mathewhe/aqua_rat huggingface dataset:
Question: Working alone at its constant rate, machine A produces x boxes in 5 minutes and working alone at its constant rate, machine B produces 2x boxes in 10 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?
(A) 3 minutes
(B) 7.5 minutes
(C) 5 minutes
(D) 6 minutes
(E) 12 minutes
Rationale: Rate = Work / Time
Given Rate of Machine A = 2X / 10 min
Machine B Produces 2x boxes in 10 min hence , Machine B produces 2x boxes in 10 min .
Rate of Machine B = 2x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = 2X / 10 min + Rate of Machine B = 2x / 10 = 4X/10
Now combine Time = combine work needs to be done / Combine Rate = 3x/4x * 10 = 7.5 Min
Ans: B
Answer: (B) 7.5 minutes
Question: Calculate how many ways a woman who has 2 bags and 5 books can put the books in her bag?
(A) 39
(B) 32
(C) 29
(D) 30
(E) 31
Rationale: First paper can be put in 2 ways, similarly second, third, forth, and fifth books also can be put in 2 ways.
So total number of ways = 2 x 2 x 2 x 2 x 2 = 32
B
Answer: (B) 32
Question: Mudit's age 22 years hence will be thrice his age four years ago. Find Mudit's present age?
(A) 12
(B) 17
(C) 27
(D) 18
(E) 15
Rationale: Explanation:
Let Mudit's present age be 'm' years.
m + 22 = 3(m - 4)
=> 2m = 34 => m = 17 years.
Answer:B
Answer: (B) 17
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
(A) 9%loss
(B) 2%loss
(C) 7%loss
(D) 8%loss
(E) 1%loss
Rationale: Explanation:
(30*30)/100
= 9%loss
Answer:A
Answer: (A) 9%loss
Question: Three people (1 couple and 1 single) are seated at random in a row of 7 chairs. What is the probability that the couple does not sit together?
(A) 3/7
(B) 4/7
(C) 5/7
(D) 6/7
(E) 9/14
Rationale: The total number of arrangements of 3 people is 7*6*5 = 210
Let's think of the couple as a single unit.
The number of arrangements when the couple sits together is 6*5*2 = 60.
Note that we multiply by 2 because the couple can switch places with each other.
The number of ways the couple won't sit together is 210 - 60 = 150
P(couple won't sit together) = 150/210 = 5/7
The answer is C.
Answer: (C) 5/7
Question: If 7 boys can color 56 m long cloth in 1 day, then 6 boys can color 36 m long cloth in
(A) day
(B) days
(C) days
(D) days
(E) days
Rationale: The length of cloth painted by one boy in one day = 56 / 7 × 1 = 8 m
No. of days required to paint 36 m cloth by 6 boys = 36/ 8 × 6 = 3/4 day.
A)
Answer: (A) day
Question: The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?
(A) 80% p.a
(B) 100% p.a.
(C) 40% p.a
(D) 44% p.a
(E) 50% p.a
Rationale: Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years
=> C.I - S.I
=>9,000 { [1 + r/100]2 - 1} = (10,000)2r /100
=> 9{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5
=> r = 0% of 40%
Since r!= 0%, r =40%
ANSWER:C
Answer: (C) 40% p.a
Question: At a local appliance manufacturing facility, the workers received a 30% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
(A) 83%
(B) 80%
(C) 23%
(D) 17%
(E) 12%
Rationale: Let's say he works usually 10 hours and earns 100 per hour.
10 * 100 = 1000
10 * 130 = 1300 (this are the new earnings after the raise)
To figure out how much he needs to work with the new salary in order to earn the original 1000:
1000/130 = 7.67
So he can reduce his work by 2.33 hours. Which is >23%.
Answer C
Answer: (C) 23%
Question: Find the greatest four digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24.
A. 9974
(A) 388
(B) 282
(C) 378
(D) 292
(E) 281
Rationale: Explanation:
Since the difference between the divisors and the respective remainders is not constant, back substitution is the convenient method. None of the given numbers is satisfying the condition.
Answer: E
Answer: (E) 281
Question: In what ratio must a grocer mix two varieties of pulses costing Rs.15 and Rs. 20 per kg respectively to
obtain a mixture worth Rs.16.50 per Kg?
(A) 1 : 2
(B) 2 : 1
(C) 3 : 7
(D) 7 : 3
(E) None of these
Rationale: Explanation :
By the rule of alligation,we have
CP of 1 kg of 1st variety pulse CP of 1 kg of 2nd variety pulse
15 20
Mean Price
16.5
20-16.5 = 3.5 16.5-15=1.5
Required Ratio = 3.5 : 1.5 = 35 : 15 = 7 : 3
Answer : Option D
Answer: (D) 7 : 3
Question: In how many ways can the word LEADING arranged if Vowels always come together?
(A) 120
(B) 720
(C) 60
(D) 8220
(E) 100
Rationale: LEADING=Has 3 vowels(EAI) and 4 consonant(LDNG)
Total letters=7
For Consonant=5!(that is 4+1 letters. one comes from the vowels )
=5*4*3*2*1=120 ways
For Vowels=3!=3*2*1=6
Total number of ways=120*6=720 ways
Option B
Answer: (B) 720
Question: Find the value of (875 233/899) × 899
(A) 786600
(B) 786658
(C) 786679
(D) 786858
(E) 786890
Rationale: (875 233/899) × 899
(786625 + 233)/899 × 899
786858/899 × 899
786858
D)
Answer: (D) 786858
Question: Kim finds a 2-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
(A) 3/5
(B) 2/5
(C) 7/5
(D) 1/2
(E) 8/15
Rationale: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be
2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15
Which gives us 2/5 + 1/15 + 2/15 -----> 3/5
Answer is A
Answer: (A) 3/5
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 11 kmph
(C) 16 kmph
(D) 18 kmph
(E) 19 kmph
Rationale: Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream = (80-60)/2 = 10 kmph.Answer: A
Answer: (A) 10 kmph
Question: A room 5m 55cm long and 3m 74cm broad is to be paved with square tiles.Find the least number of square tiles required to cover the floor?
(A) 222
(B) 267
(C) 176
(D) 287
(E) 261
Rationale: Explanation:
Area of the room=(544 * 374)
size of largest square tile= H.C.F of 544 & 374 = 34 cm
Area of 1 tile = (34 x 34)
Number of tiles required== [(544 x 374) / (34 x 34)] = 176
Answer: C) 176
Answer: (C) 176
Question: If an investor puts $900 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?
(A) $986.25
(B) $988.25
(C) $990.25
(D) $992.25
(E) $994.25
Rationale: 1.05*1.05*900=$992.25
The answer is D.
Answer: (D) $992.25
Question: About the number of pairs which have 16 as their HCF and 136 as their LCM, the conclusion can be
(A) only one such pair exists
(B) only two such pairs exist
(C) many such pairs exist
(D) no such pair exists
(E) None of these
Rationale: Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option: D
Answer: (D) no such pair exists
Question: A car moves at 80 km/hr. What is the speed of the car in meters per second ?
(A) 2029msec
(B) 2229msec
(C) 2429msec
(D) 2629msec
(E) None of these
Rationale: ExplanaƟon:
Speed=(80
∗
518)m/sec=2009m/sec=2229msec
Answer: B
Answer: (B) 2229msec
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
(A) 5729
(B) 5760
(C) 2889
(D) 6480
(E) 2799
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4.5 = 6480.Answer: D
Answer: (D) 6480
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent E of the distribution is less than m +d ?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
Rationale: D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, E=(68+16)% or (100-16)% of the population is less than m+d.D
Answer: (D) 84%
Question: If p and r are integers, and p^2 = 14r, then r must be divisible by which of the following?
(A) 2
(B) 4
(C) 5
(D) 7
(E) 14
Rationale: Ans: D
Solution: for p to be an int 14 r must be whole square of a number.
14r= 7*2*r
to make it whole square we need 7
so r can must be divisible by 7y where y is itself a whole square.
so D is the ans
Answer: (D) 7
Question: A train covers a certain distance at a speed of 320kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
(A) 850km/hr
(B) 800km/hr
(C) 740km/hr
(D) 640km/hr
(E) 600km/hr
Rationale: Explanation:
Distance = 320×4 = 1280km
Required speed = (1280/2) = 640km/hr
Answer: Option D
Answer: (D) 640km/hr
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 11 m wide at the top and 9 m wide at the bottom and the area of cross-section is 960 sq m, the depth of cannel is?
(A) 69
(B) 92
(C) 94
(D) 49
(E) 96
Rationale: 1/2 * d (11 + 9)
= 960
d = 96
Answer: E
Answer: (E) 96
Question: By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 25
Rationale: Explanation:
Let S.P. of 45 lemons be Rs. x.
Then, 80 : 40 = 120 : x or x =40X120/80=60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold =45/60X24=18.
ANSWER IS B
Answer: (B) 18
Question: If Rs.1440/- are divided among A,B and C so that A receives 1/3rd as much as B and B receives 1/4th as much as C. The amount B received is?
(A) 250
(B) 270
(C) 310
(D) 330
(E) 350
Rationale: A:B:C = 1:3:12
Total parts = 16
B's share is = 3 parts
16 -----> 1440
1 -----> 90
3 -----> 270 (B's share is 270)
B)
Answer: (B) 270
Question: A football player scores 5 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be
(A) 14
(B) 16
(C) 18
(D) 10
(E) 21
Rationale: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...
From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.
Here, I'll start with Answer E =21 goals
If....
Total goals = 21 goals
5th game = 5 goals
1st 4 games = 16 goals
Avg. for 1st 4 games = 16/4 = 4 goal/game
Avg. for all 5 games = 21/5 = 4.2 goals/game
This is an EXACT MATCH for what we're told in the prompt, so Answer E MUST be the answer.
Answer: (E) 21
Question: If P(A) = 4/7 and P (B) = 2/5, find P (A n B) if A and B are independent events.
(A) 7/25
(B) 3/25
(C) 8/35
(D) 2/13
(E) 3/17
Rationale: P (A n B) = P(A) . P(B)
P (A n B) = 4/7 . 2/5
P (A n B) = 8/35.
C
Answer: (C) 8/35
Question: If the difference between compound interest (interest compounded yearly) and simple interest on a certain sum at the rate 20% p.a. after 3 years is Rs.1280 then what is the principal?
(A) 7900
(B) 8,000
(C) 10,000
(D) 8,300
(E) 9,300
Rationale: let p is the principal,so p([120/100]^3-1)-p*20/100*3=1280
p[728/1000-3/5]=1280
p=1280*5*1000/728*5-3000=10000
ANSWER:C
Answer: (C) 10,000
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.20286/- in 3 years at the same rate of interest. Find the rate percentage?
(A) 5%
(B) 7%
(C) 9%
(D) 15%
(E) 12%
Rationale: Explanation:
The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.
S.I = 20286/- - 17640/- = Rs. 2646/-
Rate of interest = (2646/17640) × (100/1) => 15%
Answer: Option D
Answer: (D) 15%
Question: If the given two numbers are respectively 6% and 30% of a third number, then what percentage is the first of the second ?
(A) 20%
(B) 25%
(C) 18%
(D) 30%
(E) none of these
Rationale: Here, l = 6 and m = 30
Therefore, first number = l/m x 100% of second number = 6/30 x 100% of second number = 20% of second number
ANSWER:A
Answer: (A) 20%
Question: A man is riding a bike with front and back wheel circumference of 40 inches and 70 inches respectively. If the man rides the bike on a straight road without slippage, how many inches will the man have travelled when the front wheel has made 15 revolutions more than the back wheel?
(A) 3388
(B) 2882
(C) 1400
(D) 277
(E) 2282
Rationale: Explanation:
Given the ratio of the circumference of front wheel is 40 inches and back wheel is 70 inches
Distance covered = Circumference of the wheel Ã— No. of Revolutions made by the wheel
If n is the number of revolutions made by back wheel, the number of revolutions made by front wheel is n+15
Distance covered by both the wheels is the same
40*(n+3)=70n
n=20
Front wheel : Back Wheel
Circumference 40 : 70
Revolutions 35 : 20
Distance covered \small \Rightarrow 40Ã—35 = 70Ã—20 = 1400 inches.
Answer: C
Answer: (C) 1400
Question: Departments A, B, and C have 15 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
(A) 19,000
(B) 40,000
(C) 100,000
(D) 641,250
(E) 400,000
Rationale: 15c1 * 15c1* 15c1*20c2 = 15*15*15*190=641250. Hence D is the correct answer.
Answer: (D) 641,250
Question: A person buys an article at Rs.620. At what price should he sell the article so as to make a profit of 25%?
(A) 600
(B) 882
(C) 775
(D) 662
(E) 521
Rationale: Cost price = Rs.620
profit = 25% of 620= Rs.155
Selling price = Cost price + Profit
= 620 + 155 = 775
Answer: C
Answer: (C) 775
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
(A) 150, 208
(B) 150, 206
(C) 150, 200
(D) 150, 202
(E) 150, 201
Rationale: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer:C
Answer: (C) 150, 200
Question: What is the product of the greatest 2 digit multiple of 15 and the greatest 2 digit prime number?
(A) 9,312
(B) 9,408
(C) 9,506
(D) 9,603
(E) 8730
Rationale: the greatest 2 digit multiple of 15: 90
the greatest 2 digit prime numebr: 97
97*90.
8730
E
Answer: (E) 8730
Question: BMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS is ?
(A) 0.19
(B) 1.22
(C) 0.1
(D) 0.16
(E) 0.18456
Rationale: Asking atleast 6 of them continue ,
it has 3 cases.
1 all 8 professors continue.
2 7 professors continue and 1 professors discontinue.
3 6 professors continue and 2 professors discontinue.
1st case all 8 continue is = 2/10*3/10*4/10*5/10*6/10*7/10*/8/10*9/10=9factorial/10power8
=362880/100000000
=>0.00363.
2nd case any 7 professors continue, and 1out of 8 discontinue ,8C1 means 8 ways.
= 2/10*3/10.......8/10*1/10, (9/10 prodbability professor discontinue then 1/10)
in this way if we calculate for 8 possibilities then value is =>0.03733.
3rd case any 6 professors continue and 2out of 8 discontinue , 8C2 means 28 ways.
= 2/10*3/10.....2/10*1/10( 2 professors discontinue.
if we calculate for 28 possibilites P value is=>0.1436
=0.00363+0.03733+0.1436=0.18456=
E
Answer: (E) 0.18456
Question: In the Science City, Kolkata the rate of the ticket is increased by 50% to increased the revenue but simultaneously 20% of the visitor decreased. What is percentage change in the revenue. if it is known that the Science city collects one revenue only from the visitors and it has no other financial supports:
(A) + 20%
(B) - 25%
(C) + 305
(D) - 30%
(E) Cannot determined
Rationale: Solution: Let the initial revenue be 100.
100 ----- 50% ↑ (Ticket up)-----> 150 ----- 20% ↓ (Visitors down) -----> 120.
There is 20% increase in the revenue.
Answer: Option A
Answer: (A) + 20%
Question: Machine P and Machine Q are each used to manufacture 440 sprockets. It takes Machine P 10 hours longer to produce 440 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
(A) 5
(B) 4
(C) 55
(D) 95
(E) 125
Rationale: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
440/x = 440/1.1x + 11
1.1(440) = 440 + 11x
11x = 44
x = 4
The answer is B
Answer: (B) 4
Question: Find the odd one out:
125, 106, 85, 76, 65, 58, 53
(A) 33
(B) 85
(C) 26
(D) 18
(E) 222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 85 is the answer.
ANSWER: B
Answer: (B) 85
Question: A person can row at 9 kmph and still water. He takes 6 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 60 km
(B) 87 km
(C) 89 km
(D) 29 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 6.5
=> x/10 + x/8 = 13/2 => (4x + 5x)/40 = 13/2 => x
= 29 km.
Answer:D
Answer: (D) 29 km
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 10 km each. Then they turned left and ran for another 7.5 km.
What is the distance (in kilometers) between the the two twins when they stop?
(A) 21
(B) 23
(C) 25
(D) 27
(E) 30
Rationale: The distance between them is the hypotenuse of a right angle triangle with sides 15 km and 20 km. The hypotenuse = sqrt(15^2 + 20^2) = 25
The answer is C.
Answer: (C) 25
Question: A rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is:
(A) 425
(B) 430
(C) 440
(D) 450
(E) 460
Rationale: l = 378 Cm and b = 525 Cm
Maximum length of a square tile
= HCF of (378,525) = 21 Cm
Number of tiles = (378×525)/(21×21) = (18×25) = 450
Answer is D.
Answer: (D) 450
Question: Each of the three people individually can complete a certain job in 3, 4, and 6 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?
(A) 1/3
(B) 9/20
(C) 8/15
(D) 5/12
(E) 2/3
Rationale: The two slowest people work at rates of 1/4 and 1/6 of the job per hour.
The sum of these rates is 1/4 + 1/6 = 5/12 of the job per hour.
The answer is D.
Answer: (D) 5/12
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 210. The amount of the bill is
(A) 1200
(B) 1960
(C) 1600
(D) 1354
(E) None of these
Rationale: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 210.
x Ã— 16 Ã— (9/12) Ã— (1/100) = 210 or x = 1750
P.W. = Rs. 1750
Sum due = P.W. + T.D. = Rs.(1750
210) = Rs. 1960.
Answer: B
Answer: (B) 1960
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 65 kg
(B) 70 kg
(C) 75 kg
(D) 80 kg
(E) 85 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
answer :E
Answer: (E) 85 kg
Question: A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in --- proportion.
(A) 6:10:5
(B) 5:10:6
(C) 10:5:6
(D) 10:6:5
(E) 5:6:10
Rationale: Initial investment capital ratio of A and B = 3 : 5
Let initial capital of A and B be 3x and 5x respectively.
Amount that C invested after 6 months =5x (since it is equal to B's investment)
Ratio in which profit should be distributed after 1 year
=3x×12:5x×12:5x×6
=3×12:5×12:5×6
=3×2:5×2:5
=6:10:5
Answer is A.
Answer: (A) 6:10:5
Question: A bullet train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the bullet train must run to reduce the time of journey to 40min will be.
(A) 80 kmph
(B) 40 kmph
(C) 60 kmph
(D) 90 kmph
(E) 30 kmph
Rationale: C
60 kmph
Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=40/60hr=2/3hr
New speed = 40* 3/2 kmph= 60kmph
Answer: (C) 60 kmph
Question: Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 9. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
(A) (4m-27)/[m(m-3)]
(B) (4m-27)/[m(m-6)]
(C) (4m-27)/[m(m-9)]
(D) (4m-27)/[m(m-8)]
(E) (4m-20)/[m(m-10)]
Rationale: Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m
Amount of 4th Sandwich with remaining (m-9) students = 1/(m-9)
The amount of Sandwich that carol ate = 3/m + 1/(m-9) = (3m-27+m)/[m(m-9)] = (4m-27)/[m(m-9)]
Answer: C
Answer: (C) (4m-27)/[m(m-9)]
Question: If a light flashes every 6 seconds, how many times will it flash in 1/4 of an hour?
(A) 51
(B) 151
(C) 251
(D) 351
(E) 451
Rationale: In 1/4 of an hour there are 15*60 = 900 seconds
The number of 6-second intervals = 900/6 = 150
After the first flash, there will be 150 more flashes for a total of 151.
The answer is B.
Answer: (B) 151
Question: A person covered one-fourth of the total distance at 17 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 21 (1/8)
(B) 21 (19/25)
(C) 21 (8/25)
(D) 29 (1/25)
(E) 21 (4/25)
Rationale: Let the total distance be x km
total time taken = (x/4)/17 + (3x/4)/24 = 25x/544
Average speed = x/(25x/544) = = 21 (19/25)kmph.
Answer: B
Answer: (B) 21 (19/25)
Question: Dhanumjay invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
(A) 8% p.a.
(B) 5% p.a.
(C) 6% p.a.
(D) 4% p.a.
(E) 3% p.a
Rationale: Explanation:
Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
∴ R = 5
Answer: Option B
Answer: (B) 5% p.a.
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 14 years
(B) 19 years
(C) 33 years
(D) 38 years
(E) 39years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer:A
Answer: (A) 14 years
Question: How many anagrams can we make with the word 'CACAO'?
(A) 5!/(3!)2
(B) 5!/(2!)2 2!
(C) 5!/(3!)2 3!
(D) 4!/(2!)2
(E) 5!/(2!)2
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'CACAO' consists of 5 letters of which there are 2C's, 2A's and 1O.
Number of arrangements = 5!/(2!)2
Answer: E
Answer: (E) 5!/(2!)2
Question: Find the term next in series..
1,1/2,3/2,2,5,1/3,16/3,15,12,1/4,25/4,?
(A) next number is 48
(B) 58
(C) 40
(D) 43
(E) 44
Rationale: [1,1/2,3/2,2], [5,1/3/16/3,15], [12,1/4,25/4,x]
1+1/2=3/2......1/1/2=2
5+1/3=16/3.....5/1/3=15
12+1/4=25/4....12/1/4=48
ANSWER:A
Answer: (A) next number is 48