RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In how many different ways can the letters of the word 'SENDING' be arranged in such a way that the vowels always come together?
A.A)360
B.B)480
C.C)720
D.D)5040
Answer: B.B)480
Explanation: The word 'SENDING' has 7 different letters.
When the vowels EI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters SNDNG (EI).
Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.
The vowels (EI) can be arranged among themselves in 2! = 2 ways.
Required number of ways = (720 x 2) = 1440.
ANSWER:B
Question: P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in --- days
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: Work done by Q in 1 day = 1/12
Work done by P in 1 day = 2 × (1/12) = 1/6
Work done by P and Q in 1 day = 1/12 + 1/6 = ¼
=> P and Q can finish the work in 4 days
Option D
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
A.1
B.3
C.4
D.5
Answer: A.1
Explanation: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Question: if a person want to earn 500 extra from his principal amount in 3 year and rate of interest in market is 3%.how much principal amount he have to spend?
A.3500
B.4444.44
C.3000
D.5555.55
Answer: D.5555.55
Explanation: s.i=p*r*t/100
500=p*3*3/100
50000/9=p
p=5555.55
answer D
Question: The 7th grade French and Spanish classes each have 14 students in them, and there are four students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
A.20
B.21
C.22
D.23
Answer: A.20
Explanation: French class + Spanish class = 28 students.
Four students are in both classes so they were counted twice.
The number of students taking just one class is 28 - 2(4) = 20.
The answer is A.
Question: If Albert’s monthly earnings rise by 36%, he would earn $495. If, instead, his earnings rise by only 25%, how much (in $) would he earn this month?
A.643
B.652
C.454
D.460
Answer: C.454
Explanation: =495/1.36∗1.25
=454=454
Answer is C
Question: A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
A.Rs.500
B.Rs.250
C.Rs.205
D.Rs.5062.50
Answer: C.Rs.205
Explanation: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.400
(P)(8)(5)/100 = 400
P = 1000
C.I on Rs.2P i.e., Rs.2000 at 5% p.a in two years
=2000{ [1 + 5/100]2 - 1} = 2000{ 212 - 202 /202}
= Rs.205
ANSWER:C
Question: A thief steals at a car at 1.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
A.1 p.m
B.3 p.m
C.4. p.m
D.5 p.m
Answer: C.4. p.m
Explanation: C
4 p.m
Suppose the thief is overtaken x hrs after 1.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 4. p.m.
Question: The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is 96∏ cm³, what is its slant height?
A.8 cm
B.10 cm
C.12 cm
D.14 cm
Answer: B.10 cm
Explanation: Sol.
Let the radius and the height of the cone be 3x and 4x respectively. Then,
1/3 * ∏ * (3x)² * 4x = 96∏ ⇔ 36x³
= (96 * 3) ⇔ x³ = [96 * 3 / 36] = 8 ⇔ x = 2
&ther4; Radius = 6 cm, Height = 8 cm.
Slant height = √6² + 8 ² cm = √100 cm = 10 cm.
Answer B
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
A.359m
B.3320m
C.350m
D.3598m
Answer: C.350m
Explanation: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: C
Question: A certain series is defined by the following recursive rule: Sb=K(Sb-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?
A.ROOT 2
B.ROOT 3
C.64*ROOT 3
D.64*3^1/3
Answer: D.64*3^1/3
Explanation: Ans...D
No need for any GP formula here
The rule is that bth term is K times the (b-1)th term.
1st = 64
2nd = k.64
3rd = k^2.64
.
.
.
9th term = k^8 *64
.
.
.
so 25th = k^24*64
Using this solve for k and substitute k in the equation for the 9th term
Question: 1903 x 1903 = ?
A.A)3623216
B.B)3624216
C.C)3624316
D.D)3621409
Answer: D.D)3621409
Explanation: 1903 x 1903 = (1903)2
= (1900 + 3)2
= (1900)2 + (3)2 + (2 x 1900 x 3)
= 3610000 + 9 + 11400.
= 3621409.
D)
Question: To make 552185 divisible by 8, what is the least whole number that should be added to it?
A.3
B.7
C.9
D.6
Answer: B.7
Explanation: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
Here, 552185=185(no formed by last three digit)
the next multiple of 8 is 192
7 must be added to 552185 to make it divisible by 8
B
Question: Two horses begin running on an oval course at the same time. One runs each lap in 9 minutes; the other takes 18 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
A.36
B.18
C.9
D.4
Answer: B.18
Explanation: The rate of the faster horse is 1/9 lap/minute;
The rate of the slower horse is 1/18 lap/minute;
Their relative rate is 1/9-1/18=1/18 lap/minute;
The faster horse to gain one full lap will need time=distance/rate=1/(1/18)=18 minutes.
Answer: B
Question: 45 girls and 60 boys are present at a party. There are 17 girl-boy are in relationship among them. If a girl and a boy is selected at random, what is the probability that they will be not a couple?
A.17/ 2900
B.2683/2700
C.2496/2700
D.2369/2700
Answer: B.2683/2700
Explanation: In how many ways we can select a girl and a boy from 45 lady and 60 gentlemen? In 45*60 = 2,700 ways.
We have a total of 17 couples so, the probability of selecting a couple is 17/2,700 = 17/2700.
Probability of there will not be a couple = 1 - (17/2700)
= 2683 / 2700
Ans- B
Question: For what value(s) of k is the following equation satisfied: 3k-9-2k = 5k+6-4k
A.a. -5
B.b. 0 only
C.c. 5/2 only
D.d. No value
Answer: D.d. No value
Explanation: 3k-9-2k = 5k+6-4k
k - 9 = k + 6
-9 = 6, which is false.
So, no k satisfies given equation.
Answer: D.
Question: A 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds.What is the length of the other train?
A.230 m
B.240 m
C.260 m
D.320 m
Answer: A.230 m
Explanation: speed of first train= (120 * 5/18)m/sec
= 100/3 m/sec
speed of other Train= (80 * 5/18)m/sec
= 200/9 m/sec
time to cross each other= 9 sec
Let x be the length of 2nd train
therefore 9 = (270+ x)/(100/3 +200/9)
500 = 270 + x
230m = x
ANSWER:A
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.328
B.375
C.279
D.269
Answer: B.375
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
Question: What day will be 61 days after today, if today is Monday?
A.Tuesday
B.Thursday
C.Saturday
D.Friday
Answer: C.Saturday
Explanation: Explanation:
The basic concept in a problem involving days is finding the number of odd days. In 61 days:
=> 7 x 8 + 5 = 5 odd days
=> Monday + 5 days = Saturday
Hence 61 days from today will be a Saturday.
ANSWER C
Question: The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle.
A.15° ,45° ,110°
B.15° ,45° ,130°
C.15° ,45° ,110°
D.15° ,35° ,110°
Answer: C.15° ,45° ,110°
Explanation: Solution
If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
x = 15
The measures of the three angles are
x = 15°
3x = 3 × 15 = 45°
8x = 8 × 15 = 120°
ANSWER IS C
Question: Rajesh can finish 1/5 of his home work in one hour. Seema can finish 3/7 of
her homework in 90 minutes and Ramya can finish 3/4 of her homework in
three and a half hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.30 PM for 30 minutes?
A.4:30pm
B.5:30pm
C.6:30pm
D.5:10pm
Answer: B.5:30pm
Explanation: ajesh can finish his work in 5 hr,
ramya can finish her work in 4.7 hr
seema can finish in 3.5 hr
so 5:30pm they can go to play
ANSWER:B
Question: A dealer offers a cash discount of 10% and still makes a profit of 35% when he further allows 20 articles to be sold at the cost price of 15 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
A.80%
B.100%
C.120%
D.60%
Answer: B.100%
Explanation: Given
Cash Discount - 10%
Profit - 35%
Items Sold - 20
Price Sold at = List Price of 15
Assume List price = $20
Total Invoice = $300
-10% Cash Discount = $270
Let cost price of 20 items be x
So total cost = 20*x
Given the shopkeeper had a profit of 20%
20 * x * 135/100 = 270
or x = $10
Which means his products were listed at $20 which is a 100% markup over $10
Answer B
Question: James rode his bike 5 miles against the wind in 50 minutes and back 5 miles with the wind in 25 minutes. How strong is the wind in miles/hr (mph)?
A.1 mph
B.2 mph
C.3 mph
D.4 mph
Answer: C.3 mph
Explanation: Explanation:
speed against the wind = (5/50) X 60 = 6 mph
with the wind = (5/25) X 60 = 12 mph
strength of wind = 1/2(12 - 6) = 6/2 = 3 mph
Answer: Option C
Question: A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600,allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of :
A.0%
B.5%
C.7.5%
D.10%
Answer: A.0%
Explanation: Solution
C.P. = Rs. 3000. S.P. = Rs. [ 3600x 100/100+( 10x2 ) ] = Rs. 3000
Gain = 0 %.
Answer A
Question: List S consists of 12 consecutive integers. If -4 is the least integer in list S, what is the range of positive integers in list S?
A.5
B.6
C.7
D.11
Answer: B.6
Explanation: Since -4 is the least integer in list S, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is 7-1=6.
Answer: B.
Question: David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?
A.$96,000
B.$94,000
C.$88,000
D.$75,000
Answer: B.$94,000
Explanation: Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer.
Question: Sandy is younger than Molly by 8 years. If their ages are in the respective ratio of 7:9, how old is Molly?
A.18
B.27
C.36
D.45
Answer: C.36
Explanation: S = M - 8
S / M = 7/9
9S = 7M
9(M-8) = 7M
M = 36
The answer is C.
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
A.6 YEARS
B.7
C.5
D.3
Answer: D.3
Explanation: Explanation:
9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
Answer: Option D
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
A.65
B.68
C.69
D.67
Answer: B.68
Explanation: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: Option B
Question: A candidate got 35% of the votes and lost to the rival by 1650 votes. How many votes were cast?
A.5000
B.5500
C.6000
D.6500
Answer: B.5500
Explanation: 35%-----------L
65%-----------W
------------------
30% = 1650
10% = 550
100% of the votes = 5500
Answer: B
Question: The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$440 per month. The salary of the new supervisor is:
A.233
B.960
C.287
D.771
Answer: B.960
Explanation: Explanation:
Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870
Now total salary of 8 workers = 3870 âˆ’ 870 = 3000
Total salary of 9 workers including the new supervisor = 9 Ã— 440 = 3960
Salary of the new supervisor = 3960 âˆ’ 3000 = 960
Answer: B
Question: Divide Rs.32000 in the ratio 3:5?
A.12000,20000
B.12000,20092
C.12000,20029
D.12000,20007
Answer: A.12000,20000
Explanation: 3/8 * 32000 = 12000
5/8 * 32000 = 20000
Answer: A
Question: Two third of three- fifth of one fourth of a number is 24, what is 30% of that number?
A.22
B.72
C.91
D.12
Answer: B.72
Explanation: Explanation:
x * 2/3 * 3/5 * 1/4 = 24
x = 240
240 * 30/100 = 72'
Answer: B
Question: Total dinning bill for 7 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
A.$30.14
B.45.14
C.34.66
D.32.29
Answer: C.34.66
Explanation: 211*15=3165/100=31.65
211+31.65=242.65
242.65/7=34.66
ANSWER:C
Question: Convert the following unit:
2.0 hectares in ares
A.200 ares.
B.210 ares.
C.220 ares.
D.230 ares.
Answer: A.200 ares.
Explanation: 2.0 hectares in ares
1 hectare = 100 ares
Therefore, 2.0 hectares = 2.0 × 100 ares
= 200 ares.
ANSWER : OPTION A
Question: In what time will a train 100 m long cross an electric pole, it its speed be 162 km/hr?
A.2.5 sec
B.2.8 sec
C.8.5 sec
D.2.2 sec
Answer: D.2.2 sec
Explanation: Speed = 162 * 5/18
= 45 m/sec
Time taken = 100/45
= 2.2 sec.
Answer:D
Question: The sum of the present ages of a father and his son is 52 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:
A.14
B.16
C.18
D.20
Answer: D.20
Explanation: Let the present ages of son and father be x and (52 - x) years respectively.
Then, (52 - x) - 6 = 4(x - 6)
46 - x = 4x - 24
x = 14
The son's age after 6 years will be 20.
The answer is D.
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
A.Rs.2000
B.Rs.2029
C.Rs.2068
D.Rs.2297
Answer: A.Rs.2000
Explanation: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 =>
Rs.2000
Answer:A
Question: |9 - 4| - |12 - 14| = ?
A.3
B.2
C.1
D.0
Answer: A.3
Explanation: |9 - 4| - |12 - 14| = | 5 | - | -2 | = 5 - 2 = 3
correct answer A
Question: A invested $300 in a business and B invested $400 in a business. At the end of the year they got $350 as the profit. Find their share?
A.$150,$200
B.$250,$300
C.$125,$250
D.$130,$150
Answer: A.$150,$200
Explanation: A:B = 300:400
A:B = 3:4
A's share = 350*3/7 = $150
B's share = 350*4/7 = $200
Answer is A
Question: In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?
A.11
B.14
C.12
D.13
Answer: D.13
Explanation: Explanatory Answer
Step 1: Find the first number common to both the sequences.
The first sequence: Numbers leaving a remainder of 4 when divided by 7: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, ....
The second sequence: Numbers leaving a remainder of 9 when divided by 11: 9, 20, 31, 42, 53, 64, .....
From the listing of the two sequences we can identify the first number that is a part of the both the sequences is 53.
Step 2: Compute common difference of terms common to both sequences and find number of terms.
The common difference of the first sequence is 7 and that of the second sequence is 11.
Elements common to both the sequences will have a common difference that is the LCM of 7 and 11.
77 is the LCM of 7 and 11.
Every 77th number after 53 will satisfy both the conditions.
The terms that are common to both the arithmetic sequences can be expressed as 77k + 53.
Because we are interested in the first 1000 natural numbers, k will take values from 0 to 12.
i.e., a total of 13 values.
Choice D is the correct answer.
Question: Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
A.22
B.24
C.99
D.27
Answer: B.24
Explanation: Explanation:
Less Cogs more turns and less time less turns
Number of turns required=80 × × = 24 times
Answer: B) 24
Question: (?)+3699+1985-2047=31111
A.34748
B.27474
C.30154
D.27574
Answer: B.27474
Explanation: x+3699+1985-2047=31111
=x+3699+1985=31111+2047
=x+5684=33158
=x=33158-5684
=27474
Answer is B
Question: tom and Bonnie are opposing participants in an online auction. Each has a constant bidding strategy: tom always bids up by raising $40 over any previous bid. Bonnie always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: tom bids up first, and Bonnie follows. tom bids up again, and Bonnie follows and raises the bid to a final $600. What was the dollar value of the initial price?
A.90
B.45
C.46
D.255
Answer: A.90
Explanation: Initial bid = p$
tom = p+40
Bonnie = 2p
The sequence is R---> B ---> R -----> B ---> 600
Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)
Now given, 2(2p+120) = 600----> p =90$. Thus A is the correct answer.
Question: The average weight of 20 boys sitting in a boat had some value. A new person added to them whose weight was 50 kg only. Due to his arrival, the average weight of all the boys decreased by 8 kg. Find the average weight of first 20 boys?
A.150
B.154
C.218
D.182
Answer: C.218
Explanation: 20x + 50 = 21(x â€“ 8)
x = 218
C
Question: Difference between the length&breadth of a rectangle is 23m. If its perimeter is 206m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
A.2430 m^2
B.2640 m^2
C.2520 m^2
D.2650 m^2
Answer: C.2520 m^2
Explanation: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
A.31 kg
B.32 kg
C.33 kg
D.34 kg
Answer: A.31 kg
Explanation: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (43 x 2) = 86 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)
Subtracting (i) from (iv), we get : B = 31.
B’s weight = 31 kg.
Answer: A
Question: What is the ratio of 4/7 to the product 2*(7/3)?
A.6:49
B.1:3
C.3:21
D.1:7
Answer: A.6:49
Explanation: 4/7 / 14/3 = 6/49...
IMO option A.
Question: 45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
A.77
B.77
C.66
D.55
Answer: D.55
Explanation: (45 * 8)/30
= (x * 6)/50
=> x =100
100 – 45
= 55
Answer:D
Question: The value of (0.625 * 0.0729 * 28.9)/(0.0017 * 0.025 * 8.1) is
A.0.3825
B.3.825
C.38.25
D.382.5
Answer: D.382.5
Explanation: (0.625*0.0729*28.9)/(0.0017)*0.025*8.1
={(625/1000)*(729/10000)*(289/10)}/{(17/10000)*(25/1000)*(81/10)
=382.5 ANSWER:D
Question: George's drawer has 7 loose black socks, 11 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that he had at least two matching pairs of socks in two different colors?
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: The worst case scenario is choosing 11 blue socks. Then he would need 3 more socks to be sure of a matching pair of black socks or white socks.
The answer is C.
Question: What is the greatest prime factor of 11!10! + 10!9! ?
A.11
B.17
C.29
D.37
Answer: D.37
Explanation: 11!10! + 10!9! = 10!9!(11*10+1) = 10!*9!*111 = 10!*9!*3*37
The answer is D.
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
A.50
B.100
C.150
D.200
Answer: C.150
Explanation: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
25p of x,10p of 2x,5p of 3x;
25p=25/100=1/4;
10p=10/100=1/10;
5p=5/100=1/20;
1x/4 + 2x/10 + 3x/20=30;
5x+4x+3x=600;
12x=600 (3*50)
x=150 answer : C
Question: What is the perimeter of a regular polygon with sides of length 10 cm and internal angles measuring 140° each?
A.90 cm
B.108 cm
C.120 cm
D.132 cm
Answer: A.90 cm
Explanation: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 140*n
from here
n = 9
So perimeter becomes 10*9= 90
Answer: A
Question: If n = 2×3×5×7×11×13×18, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
A.I only
B.II only
C.III only
D.I and III
Answer: D.I and III
Explanation: Statement I: this is true.
Statement 2 this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2, So this is true.
Hence option (D).
Question: If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 6n years to that after 3n years?
A.(1+n/100)^k
B.(1+k)^n
C.(1+kn/100)
D.(1+k/100)^3n
Answer: D.(1+k/100)^3n
Explanation: Amount after 6n years will be = x ( 1 + k/100)^6n
Amount after 3n years will be = x ( 1 + k/100)^3n
So, required ratio will be -
{ x ( 1 + k/100)^6n } / {x ( 1 + k/100)^3n } = (1+k/100)^3n
Hence answer will be a. (1+k/100)^3n
D
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?
A.20%
B.26%
C.42%
D.5%
Answer: D.5%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 70
2/3 SP1 = 70
SP1 = 105
100 --- 5 => 5%
Answer: D
Question: A can complete the job in 3 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
A.1/6
B.3/10
C.1/2
D.5/6
Answer: A.1/6
Explanation: 1/6=A
Question: Twelve machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
A.2
B.3
C.4
D.6
Answer: D.6
Explanation: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
So 3/2*12 =18
So we need 18-12 = 6 more machines.
Answer : D
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
A.6 kmph
B.7 kmph
C.9 kmph
D.4 kmph
Answer: A.6 kmph
Explanation: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
A.87
B.27
C.25
D.26
Answer: C.25
Explanation: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25
Answer: C
Question: A and B finish the job in 15 days.while A,B and C can finish it in 5 days . C alone will finish the job in
A.4.50 days
B.3.50 days
C.6.0 days
D.7.5 days
Answer: D.7.5 days
Explanation: Explanation:
5 = (15 * x)/(15 + x)
75+5x=15x
10x=75
X=7.5
Answer: Option D