RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
A.125/129
B.125/122
C.125/126
D.125/121
Answer: C.125/126
Explanation: Required probability
= 1 - 1/126
= 125/126
Answer: C
Question: Concentrated grapes juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated grapes juice, at the most, can fit into 3 wooden boxes?
A.24.
B.28.
C.36.
D.42.
Answer: A.24.
Explanation: Concentrated grapes juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way .
now, diameter of each tube = 5 inches
therefore, 4*2 can be put in each wooden box
in 3 boxes 3*4*2 can be accommodated
= 24=A
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $74. If $2,000 is the total amount invested, how much is invested at 8 percent?
A.$600
B.$700
C.$800
D.$900
Answer: B.$700
Explanation: 0.1x = 0.08(2000-x)+74
0.18x = 234
x = 1300
Then the amount invested at 8% is $2000 - $1300 = $700
The answer is B.
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
A.1/13
B.1/19
C.1/20
D.1/21
Answer: C.1/20
Explanation: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
C)
Question: At McDonalds you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number such that you can not order any combination of the above to achieve exactly the number you want?
A.43
B.53
C.63
D.73
Answer: A.43
Explanation: The answer is 43.
For any desired number if it is divisible by 3 it can easily be made with 6 and 9 packs, except if the number is 3 itself. If you can't use all six packs then use one 9 pack and you can do the rest with six packs.
If the number is not divisible by 3 then use one 20 pack. If the remaining number is divisible by 3 then use the above method for the rest.
If the number still isn't divisible by 3 use a second 20 pack. The remainder must be divisible by 3, in which case use the 6 and 9 packs as above.
The largest impossible number would be such that you would have to subtract 20 twice to get a remainder divisible by 3. However, you can't make 3 itself with 6 and 9 packs. So the largest impossible number is 2*20+3=43.
correct answer A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.120 m
B.240 m
C.300 m
D.200 m
Answer: B.240 m
Explanation: Explanation:
Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
ANSWER IS B
Question: By how much is three-fifth of 620 greater than four- seventh of 210 ?
A.520
B.215
C.252
D.None of these
Answer: C.252
Explanation: Solution
3/5 of 620 - 4/7 of 210 = 252.
Answer C
Question: A man is walking at the rate of 9 km/hr crosses a bridge in 15 minutes. The length of the bridge is
A.1000 meters
B.1050 meters
C.2200 meters
D.2250 meters
Answer: D.2250 meters
Explanation: Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
Speed=9âˆ—5/18=5/2m/sec
Time=15âˆ—60seconds=900seconds
Distance=Timeâˆ—Speed/Distance=5/2âˆ—900=2250meter
Option D
Question: which one is odd?
4377
3954
9863
8454
9831
A.4377
B.3954
C.9863
D.8454
Answer: C.9863
Explanation: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9863 is 26
Question: It takes Beth 9 minutes to do one oil change, and it takes Logan 12 minutes. At 4:56 pm, they both finish an oil change simultaneously. If Beth and Logan both began doing oil changes at exactly the same time and worked without pausing, when did they both start doing oil changes?
A.4:11 pm
B.4:20 pm
C.4:29 pm
D.4:38 pm
Answer: B.4:20 pm
Explanation: Since Beth finishes s oil changes after s × 9 minutes and Logan finishes c oil changes after c × 12 minutes, they both finished doing an oil change at the same time when s × 9 = c × 12. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 9 and 12. The question asks for the first time they began a car simultaneously, so you must find the least common multiple and subtract. The least common multiple of 9 and 12 is 36, so in the context of the question, this would be 36 minutes. Therefore, they began changing the oil of a car at the same time at 4:56 - 36 minutes, or 4:20 p.m. The answer is (B).
Question: A man can row with a speed of 30 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
A.A)63kmph
B.B)63kmph
C.C)35kmph
D.D)62kmph
Answer: C.C)35kmph
Explanation: Explanation:
M = 30
S = 5
DS = 30 + 5 = 35
Answer: Option C
Question: Every Sunday, Giri jogs 3 miles. For the rest of the week, each day he jogs 1 mile more than the previous day. How many miles does giri jog in 2 weeks ?
A.42
B.63
C.84
D.98
Answer: C.84
Explanation: In one week, Giri jogs 3 + 4 + 5 + 6 + 7 + 8 + 9 = 42 miles
In two weeks, Giri jogs 84 miles.
ANSWER:C
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.83. How much was lent at 5%?
A.700
B.299
C.266
D.500
Answer: A.700
Explanation: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 83
5x/100 + 90 â€“ 6x/100 = 83
x/100 = 7
=> x = 700
Answer:A
Question: Sam and Nik start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between A and B, Sam and Nik proceed to their destinations of B and A respectively. Sam reaches B 60 minutes after the two meet and Nik reaches A 90 minutes after their meeting. How long did Sam take to cover the distance between A and B?
A.60 minutes
B.120 minutes
C.200 minutes
D.225 minutes
Answer: B.120 minutes
Explanation: t-time taken for AB to meet
(Vs+Vn)t=Vs*60+Vn*90;
Vs(t-60)=Vn(90-t)
This means 60<t<90
so ans will be 60+t
Only B fits this eqn
Question: If log 27 = 1.431, then the value of log 9 is:
A.0.934
B.0.954
C.0.955
D.0.945
Answer: D.0.945
Explanation: log 27 = 1.431
Log 3^3 = 1.431
log 3 = 0.477
log 9 = log(3^2) = 2 log 3 = (2*0.477) = 0.954
ANSWER D
Question: What do you get if you add 7 to 290 three times?
A.305
B.296
C.289
D.297
Answer: D.297
Explanation: D
297 , 297 , 297
Question: On taking delivery of a consignment of eggs the market stall owner was furious to find that several were cracked. In fact, on counting them up in order to assess the damage he found that 72 were cracked, which was 12 per cent of the total consignment. How many eggs in total were in the consignment?
A.700
B.350
C.500
D.600
Answer: D.600
Explanation: D
600
= 72 ÷ 12 × 100
= 600.
Question: A train 275 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A.5
B.6
C.7
D.15
Answer: D.15
Explanation: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [275 * 3/55] sec
= 15 sec
Answer: D
Question: If neha is 10
Both Sonali and priyanka is 15
Both sadaf and tanu is 10.
how much is prinka by the same system ?
A.8
B.9
C.10
D.11
Answer: C.10
Explanation: Solution:
prinka is 10, in a system that awards five for each vowel.
Answer C
Question: 15 people can write 90 book in 20 days working 7 hour a day.then in how many day 240 can be written by 72 people?
A.240/9
B.309/28
C.100/9
D.200/9
Answer: C.100/9
Explanation: work per day epr hour per person= 90/(20*7*15) // eq-1
people= 72; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 240/(p*7*72) // eq-2
eq-1==eq-2;
p= 100/9
ANSWER:C
Question: A 12 month project had a total budget of $24,000. After seven months, the project had spent $12,500. At this point, how much was the project under budget?
A.$1500
B.$1600
C.$1700
D.$1800
Answer: A.$1500
Explanation: Each month, the project should spend $24,000 / 12 = $2000.
In 7 months, the project should spend 7*$2000=$14,000.
The project is under budget by $14,000 - $12,500 = $1500.
The answer is A.
Question: A cube has two of its faces painted half red and half white. The other faces are completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?
A.1:5
B.3:6
C.1:2
D.2:9
Answer: A.1:5
Explanation: Let x be the area of each face of the cube.
The area painted red is 2(x/2) = x
The area painted white is 2(x/2) + 4x = 5x
The ratio of red to white is x:5x which is 1:5.
The answer is A.
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
A.5402
B.542
C.5400
D.5429
Answer: C.5400
Explanation: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer:C
Question: In a bank investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
A.1.2
B.1
C.4
D.2
Answer: C.4
Explanation: Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+34.1)/100 => x*4/3
now we need to find n for x * (4/3)^n = 3x
or in other words n = 4
C
Question: What is the tens digit of 6^18?
A.1
B.3
C.5
D.7
Answer: A.1
Explanation: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3.
The tens digit of 6^3=216 is 1.
The tens digit of 6^4=...96 is 9.
The tens digit of 6^5=...76 is 7.
The tens digit of 6^6=...56 is 5.
The tens digit of 6^7=...36 is 3 again.
etc...
18 has the form 5n+3, so the tens digit of 6^18 is 1.
The answer is A.
Question: A and B together invested Rs. 15,000 in a business. At the end of the year, out of total profit is Rs. 2,000 B's share was Rs. 600. A's investment was
A.Rs. 4,500
B.Rs. 8,250
C.Rs. 10,500
D.Rs. 11,250
Answer: C.Rs. 10,500
Explanation: A+B=15000
total profit=2000
2000-600=1400
1400;600=7:3
then 7*15000/10=10500
ANSWER:C
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
A.42 6/5
B.42 6/0
C.42 6/3
D.42 6/7
Answer: D.42 6/7
Explanation: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer:D
Question: The average age of a committee of 8 members is 36 years. A member aged 55 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
A.39 years
B.34 years
C.36 years
D.35 years
Answer: B.34 years
Explanation: Exp. Total age of the committee = 36*8 = 288,
Total age when a member is retired
and a new one was joined = 288-55 +39, =272
Average age of present committee = 272/8 = 34.
Answer: B
Question: Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 6, while all other numbers remain the same, what is the new average of Set S?
A.6.6
B.6.7
C.6.8
D.6.85
Answer: C.6.8
Explanation: Old set S - Total is avg * no of elements = 6.2*10 = 62
If one number is increased by 6 then total increased to 62+6=68
New avg - 68/10 = 6.8.
Hence answer is C.
Question: Car A is 10 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
A.1.5
B.2.25
C.2.75
D.2.5
Answer: B.2.25
Explanation: Relative speed of car A is 58-50=8 miles per hour, to catch up 10 miles and drive 8 miles ahead so to drive 18 miles it'll need 18/8=2.25 hours.
Answer: B
Question: If a/b = 4/3, Then (3a + 2b) / (3a - 2b) = ?
A.6
B.3
C.5
D.-1
Answer: B.3
Explanation: Answer
Dividing numerator as well as denominator by b, we get
Given Exp. = (3a + 2b) / (3a - 2b) = (3a/b + 2) / (3a/b - 2)
= [ (3 x 4) / 3 + 2 ] / [ (3 x 4)/3 - 2 ]
= (4 + 2) / (4 - 2)
= 3
Option: B
Question: The positive two-digit integers p and q have the same digits, but in reverse order. Which of the following must be a factor of p + q?
A.66
B.9
C.10
D.12
Answer: A.66
Explanation: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9
and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187
66 is multiple of 11
Answer : A
Question: P runs 20% faster than Q so P gives Q a 50 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?
A.250
B.300
C.350
D.400
Answer: B.300
Explanation: Let D be the race distance that P ran.
Let T be the time it took to complete the race.
Let V be Q's speed.
T = D/1.2V = (D-50) / V
D=1.2D-60
0.2D=60
D=300 meters.
The answer is B.
Question: A Cricketer makes a score of 134 runs in the 22nd inning and thus increases his average by 3.5. Find his average after 22nd inning.
A.40
B.60.5
C.52
D.55
Answer: B.60.5
Explanation: Explanation :
Let the average after 22nd innings = x
Then average after 21th innings = (x-3.5)
Therefore 21(x-3.5) + 134 = 22x
Therefore x = 60.5
Answer : B
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A.7
B.6
C.5
D.4
Answer: B.6
Explanation: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 432
12R2 = 432
R2 = 36 => R = 6.
Answer: B
Question: If x and y are three-digit integers such that x > 400 and y<700, which of the following is closest to the maximum possible value of xy ?
A. 698,301
B. 2,800
C. 45,000
D. 76,000
Answer: A. 698,301
Explanation: To get the maximum possible value of xy, we need maximize the value of both x and y
max x can be = 999 (given x is a two-digit integer > 400)
max y can be = 699 (given y is a two-digit integer < 700)
xy = 999*699 = 698,301
Answer (A)
Question: A person covers a distance in 12 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
A.8 m/s
B.4 m/s
C.15 m/s
D.10 m/s
Answer: A.8 m/s
Explanation: Explanation:
T = 12 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
12 x (10/3) = 5x
x = 8 m/s
Answer: Option A
Question: How many number of 4 digits can be formed with the digits 1,2,3,4,5 if repetition of digits is not allowed?
A.60
B.120
C.180
D.240
Answer: B.120
Explanation: n = number of digits = 5
r = number of places to be filled up = 4
Required number = 5P4 = 5!/1! = 120
Answer is B
Question: You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.
What is the probability that you get a sum of 4 before the sum of 7?
A.5/6
B.4/5
C.2/5
D.1/8
Answer: C.2/5
Explanation: C
2/5
This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.
Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.
Thus, the probability that we get the sum of 4 before the sum of 7 will be:
4/(4+6) = 4/10 = 2/5.
Question: Marge has C candies, where C is an integer such that 20 <C< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
A. 0
B. 1
C. 2
D. 3
Answer: C. 2
Explanation: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.
This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47
If she divides the candies among 6 children, she will have 1 candy remaining.
this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49
ONLY 37 is common, so candies are 37 in number..
if 37 is divided in 7 kids, remainder C= 2
C
Question: A,B,and C were started a business, the total profit for one year is $56700.The profit sharing ratio is 8:9:10 (according to their investment they divide their profit).what is the profit of c?
A.$5670
B.$18900
C.$21000
D.$13500
Answer: C.$21000
Explanation: A:B:C = 8+9+10=27; C'share = 10/27 of the total profit. c will get = 10/27*$56700=$21000.
Answer : C
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 11 a.m. and travels towards B at 100 km/hr. Another starts from B at 12 P.m. and travels towards A at 150 km/hr. At what time do they meet?
A.11am.
B.12p.m.
C.3pm.
D.4p.m.
Answer: D.4p.m.
Explanation: Suppose they meet x hrs after 11 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 11+5 = 4 p.m.
Answer is D
Question: One third of a two digit number exceeds its one fourth by 3. What is the sum of the digits of the number?
A.seven
B.eight
C.nine
D.ten
Answer: C.nine
Explanation: Explanation:
x/3 – x/4 = 3 => x =36
3 + 6 = 9
C
Question: Find the one which does not belong to that group ?
A.36
B.77
C.28
D.99
Answer: C.28
Explanation: Explanation:
16, 36, 64 and 4 are perfect squares but not 28.
Answer:C
Question: If c = (1/4)a and b = 3c, then which of the following represents the result of a^2+b^2+c^2 in terms of c
A.26c^2
B.15c^2
C.25c
D.56c^2
Answer: A.26c^2
Explanation: a = 4c and b =3c.
a^2+b^2+c^2 = (4c)^2+(3c)^2+c^2 = 26c^2.
Answer is A
Question: If -13 < 7x + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of x + y?
A.-23
B.-18
C.-13
D.-14
Answer: D.-14
Explanation: Really nice question and plays with a classic GMAT trap. We arrive at the final equation that a + b < -13. So the maximum integer values of a + b should be LESSER THAN -13 and that can only be -14.
-13 < 7a + 1 < 29
Subtracting 1 from the equation
-14 < 7a < 28
Dividing by 7
-2 < a < 4 ........... (1)
19 < 2 - b < 23
Multiplying by -1
-23 < b - 2 < -19
Adding 2 to the equation
-21 < b < -17 ........... (2)
Adding 1 and 2
-23 < a + b < -13
Answer is D
Question: How many even number in the range between 15 to 100 inclusive are not divisible by 3
A.29
B.30
C.31
D.33
Answer: A.29
Explanation: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
16,18...100
using AP formula, we can say 100 = 16 + (n-1) *2
or n=43.
For 6,
18,...96
using AP formula, we can say 96 = 18 + (n-1) *6
or n=14.
Hence, only divisible by 2 but not 3 = 43-14 = 29. hence, Answer A
Question: On a certain road, 20% 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.25%
Answer: D.25%
Explanation: suppose there are X motorists.
20% of them exceeded the speed limit and received the ticket, i.e. X/5.
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/5
or Y/X=1/4
or Y/X * 100= 1/4 * 100= 25%
D
Question: If 2x = 3y = 20, then 12xy = ?
A. 1,200
B. 800
C. 120
D. 40
Answer: B. 800
Explanation: 2x = 20;x=10
3y = 20;y=20/3
Multiply: 12xy=12*10*20/3=800.
Answer: B.
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
A.10
B.12
C.15
D.20
Answer: B.12
Explanation: Answer: Option B
Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Question: The value of AA+A(2A)(A)when A =4 is:
A.144
B.145
C.132
D.125
Answer: A.144
Explanation: Solution:
AA+A(2A)(A)
Put the value of A= 4 in the above expression we get,
16+ 4(2 x 4)(4)
= 16+ 4(8)(4)
= 16 + 4(32)
=144
Answer :A
Question: The fourth proportional to 12, 14 and 18 is?
A.21
B.66
C.77
D.88
Answer: A.21
Explanation: (14*18)/12 = 21
Answer: A
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements T.
A.a) T=48
B.b) T=144
C.c) T=240
D.d) T=288
Answer: C.c) T=240
Explanation: One specific boy is seated to either of end seat, lets call him b1
One specific girl is seated in the middle, lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Question: The present ages of three persons in proportions 10 : 1 : 5. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
A.50, 5, 25
B.16, 28, 36
C.16, 28, 35
D.16, 28, 34
Answer: A.50, 5, 25
Explanation: Let their present ages be 10x, 1x and 5x years respectively.
Then, (10x - 8) + (1x - 8) + (5x - 8) = 56
16x = 80
x = 5.
Their present ages are 10x = 50 years, 1x = 5 years and 5x = 25 years respectively.
Answer:A
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 65, then the average marks of all the students is:
A.53.33
B.54.68
C.55
D.56.09
Answer: D.56.09
Explanation: Explanation:
Required average = (55 × 50 + 60 × 55 + 45 × 65/55 + 60 + 45)
= (2750 + 3300 + 2925/160)
= 8975/160
= 56.09
Answer: D
Question: The sum of the terms of an infinite G.P is 7 and the sum of the cubes of the terms is 1,225. Find the first term of the series.
A.35/3
B.35/2
C.15/2
D.9/4
Answer: A.35/3
Explanation: S a = a/ ( 1 – r ) = 7 …………. (1)
Sum to infinity of the cubes = a 3 / 1 –r 3 = 1,225
From (1) a 3 / ( 1 – r ) 3 = 7 3 = 343
Therefore, ( 1 – r ) 3 / 1 – r 3 = 1225/343,
(1+ r 2 -2r)/ ( 1 + r 2 + r ) = 25/7
7 + 7 r 2 –14r = 25 + 25 r + 25 r 2
18 r 2 +39r + 18 = 0, on solving r = -3/2 or -2/3
for an infinite G.P | r | < 1, r = - 2/3
Therefore, a / [ 1 – ( - 2/3 ) ] = 7, a = 7 * 5/3 = 35/3 ANSWER:A
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?
A.8 kmph
B.12 kmph
C.5 kmph
D.6 kmph
Answer: B.12 kmph
Explanation: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
B
Question: A boat crossed a lake from North to West at the speed of 5 km/h, entered a river and covered twice as much distance going upstream at 4 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.6 km/h that day, what was its approximate downstream speed?
A.2
B.3
C.6
D.7
Answer: C.6
Explanation: One way of solving this is:
Speed of boat on still water (lake)=5kmph
Speed upstream = 4kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 5+1 =6kmph
Ans is C