mathewhe/aqua_rat huggingface dataset:
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 79 kmph
(B) 85 kmph
(C) 34 kmph
(D) 23 kmph
(E) 14 kmph
Rationale: S = (90 + 60)/2
= 75 kmph
Answer:B
Answer: (B) 85 kmph
Question: Y and Z are in a relay race. Y runs the first leg of the course in 58 seconds. Z runs the second leg of the course in 26 seconds. What was the average time they took to run a leg of the course?
(A) 39
(B) 40
(C) 41
(D) 42
(E) 43
Rationale: (58 seconds +26 seconds)/2= 42 seconds
Correct option is: D
Answer: (D) 42
Question: Along a yard 441 metres long, 22 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
(A) 18
(B) 19
(C) 20
(D) 21
(E) 12
Rationale: Explanation:
22 trees have 21 gaps between them,
Required distance (441/21) = 21
Option D
Answer: (D) 21
Question: A military garrison in a wild frontier has 600 men who have provisions to last 25 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
(A) 13 1/3
(B) 12 1/3
(C) 38
(D) 36
(E) 12 3/4
Rationale: Total provisions=600*25*7=105000
Provisions used for in 6 weeks=6*7*600=25200
remaining provisions=79800
remaining provisions need to be split between 900(600+300) people.
Number of provisions per person= 79800/900
we need to find the answer in terms of weeks=(79800/900)/7=38
Answer:C
Answer: (C) 38
Question: An outlet pipe can empty 2/3 rd of a cistern in 16 minutes. In 8 minutes, what part of the cistern will be emptied?
(A) 1/3
(B) 4/3
(C) 4/2
(D) 4/8
(E) 4/1
Rationale: 2/3 ---- 16
? ----- 8 ==> 1/3
Answer: A
Answer: (A) 1/3
Question: Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 1512x is the cube of a positive integer?
(A) 7
(B) 14
(C) 28
(D) 35
(E) 49
Rationale: We want to know the smallest x that will make 1512x a CUBE of some number. Let's call that number y.
Let's first figure out what we're working with. The prime factorization of 450 can be visualized:
.........1512
......../.......\
......216......7
...../.. \....
...36.... 6...
.../. \..../.\..
..6….6…2…3
./.\ ../\
2..3 2…3
So, we have 2 * 2 * 2 * 3 * 3 *3 * 7 that can be multiplied together to get 1512. Now we need to figure out what we need to make 1512 * x into a cube of y (y^3=1512*x).
We have two 5s, two 3s, and one 2. To arrange these numbers in identical triples (2,3,7), we need at least one more 5, one 3, and two 2's. Each of these triples will give us the value of y (2*3*7=42), which, multiplied by itself three times, gives us 1512 * x.
Looking at the factors we need to complete the triples, we get 7 * 7 = 49. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.
Therefore, we can go with answer choice D.
If time permits, we can do a sanity check. We calculated that y should be 2 * 3 * 7, or 42. 42 * 42 * 42 = 74088. Also, 1512 * 49 = 74088.
Answer: E
Answer: (E) 49
Question: Which one of the given numbers is divisible by 11?
(A) 4823718
(B) 8423718
(C) 8432718
(D) 4831728
(E) 4852718
Rationale: Explanation:
4831728 = (4+3+7+8) – (8+1+2) = 11
So, the given number is divisible by 11
Answer:D
Answer: (D) 4831728
Question: How much more would Rs.50000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 482
(B) 1205
(C) 992
(D) 837
(E) 923
Rationale: 50000(11/10)4 - 50000(6/5)2 = 1205
Answer:B
Answer: (B) 1205
Question: Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?
(A) 2/9
(B) 3/11
(C) 4/13
(D) 4/11
(E) 5/12
Rationale: Here, n(S) = 52
There are 13 cards of diamond (including one king) and there are 3 more kings.
Let E = event of getting a diamond or a king.
Then, n(E) = (13 + 3) = 16
P (E) = 16 / 52 = 4/13
C
Answer: (C) 4/13
Question: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak English. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
(A) 12
(B) 15
(C) 120
(D) 224
(E) 240
Rationale: Assume the total members = x
Farsi = .4x
English= .75x
Farsi + English= 1.15x, but this is not possible hence 15 people speak both languages.
Only Farsi = .25x, Only English= .6x, both = .15x
Since these are all people, all of these should be whole numbers.
Checking the options:
A. 12. Only English= 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only Farsi = 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 120 Only Farsi = .25*120 = 30, Only Hebrew = .6*120 = 72, both = .15*120 = 18. We have the people as whole numbers. CORRECT
D. 224
E. 240
Since we have to find the lowest number, no need to calculate for the rest of the options.
Correct Option: C
Answer: (C) 120
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is?
(A) 39yr
(B) 42yr
(C) 45yr
(D) 32yr
(E) 50yr
Rationale: Let B's present age = x years
Then A's present age = x+9 years
x+9+10 = 2(x-10)
x + 19 = 2x - 20
x = 39years
Answer is A
Answer: (A) 39yr
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
(A) 180
(B) 288
(C) 276
(D) 288
(E) 212
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer: A
Answer: (A) 180
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 363 sq m, then what is the breadth of the rectangular plot?
(A) 11
(B) 17
(C) 18
(D) 101
(E) 1322
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 363
3b2 = 363
b2 = 121 = 11 (b > 0)
b = 11 m.
Answer: A
Answer: (A) 11
Question: A clothing store prices jeans at 30% above the wholesale price of $50. They have a sale for 25% off all jeans. How much would a customer pay for 2 pairs of jeans during the sale?
(A) $98.5
(B) $97.25
(C) $48.75
(D) $97.50
(E) $95
Rationale: Wholesale cost of jeans = $50
Jeans were priced at 30% above $50 = $65
% discount given by sale = 25%
Customer paid = .75 * 65 = $48.75
Cost of 2 pairs of jeans = 48.75 * 2 = $97.5
Answer D
Answer: (D) $97.50
Question: A, B and C enter into a partnership by investing $7000, $11000 and $18000 respectively. At the end of 8 months, B receives $2200 as his share. Find the share of A.
(A) $1200
(B) $1300
(C) $1400
(D) $1500
(E) $1600
Rationale: The ratio of capital of A, B and C = 7000 : 11000 : 18000 = 7 : 11 : 18
A's share = (7/11)*2200 = $1400
The answer is C.
Answer: (C) $1400
Question: How many halves are there in nine-fourth?
(A) 8
(B) 4.5
(C) 3.2
(D) 7
(E) 3
Rationale: divide 9/4 by 1/2
=9/4÷1/2
=9/4*2/1
=18/4
=4.5.
Answer is B.
Answer: (B) 4.5
Question: The sale price sarees listed for Rs.278 after successive discount is 18% and 19% is?
(A) 321
(B) 276
(C) 342
(D) 265
(E) 198
Rationale: Explanation:
278*(88/100)*(81/100) = 198
Answer: E
Answer: (E) 198
Question: The unit digit in the product 784*618*917*463 is?
(A) 3
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: Unit digit in the given product = unit digit in 4*8*7*3 = 2
Answer is B
Answer: (B) 2
Question: A number is selected at random from the first 30 natural numbers. What is the probability that the number is a multiple of either 5 or 12?
(A) 17/30
(B) 2/5
(C) 7/15
(D) 4/15
(E) 11/30
Rationale: Number of Multiples of 5 from 1 through 30 = 30/5 = 6
Number of Multiples of 12 from 1 through 30 = 30/12 = 2
Number of Multiples of 5 and 12 both from 1 through 30 = Number of Multiples of 12*5(=60) = 0
Total favourable cases = 6 + 2 - 0 = 8
Probability = 8 / 30 = 4/15
Answer: option D
Answer: (D) 4/15
Question: 21 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
(A) 22
(B) 21
(C) 44
(D) 45
(E) 46
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 21.
ANSWER:B
Answer: (B) 21
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 288
(B) 492
(C) 877
(D) 278
(E) 178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 20 + 21 = 41
T = 12
D = 41 * 12 = 492
Answer: B
Answer: (B) 492
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 28%
(B) 40%
(C) 64.8%
(D) 70%
(E) 72%
Rationale: Let initial price be 1000
Price in day 1 after 10% discount = 900
Price in day 2 after 10% discount = 810
Price in day 3 after 20% discount = 648
So, Price in day 3 as percentage of the sale price on day 1 will be = 648/900*100 => 72%
Answer will definitely be (E)
Answer: (E) 72%
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 10.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
(A) $0.50
(B) $1.00
(C) $1.25
(D) $1.50
(E) $1.75
Rationale: OA is definitely wrong. The answer should be D.
Answer: (D) $1.50
Question: Joe bought a concert ticket for a 40% off the original price. If the ticket cost him $46.35, what is the original selling price of the ticket?
(A) $115.88
(B) $77.25
(C) $64.89
(D) $74.16
(E) None of these.
Rationale: Explanation:CP of Joe is 40% of the Original SP.:. Original SP = $46.35x100/60 = $77.25.Answer: Option B.
Answer: (B) $77.25
Question: How many odd integers between 200 and 600 are there such that their tens digit is even?
(A) 20
(B) 25
(C) 100
(D) 150
(E) 200
Rationale: The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;
Total: 4*5*5=100.
Answer: C
Answer: (C) 100
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 8 1/3
(B) 8 1/6
(C) 8 1/2
(D) 8 1/9
(E) 8 1/4
Rationale: (4000*3*R)/100
= (5000*5*4)/100
R = 8 1/3
Answer: A
Answer: (A) 8 1/3
Question: If the area of a circle is 49pi square feet, find its circumference.
(A) 14 pi feet
(B) 28 pi feet
(C) 38 pi feet
(D) 48 pi feet
(E) 58 pi feet
Rationale: The area is given by pi *r* r. Hence
pi * r *r = 49 pi
r * r = 49; hence r = 49 feet
The circumference is given by
2 * pi * r = 2 * pi * 7 = 14 pi feet
correct answer A
Answer: (A) 14 pi feet
Question: In a set of three numbers,the difference between the largest and the second largest numbers is added to the smallest number.The average of the largest,second largest and the new number formed exceeds the average of the original three numbers by 5.The largest number exceeds the second largest number by how much ?
(A) 5
(B) 10
(C) 15
(D) 30
(E) 60
Rationale: Let the numbers in increasing order be A<B<C...
since the new number(N) increase the average of new set of numbers by 5 after replacing the smallest number,A,
the new number,N, exceeds the smallest,A, by 3*5=15 or N=15+A..(1)
and what is the new number,N,---- C-B (diff in the largest and second largest)+A...(2)...
from (1) & (2) C-B=15...
Answer:-C
Answer: (C) 15
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
(A) 187 m
(B) 278 m
(C) 876 m
(D) 200 m
(E) 267 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 12) m
= 200 m.
Answer: D
Answer: (D) 200 m
Question: J is 25% less than P and 20% less than T. T is q% less than P. What is the value of q?
(A) 93.5
(B) 90
(C) 6.75
(D) 6.25
(E) 2
Rationale: Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables.
Let, P = 400
then J = (75/100)*400 = 300
also J = (80/100)*T
i.e. T = 300*100/80 = 375
and T = [1-(q/100)]*P
i.e. 100-q = 100*T/P = 100*375/400 = 93.75
i.e. q = 6.25
Answer: Option D
Answer: (D) 6.25
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table?
(A) 7297
(B) 2977
(C) 2871
(D) 6925
(E) 2981
Rationale: Explanation:
CP = SP * (100/(100 + profit%))
= 8587(100/124) = Rs. 6925.
Answer: D
Answer: (D) 6925
Question: let S is a set of all natural numbers less than 120 such that HCF of any element in S and 120 is 1. Find the sum of all elements in S?
(A) 1584
(B) 7640
(C) 5640
(D) 7240
(E) 6780
Rationale: S is a set of all natural numbers less than 120 such that HCF of any element in S and 120 is 1.
Such numbers are,
S = {1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113}
Sum of S = 1584.
ANSWER:A
Answer: (A) 1584
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
(A) Rs.8082
(B) Rs.7800
(C) Rs.8100
(D) Rs.8112
(E) Rs.9000
Rationale: Explanation:
A = 7500(26/25)2 = 8112
ANSWER IS D
Answer: (D) Rs.8112
Question: Calculate 12351 ÷ ? = 69
(A) 179
(B) 119
(C) 129
(D) 173
(E) 156
Rationale: Answer
Let 12351 ÷ ? = 69
Then X = 12351/69 = 179.
Option: A
Answer: (A) 179
Question: find remainder when (10^3+9^3)^1000 divided by 12^3
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (10^3+9^3)^1000 / 12^3
= 1729^1000 / 1728
=> (1728*1+1)^1000 / 1728
=> 1^1000 / 1728
=> rem = 1
ANSWER:B
Answer: (B) 1
Question: How many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 17 sec
(B) 21 sec
(C) 25 sec
(D) 27 sec
(E) 29 sec
Rationale: D = 120 + 150 = 270
S = 36 * 5/18 = 10 mps
T = 270/10 = 27 sec
Answer: (D) 27 sec
Question: Evaluate: 6602.5 + 660.25 + 66.025 + 6.6025 + 0.66025
(A) 6819.59775
(B) 7336.03775
(C) 6918.59775
(D) 6198.59775
(E) 6891.59775
Rationale: 6602.5
660.25
66.025
6.6025
+ 0.66025
---------------
7336.03775
Answer is B.
Answer: (B) 7336.03775
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 2387
(B) 1298
(C) 1128
(D) 1237
(E) 1200
Rationale: l * 30 = 1200 l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
E
Answer: (E) 1200
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 50 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 50 / 10 = 5 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 5 = 30 kms... Answer - E
Answer: (E) 30
Question: When a Laptop is sold for Rs. 49,000, the owner loses 30%. At what price must that Laptop be sold in order to gain 30%?
(A) 87000
(B) 88000
(C) 89000
(D) 90000
(E) 91000
Rationale: 70 : 49000 = 130 : x
x = (49000 x 130)/70 = 91000.
Hence, S.P. = Rs. 91,000.
Answer: Option E
Answer: (E) 91000
Question: Find the cost of fencing around a circular field of diameter 16 m at the rate of Rs.3 a meter?
(A) 150.84
(B) 160.6
(C) 150.45
(D) 160.99
(E) 180.4
Rationale: 2 * 22/7 * 8 = 50.28
50.28 * 3= Rs.150.84
Answer: A
Answer: (A) 150.84
Question: The difference between simple interest and compound interest on Rs.1400 for one year at 20% per annum reckoned half-yearly is:
(A) $185.63
(B) $852.36
(C) $875.5
(D) $989.9
(E) $875.8
Rationale: S.I= [(1400*20*1)/100]= $280.
C.I=[1400*(1+(5/100)^2)-1400]=$1269.8.
Difference=(1269.8-280) =$989.8
Answer(D)
Answer: (D) $989.9
Question: Sambhu buys rice at Rs. 10/kg and puts a price tag on it so as to earn a profit of 20%. However, his faulty balance shows 1000 gm when it is actually 800 gm. What is his actual gain percentage ?
(A) 20%
(B) 30%
(C) 50%
(D) 40%
(E) 60%
Rationale: 1kg rice =Rs. 10 => 800gm actual cost =Rs. 8.
But he wants to earn a profit of 20% => 1kg = Rs.12.
Moreover his faulty balance shows 800 gm = 1000gm (1 kg)
=> He sells 800 gm for Rs.12
Therefore the actual profit earned by him is (12-8)/8 * 100 =50%
ANSWER:C
Answer: (C) 50%
Question: In Town P, 60 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town P are females?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: The percent of the population who are employed females is 60-48 = 12%
The percent of employed people who are female is 12% / 60% = 20%.
The answer is A.
Answer: (A) 20%
Question: Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 7
(C) 12
(D) 16
(E) 24
Rationale: Number of ways First-place medal can be awarded to four contestants = 4
Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3
Therefore number of possibilities = 4 *3 =12
Answer: C
Answer: (C) 12
Question: If in a certain sequence of consecutive multiples of 50, the median is 625, and the greatest term is 750, how many terms that are smaller than 625 are there in the sequence?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 3
Rationale: Since the median is 625 we know there must be a even number of integers because 50 is not a multiple of 625.
So the list around 625 must go. 600 (625) 650 700 750
Since we know there are 3 numbers greater than 625 then there must be 3 numbers less then 625.
E
Answer: (E) 3
Question: A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
(A) 2 hr 30 min
(B) 2 hr
(C) 4 hr
(D) 1 hr 15 min
(E) None of these
Rationale: Explanation :
Speed upstream = 2/2 = 1 km/hr
Speed downstream = 1/((20/60)) = 3 km/hr
Speed in still water = 1/2(3+1) = 2 km/hr
Time taken to travel 5 km in still water = 5/2 = 2(1/2) hours = 2 hour 30 minutes. Answer : Option A
Answer: (A) 2 hr 30 min
Question: To a sugar solution of 3 litres containing 40% sugar, one litre of water is added. The percentage of sugar in the new solution is ?
(A) 22%
(B) 15%
(C) 26%
(D) 40%
(E) 30%
Rationale: Quantity of sugar = 40*3/100 = 1.2kg
new percentage = (1.2*100/4)% = 30%
Answer is E
Answer: (E) 30%
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/11
II. 1/10
III. 1/10
(A) II only
(B) I only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us A a as the only possible answer.
Answer: (A) II only
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a + b + c > a^3
II. a × b × c < a^3
III. 4b < bc
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
Rationale: Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'A' seems valid.
Answer: (A) I only
Question: If the product of the integers from 1 to n is divisible by 210, what is the least possible value of n?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
Rationale: 210 = 2 x 3 x 5 x 7
N must include at least up to the number 7.
The answer is A.
Answer: (A) 7
Question: The probability that A speaks truth is 5/9 and that of B speaking truth is 7/11. What is the probability that they agree in stating the same fact?
(A) 68/95
(B) 12/85
(C) 59/99
(D) 33/39
(E) None of these
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 5/9 * 7/11 + 4/9 * 6/11
= 35/99 + 24/99 = 59/99
ANSWER:C
Answer: (C) 59/99
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 40 km / hr. In the return trip, he covers the same distance at an average speed of 20 km / hr. The average speed of the car over the entire distance of 400 km / hr.
(A) 22 km/hr
(B) 28.56 km/hr
(C) 26.67 km/hr
(D) 30 km/hr
(E) None
Rationale: Sol.
Average speed = (2×40×20 / 40 + 60) km/hr
= (80/3)km/hr
= 26.67 km/hr.
Answer C
Answer: (C) 26.67 km/hr
Question: If the selling price of 8 articles is same as the cost price of 10 articles. Find the gain or loss percentage?
(A) 25%
(B) 45%
(C) 35%
(D) 65%
(E) 55%
Rationale: Let the C.P of each article be Re 1. Then,
S.P of 8 articles = C.P of 10 articles = Rs. 10
Now, C.P of 8 articles = Rs. 8, S.p of 8 articles = Rs 10
Gain = Rs ( 10 - 8 ) = Rs 2.
Gain% = ( 2/8 × 100 ) % = 25%
Answer : A
Answer: (A) 25%
Question: Find the value of x when the average of 3x,(5x+6),(7x-4) is 51?
(A) 5
(B) 10
(C) 15
(D) 12
(E) 20
Rationale: Average = (3x+5x+6+7x-4)/3 = (15x+3)/3 = 5x+1
5x+1 = 51
x = 50/5 = 10
Answer is B
Answer: (B) 10
Question: The average speed of a train running at a speed of 30 km/hr during the first 100 kilometres, at 40 km/hr during the second 100 kilometres and at 50 km/hr during the last 100 kilometres is nearly?
(A) 38.5 km/hr
(B) 38.3 km/hr
(C) 40.0 km/hr
(D) 39.2 km/hr
(E) None of these
Rationale: Time taken to cover first 100 kilometres = 100/3 = 3(1/3) hours
Time taken to cover second 100 kilometres =100/40 = 2(1/2) hours
Time take to cover last 100 kilometres = 100/2 = 2 hours
Total distance covered = 300 km.
Total time taken = 47/6 hours
Thus, average speed = 300/(47/6) = 38.3 km/hr.
ANSWER:B
Answer: (B) 38.3 km/hr
Question: The age of man is three times the sum of the ages of his two sons.Five years hence,his age will be double of the sum of the ages of his sons.The father's present age is :
(A) 50 years
(B) 46 years
(C) 20 years
(D) 45 years
(E) 30 years
Rationale: Let the sum of present ages of the two sons be x years.
then father's present age =3x years.
(3x+5)=2(x+10)
3x+5=2x+20
x=15.
Hence, father's present age =45 years.
Answer is D
Answer: (D) 45 years
Question: y w v t r p n
Next letter in the series
(A) L
(B) M
(C) N
(D) O
(E) P
Rationale: y--w(y-2)
v--t(v-2)
r--p(r-2)
n--l(n-2)
so ans is l
ANSWER:A
Answer: (A) L
Question: On a certain number line, conditions are x<Y<z<U<v. xyzuv>0 Which of the following must be true?
I xy>0
II zu>0
III uv>0
(A) I only
(B) II only
(C) I and II
(D) III only
(E) II and III only
Rationale: Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve.
We are given : I xy>0 II yz>0 III uv>0
case 1: x and y can be negative/positive and if they are... we get greater than 0.
case 2: we have zu , then z and u both can be negative/positive and if they are... we get greater than 0.
C
Answer: (C) I and II
Question: (0.96)(power 3) - (0.1)(power 3)/ (0.96)(power 2) + 0.096 + (0.1)(power 2) is:
(A) 0.68
(B) 0.086
(C) 0.86
(D) 0.068
(E) None of them
Rationale: Given expression
= (0.96) (power 3) - (0.1)(power 3) / (0.96)(power 2) + (0.96 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.96 - 0.1)
= 0.86
Answer is C.
Answer: (C) 0.86