)
Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)
So, R=8*9*9*1=648 (A)
Answer: (A) 648
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by N percent, which of the following expressions represents the final price of the item?
(A) (10,000z + 100z(x – y) – xyz)/10,000
(B) (10,000z + 100z(y – x) – xyz)/10,000
(C) (100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) (A+ Ax/100) - N/100 ( A +Ax/100)
Rationale: .value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by N% on Total N/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - N/100 ( A +Ax/100)
E
Answer: (E) (A+ Ax/100) - N/100 ( A +Ax/100)
Question: Three pipes of same capacity A,B,C can fill a tank in 6 hours. If there are only two pipes B and C of same capacity, the tank can be filled in?
(A) 2
(B) 4
(C) 9
(D) 12
(E) 16
Rationale: The part of the tank filled by three pipes in one hour
= 1/6
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/6 = 1/9.
The tank can be filled in 9 hours.
Answer:C
Answer: (C) 9
Question: The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 1752
(B) 1799
(C) 1719
(D) 1750
(E) 1800
Rationale: Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 60 Ã¨ x = 60 * 60 / 2 = 1800
Answer: E
Answer: (E) 1800
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 278
(B) 276
(C) 20
(D) 288
(E) 21
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: (C) 20
Question: In a fuel station the service costs $4.25 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
(A) 122.6$
(B) 128.9$
(C) 243.7$
(D) 298.85$
(E) 309.85$
Rationale: Service cost of 3 van and 2 truck = 4.25*(3+2)=21.25
Fuel in 3 Van = 3*65=195 litre
Fuel in 2 Trucks =2 * 65(1+120/100)= 286
Total fuel(Van+Truck) = 481 Litre
Total Fuel cost = 481*0.6 =288.6
TOTAL COST =FUEL+SERVICE=288.6+21.25=309.85
ANSWER IS E
Answer: (E) 309.85$
Question: The speeds of 3 trains in the ratio 4:12:24. The ratio between time taken by them to travel the same distance is?
(A) 6:2:1
(B) 1:2:3
(C) 4:8:9
(D) 6:5:2
(E) 4:8:7
Rationale: Ratio of time taken is = 1/4 : 1/12 : 1/24 = 6:2:1
Answer is A
Answer: (A) 6:2:1
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x?
(A) 2/5
(B) 3/4
(C) 4/5
(D) 5/4
(E) 2/7
Rationale: a/b = 4/5
m/x = (2/5)*5 / (7/4)*4 = 2/7
The answer is E.
Answer: (E) 2/7
Question: The ratio of ages of A and B at present is 2:3. After five years the ratio of their ages will be 3:4 What is the present age of A in years?
(A) 10
(B) 15
(C) 25
(D) 30
(E) 35
Rationale: ( 2x+5 ) /( 3x+5) = 3/4
or, 8x+20=9x+15
or,x=5
So, Present age of A = 2x = (2*5) = 10
ANSWER:A
Answer: (A) 10
Question: In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
(A) 24
(B) 144
(C) 292
(D) 584
(E) None of these
Rationale: 5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
Answer:D
Answer: (D) 584
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.
(A) 37.5 %
(B) 38.5 %
(C) 42 %
(D) 27.5 %
(E) none
Rationale: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 64. S.P = Rs. 88.
∴ Gain % = [24/64 * 100]% = 37.5%.
Answer A
Answer: (A) 37.5 %
Question: Combine terms: 12a + 26b -4b – 16a.
(A) 4a + 22b
(B) -28a + 30b
(C) -4a + 22b
(D) 28a + 30b
(E) 30a-28b
Rationale: 12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
correct answer C
Answer: (C) -4a + 22b
Question: What least number must be added to the least number of six digits so that the resulting number may be a perfect square.
(A) 489
(B) 267
(C) 278
(D) 199
(E) 111
Rationale: The least number of six digits = 100000 3 10 00 00 317 9 61 100 61 627 3900 4389 – 489 Least number to be added = 489.
Answer:A
Answer: (A) 489
Question: what is the remainder when 789456123 is divided by 999
(A) 349
(B) 359
(C) 369
(D) 379
(E) 389
Rationale: there is a simple trick for 99 or 999..u have to add the digits from right side for 99 you will select the last 2 digits and add with next two last digits and go on..similarly for 999 u will add last three digits then its next two last digits and so on..
so you will get 123 + 456 +789 =1368 again select last 3 and add them u will get 368 + 001 i.e 369
ANSWER:C
Answer: (C) 369
Question: In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
(A) 19%
(B) 15%
(C) 25%
(D) 40%
(E) 9.4%
Rationale: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)
Originally,
C = FNP
When number of students decrease by 8%, and the price of food increases by 20%,
C = F(new) * (0.92N) * (1.2P)
=> F(new) = F/(0.92*1.2)
=> F(new) = 0.906F
Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4%
ANSWER:E
Answer: (E) 9.4%
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
(A) 6 days
(B) 10 days
(C) 15 days
(D) 16 days
(E) 20 days
Rationale: Work done by X in 4 days =(1/20)*4=1/5
Remaining work =1 -1/5=4/5	.
(X + Y)'s 1 day's work =1/20+1/12 =	8/60	=	2/15	.
Now,	2/15	work is done by X and Y in 1 day.
So,	4/5	work will be done by X and Y in	(15/2x4/5)= 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
Option B
Answer: (B) 10 days
Question: A toy store sells small, medium, and large toy trucks in each of the colors red, blue, black, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
(A) 2/5
(B) 7/15
(C) 11/15
(D) 7/20
(E) 11/30
Rationale: Probability of NOT selecting medium out of 3 sizes = 2/3
Probability of NOT selecting red out of 5 colours = 4/5
Total probability of NOT selecting red and medium = (2/3)*(4/5) = 8/15
Required probability = 1 - 8/15 (this will select at least one of red and medium)
= 7/15
The answer is B.
Answer: (B) 7/15
Question: A student scored an average of 60 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
(A) 86
(B) 160
(C) 76
(D) 140
(E) 26
Rationale: Given M + P + C = 60 * 3 = 180 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 180
= 140
Answer:D
Answer: (D) 140
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
(A) 4:8
(B) 4:3
(C) 4:2
(D) 4:1
(E) 4:6
Rationale: 4 πr2 : 3 πr2 => 4:3
Answer: B
Answer: (B) 4:3
Question: What least value should be replaced by * in 483*4312 so the number become divisible by 6
(A) 3
(B) 4
(C) 5
(D) 2
(E) 7
Rationale: Explanation:
Trick: Number is divisible by 6, if sum of all digits is divisible by 3 and 2,
Last digit is 2 so it is dividable by 2
so (4+8+3+*+4+3+1+2) = 25+* should be divisible by 6,
15+ will be divisible by ,
so that least number is 2.
Answer: Option D
Answer: (D) 2
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $80, and the total cost is $16,000, what is the value of n?
(A)  30
(B)  50
(C)  60
(D)  75
(E)  100
Rationale: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $10,000 + n * $80 --> n = 75.
Answer: D.
Answer: (D)  75
Question: How many odd numbers are possible between 1 to 10000? find out the number of odd number of digits?
(A) 2999
(B) 3500
(C) 4000
(D) 4599
(E) 4999
Rationale: There are always one odd and one even no. And the question is odd no. Between 1 to 10000
So we have to find no. Between 1 to 10000 so we should not includes 1
10000/2 -1=4999
ANSWER:E
Answer: (E) 4999
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 4x+ 4y > 4z
III. yz > xz
IV. xy > y + z
(A)  I only
(B)  II only
(C)  II and III only
(D)  II and IV only
(E)  III and IV only
Rationale: we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 4x+ 4y > 4z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B
Answer: (B)  II only
Question: A large delicatessen purchased p pounds of cheese for K dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)
(A) (p − d)(s − c)
(B) s(p-d) - Kp
(C) c(p − d) − ds
(D) d(s − c) − pc
(E) pc − ds
Rationale: Total cost price = K*p ............... (1)
Wastage = d pounds
Quantity sold = p-d
Selling price per pound = s
Total selling price = s(p-d) ........... (2)
Profit = (2) - (1)
= s(p-d) - Kp
B
Answer: (B) s(p-d) - Kp
Question: A jogger running at 9 km/hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 88
(B) 27
(C) 36
(D) 31
(E) 12
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 190 + 120 = 310 m.
Time taken = 310/10 = 31 sec.
Answer: D
Answer: (D) 31
Question: A new basketball cost increased 5% last week. A basketball coach wanted to buy two dozen basketballs in bulk for his team. He was able to negotiate paying only 90% of the posted price for the bulk purchase. How much did the coach save by purchasing in bulk?
(A) 2.5%
(B) 3.5%
(C) 4.5%
(D) 5.5%
(E) 6.5%
Rationale: Quantity X Rate = Price
1 X 1 = 1
0.9 X 1.05 = 0.945
Decrease in price = (0.055/1) Ã— 100 = 5.5%
Answer = Option D
Answer: (D) 5.5%
Question: The average age 12 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 24 years
(B) 21 years
(C) 18 years
(D) 29 years
(E) 30 years
Rationale: 12 * 2 = 24 years
Answer:A
Answer: (A) 24 years
Question: 29 persons can repair a road in 16 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 12.88
(B) 3.88
(C) 13.88
(D) 15
(E) 18.8
Rationale: Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
Hence we can write as
(persons)29:30
}::x:16
(hours)5:6
29*5*16=30*6*x
x=12.88
ANSWER:A
Answer: (A) 12.88
Question: If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king?
(A) 6/13
(B) 7/10
(C) 4/11
(D) 7/13
(E) 5/26
Rationale: There are 26 black cards and 2 red kings.
P(black card or king) = 28/52 = 7/13
The answer is D.
Answer: (D) 7/13
Question: Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)
(A) 14/15
(B) 15/14
(C) 4/5
(D) 21/25
(E) Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 42 /5
Average Speed of Jill = 42/(4.2) = 10
Ratio of Average speed of Jack to Jill = (42/5)/10 =42/50 =21/25
Answer D
Answer: (D) 21/25
Question: The S.I. on a certain sum of money for 2 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
(A) 2197
(B) 1267
(C) 1750
(D) 2267
(E) 2625
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(2 * 8) = Rs. 2625
Answer:E
Answer: (E) 2625
Question: The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is
(A) 2488
(B) 378
(C) 739
(D) 474
(E) 291
Rationale: Explanation:
Area of 4 walls = 2(l+b)h
=2(10+7) x 5 = 170 sq m
Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m
area to be planted = 170 -12 = 158 sq m
Cost of painting = Rs. 158 x 3 = Rs. 474
Answer:D
Answer: (D) 474
Question: In how many ways can the letters of the word AEOGHYI be rearranged such that the vowels always appear together?
(A) 254
(B) 576
(C) 476
(D) 765
(E) 398
Rationale: AEOGHYI
AEOI will come together as a group which can be arranged in 4!=24ways.
AEOI, G,H,Ycan be arranged in 4!=24 ways.
total possible arrangements = 24*24=576 ways
ANSWER:B
Answer: (B) 576
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
(A) 50400
(B) 50420
(C) 50500
(D) 50540
(E) 50590
Rationale: The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.
Number of ways to arrange these letters
=
7
!
2
!
=
7
×
6
×
5
×
4
×
3
×
2
×
1
2
×
1
=
2520
=7!2!=7×6×5×4×3×2×12×1=2520
In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves
=
5
!
3
!
=
5
×
4
×
3
×
2
×
1
3
×
2
×
1
=
20
=5!3!=5×4×3×2×13×2×1=20
Hence, required number of ways
=
2520
×
20
=
50400
=2520×20=50400
A)
Answer: (A) 50400
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 1/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 7/17
(B) 14/31
(C) 7/15
(D) 14/19
(E) 1/2
Rationale: # of basic stereos was 1/3 of total and # of deluxe stereos was 2/3 of total, let's assume total=15, then Basic=5 and Deluxe=10.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 5*1=5 and total time for Deluxe would be 10*7/5=14 --> total time for both of them would be 5+14=19--> deluxe/total=14/19.
Answer: D.
Answer: (D) 14/19
Question: A corporation that had $10 billion in profits for the year paid out $200 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
(A) 50%
(B) 20%
(C) 5%
(D) 2%
(E) 0.2%
Rationale: required answer = [employee benefit/profit] *100
=[(200 million)/(10 billion)]*100
=[(200*10^6)/(10*10^9)]*100
=(20/1000)*100
=2%
So answer is (D)
Answer: (D) 2%
Question: What will come in place of the x in the following Number series? 177147 ,59049 ,19683 ,6561, 2187 , x
(A) 727
(B) 729
(C) 726
(D) 722
(E) 723
Rationale: Go on dividing by 3 to the next number
Answer : B
Answer: (B) 729
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
(A) 12
(B) 16
(C) 24
(D) 48
(E) None
Rationale: EXPLANATION
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
Answer D
Answer: (D) 48
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1726 liters
(B) 1362 liters
(C) 1280 liters
(D) 1184 liters
(E) 1173 liters
Rationale: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
Answer:D
Answer: (D) 1184 liters
Question: The difference of two numbers is 8 and one-fourth of their sum is 6. Find the numbers.
(A) 16,8
(B) 10,2
(C) 17,6
(D) 14,10
(E) 12,4
Rationale: Let numbers be x and y.
Equation (i): x - y = 8
Equation (ii): (x + y)/4 = 6
Solve system of equations: x=16, y=8
A is the correct answer.
Answer: (A) 16,8
Question: In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 50, what is the greatest possible value of B × A?
(A) 0
(B) 5
(C) 20
(D) 15
(E) 25
Rationale: You should notice that 50*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*4=20 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).
Answer: C.
!
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C
Answer: (C) 20
Question: If three sides of the triangle are 8 , 15 and G respectively then the how many values can G ?
(A) [A] 6
(B) [B] 7
(C) [C] 8
(D) [D]9
(E) [E] infinite number of values
Rationale: Needed: How many Values can G take
Concept: Sum of any two sides of a triangle is greater then the third side.
Case 1: 8+5 > G => G<13
Case 2: 5+G > 8 => G >3
Case 3: 8+G > 5 => G > -3 (Always true since G is one side of a Triangle)
Finally, 3 < G < 13. So, we can have infinite number of sides between 3 and 13.
Answer = E
PS: If question said G can take only integer value, the G = 9. Answer choice D.
Answer: (D) [D]9
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
(A) 22
(B) 88
(C) 55
(D) 200
(E) 21
Rationale: T = (660 + 165)/54 * 18/5
T = 55.Answer: C
Answer: (C) 55
Question: 3x+4y=10
x^3+y^3=6
What is the minimum value of 3x+11y=?
(A) 32
(B) 34
(C) 35
(D) 36
(E) 38
Rationale: on subtracting 2 eqns we get y=4 and x=-2.
therefore 3x+11y=-6+44
=38.
ANSWER:E
Answer: (E) 38
Question: Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations E of classes are available?
(A) 3
(B) 6
(C) E=7
(D) E=9
(E) E=12
Rationale: I think it should be E only.
No where it is given that he attends different classes on each day.
Experts please provide your views.
--- EDITED my Response. It was a typo. I meant 12 is the answer.
If only Day 1 : 3 options
If Day 1 and Day 2 : 3*3 = 9 Options
So, Total = 3+9= 12.
Answer: (D) E=9
Question: How many independent words can 'HEARTLESS' be divided into without changing the order of the letters and using each letter only once ?
(A) 1
(B) 2
(C) 5
(D) 3
(E) 4
Rationale: Explanation:
The words are HE, ART and LESS.
Answer: D) 3
Answer: (D) 3
Question: A cylinder has a base with a circumference of 20pi meters and an equilateral triangle inscribed on the interior side of the base. A marker is dropped into the tank with an equal probability of landing on any point on the base. If the probability of the marker landing inside the triangle is (Sqrt 3)/4 , what is the length of a side of the triangle?
(A) 3(sqrt 2pi)
(B) 3(sqrt 3pi)
(C) 10*sqrt (pi)
(D) 10(sqrt 3pi)
(E) 20 pi
Rationale: Prob of marker landing in the triangle = area of triangle / area of base = sqrt(3)/4
Circumference of base = 20pi meters
=> Radius of base = 10 meters
=> Area of base = 100 pi sq m
Therefore area of the triangle = 100 pi * sqrt(3)/4
As the area of an equilateral triangle is sqrt(3)*(side^2)/4,
any side of the triangle = 10*sqrt(pi)
ANSWER:C
Answer: (C) 10*sqrt (pi)
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?
(A) 22
(B) 16
(C) 82
(D) 27
(E) 15
Rationale: Explanation:
Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 12
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2
=> 2a = 32 => a = 16.
Answer: B
Answer: (B) 16
Question: Solve: 387 x 387 + 114 x 114 + 2 x 387 x 114
(A) 251001
(B) 251000
(C) 251010
(D) 250101
(E) None of them
Rationale: = (387)2+ (114)2+ (2 x 387x 114)
= a2 + b2 + 2ab, where a = 387,b=114
= (a+b)2 = (387 + 114 )2 = (501)2 = 251001.
Answer is A
Answer: (A) 251001