RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In how many ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?
A.720
B.864
C.900
D.936
Answer: D.936
Explanation: Total number of four letter passwords = 6*6*6*6= 1296 ------(1)
Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2)
therefore required value = (1)-(2)= 1296-360=936
ANSWER:D
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
A.2400
B.2499
C.2779
D.2729
Answer: A.2400
Explanation: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Anawer:A
Question: 10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
A.5000
B.6000
C.7000
D.8000
Answer: B.6000
Explanation: Let the total number of original inhabitants be x. Then,
(100 – 25)% of (100 –10)% of x = 4050
⇒ (75/100×90/100×x) = 4050 ⇒ 27⁄40x = 4050
⇒ x = 4050×40/27=6000
∴ Number of original inhabitants = 6000.
Answer B
Question: A bag contains 15 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
A.2/35
B.1/15
C.6/35
D.13/70
Answer: C.6/35
Explanation: We have 15 scarves: 1 red, 1 green and 13 other. We're asked for the probability of grabbing 3 scarves that include the 1 red but NOT the 1 green scarf.
Even though the question states that we are supposed to grab all 3 scarves simultaneously, we can still refer to them as 1st, 2nd and 3rd. There are 3 ways to get what we *want*
R = Red
O = Other
ROO
ORO
OOR
The probability of getting ROO = (1/15)(13/14)(12/13) = 2/35
The probability of getting ORO = (13/15)(1/14)(12/13) = 2/35
The probability of getting OOR = (13/15)(12/14)(1/13) = 2/35
Total ways = 2/35 + 2/35 + 2/35 = 6/35
ANSWER:C
Question: The probability that a card drawn from a pack of 52 cards will be a diamond or a king is
A.2/13
B.4/13
C.1/13
D.1/52
Answer: B.4/13
Explanation: Solution
Here, n(S) = 52.
There are 13 cards of diamond(including 1 king) and there are 3 more kings.
Let E = event of getting a diamond or a king.
Then, n(E) = (13+3)
= 16.
Therefore, P(E) = n(E)/n(S)
= 16 / 52
= 4 / 13.
Answer B
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
A.5
B.6
C.8
D.4
Answer: A.5
Explanation: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
Question: the probability that I will sit next to Ann is 1/12.
the probability that I won't sit next to Alice is 11/12.
What is the probability that I will sit next to Alice and not next Ann?
A.1/6
B.11/12
C.11/144
D.1/12
Answer: C.11/144
Explanation: the probability that I won't sit next to Ann is 1-1/12=11/12.
the probability that I will sit next to Alice is 1-11/12 = 1/12.
Therefore the probability that I will sit next to Ann and Alice is 11/12*1/12=11/144
Answer:C
Question: For any integer z, the function PODD(z) is defined as the product of all odd integers between –z and z, inclusive. Which of the following numbers will not divide PODD(-15) completely?
A.3^8
B.5^5
C.7^3
D.Options B and C
Answer: D.Options B and C
Explanation: Solution 1:
Given PODD(Z) is product of all odd integers -Z to Z, so doesn't matter what the prime factors are, they will have even powers, So B and C WILL NOT divide PODD(-15) completely(!!!!, when you say completely i hope you meant without any remainder)
Solution 2:
PODD(-15) = (15.13.11.9.7.5.3)^2 and breaking down to prime factors (5.3.13.11.3.3.7.5.3)^2 = (13^2.11^2.7^2.5^4.3^8)
ANSWER:D
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of the mother?
A.25
B.30
C.35
D.40
Answer: D.40
Explanation: Let present age of the mother =5x
Then, present age of the person =2x
5x+8=2(2x+8)5x+8=4x+16x=8present age of the mother =5x=40
Answer is D.
Question: There are 11 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?
A.3/17
B.4/19
C.5/21
D.6/22
Answer: D.6/22
Explanation: P(first stamp is different) = 6/11
P(second stamp is different) = 5/10
P(both stamps are different) = 6/11*5/10 = 6/22
The answer is D.
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
A.28 sec
B.23 sec
C.24 sec
D.25 sec
Answer: D.25 sec
Explanation: D
25 sec
D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Question: Look at this series: 544, 509, 474, 439,404, 369, 334, ... What number should come next?
A.206
B.299
C.306
D.507
Answer: B.299
Explanation: 299
This is a simple subtraction series. Each number is 35 less than the previous number.
B
Question: In how many ways can the letters of the word "SATURN" be arranged?
A.560
B.640
C.720
D.800
Answer: C.720
Explanation: The total ways of arranging the letters = 6! = 720
The answer is C.
Question: If TIER is written as 9163 and BRAIN is written as 23415, how is RENT coded ?
A.3653
B.3657
C.2977
D.3659
Answer: D.3659
Explanation: Explanation:
Given :
Letter : T I E R B A N
Code : 9 1 6 3 2 4 5
Thus, the code for RENT is 3659.
ANSWER:D
Question: An investor bought N shares of company X at $15 per share and N shares of company Y at $20 per share. If a month later the investor sold all the shares at $20 per share and made a profit of $200, then what is the value N?
A.35
B.40
C.50
D.60
Answer: B.40
Explanation: The investor made a profit of (2∗N∗20)−(15N+20N)=200. This equation simplifies to 5N=200 from where N=40.
Answer: B
Question: If 1488 / 1.24 = 1200, then 148.8 / 12.4 is equal to ?
A.17
B.10
C.14
D.12
Answer: D.12
Explanation: Answer
Given expression 148.8 / 12.4 = 1488 / 124
= 1488 / (1.24 x 100)
= 1200/100
=12
Correct Option: D
Question: Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)?
A.1/4
B.1/7
C.3/7
D.4/9
Answer: A.1/4
Explanation: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
A)
Question: 2,6,30,60,130,221...tell 8th digit in series??
A.458
B.504
C.524
D.534
Answer: B.504
Explanation: in this series
T(n)=n^3+/- n
+ for odd n and - for even n
n=1 T(n)=1+1=2
n=2 T(n)=8-2=6
n=3 T(n)=27+3
n=4 T(n)=64-4=60
n=5 T(n)=125+5=130
n=6 T(n)=216-6=210
n=7 T(n)=343+7=350
n=8 T(n)=512-8=504
ANSWER:B
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
A.Rs.647
B.Rs.640
C.Rs.621
D.Rs.619
Answer: B.Rs.640
Explanation: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer:B
Question: A dog buys a boat for rs.132.44 and sells it for rs.263.59. Find her gain %.
A.10%
B.99.03%
C.87%
D.16%
Answer: B.99.03%
Explanation: sol. cp=rs 132.44, sp=rs 263.59
gain=rs(263.59 –132.44)=rs 131.15
so gain%={(131.15/132.44)*100}=99.03%
Answer is B.
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
A.5/7
B.5/3
C.5/1
D.5/6
Answer: D.5/6
Explanation: P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer: D
Question: Evaluate 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 =?
A.3043
B.5050
C.5176
D.9356
Answer: B.5050
Explanation: B
5050
You must have noticed that 50 pairs of n^2 – (n-1) ^2 exist.
n^2 – (n-1)^2 = n + (n – 1)
In such case, we may as well write 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 as 100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050
Question: The compound interest on $ 27,000 at 11% p.a is $ 11,000.Find out the period (in years) ?
A.2.5
B.3 1/4
C.3
D.2 3/4
Answer: B.3 1/4
Explanation: Amount = 27,000 + 11,000
= 38,000 ......... Now by using compound interest formula we get, 27,000 * (111/100)^n = 38000 ====> n == 3 1/4 years
Ans - B
Question: What is the units digit of (3^10)(4^13)?
A.2
B.4
C.6
D.7
Answer: C.6
Explanation: -> The ones place of (~3)^n repeats after 4 times like 39713.
The ones place of (~4)^n repeats after 2 times like 464.
Then, 3^10=3^4*2+23^2.,
4^13=4^2*6+1=4^1=~4
which is (3^10)(4^13) (3^2)(~4)=(~9)(~4)=~6. Therefore, the answer is C.
Question: The sector of a circle has radius of 7 cm and central angle 135o. Find its perimeter?
A.91.5 cm
B.92.2 cm
C.28.9 cm
D.30.5 cm
Answer: D.30.5 cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 7) + 2(7)
= 16.5 + 14 =30.5 cm
Answer:D
Question: If Josh, Doug, and Brad have a total of $68 between them, and Josh has two times as much money as Brad but only three-fourths as much as Doug, how much money does Brad have?
A.$10
B.$24
C.$26
D.$12
Answer: D.$12
Explanation: Josh+Doug+Brad = 68 ; Josh = 2 Brad, Josh =3/4 Doug
Josh+1/2 Josh+ 4/3 Josh = 68 (substituted the given values)
Josh = 24. 24= 3/4 Doug => Doug =32
Josh+Doug+Brad = 68
24 + 32 + Brad = 68
Brad = 12
Answer is D.
Question: A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
A.28
B.50
C.77
D.22
Answer: C.77
Explanation: Speed of the train relative to man = (200/10) m/sec = (20) m/sec. [(20) * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72 ==> x
= 77 km/hr.Answer:C
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
A.21 sec
B.16 sec
C.71 sec
D.18 sec
Answer: B.16 sec
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35
= 16 sec
Answer: B
Question: Lines y=4√5·x−2 and y=3√5·x−1 intersect at what height above the x axis?
A.0
B.2√5
C.2
D.3√5
Answer: C.2
Explanation: Solve two equations for y
y=4√5·x−2
y=3√5·x−1
Set the two equations equal to each other and solve for x
4√5·x−2=3√5·x−1
√5·x = 1
x = 1/√5
Plug x = 1/√5 into any one of the original equations to find the y value (height above x axis) where the two lines intersect
y=4√5·x−2
y=4√5·(1/√5)−2
y=4·1 - 2
y = 4 - 2
y = 2
Final answer:
C) 2
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1â„4 of the same job. How many days will 10 men and 8 women together take to complete the same job?
A.6
B.13 1â„2
C.18
D.Data inadequate
Answer: C.18
Explanation: 12 M Ã— 18 = 12 W Ã— 18 Ã— 4â„1
\ w = 1/4 M
10M + 8W = 10M + 8 Ã— 1â„4M = 12 M
\12 men can complete the same work
in 12Ã—18/12=18days
Answer C
Question: find value for x from below equation?
x + 1 = -3
A.-2
B.-4
C.-1
D.-5
Answer: B.-4
Explanation: 1. Subtract 1 from both sides:
x + 1 - 1 = -3 - 1
2. Simplify both sides:
x = -4
B
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
A.11
B.15
C.16
D.28
Answer: D.28
Explanation: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Question: The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?
A.Rs.16500/-
B.Rs.17000/-
C.Rs.18000/-
D.Rs.19000/-
Answer: C.Rs.18000/-
Explanation: For 2 years = (1002D)/R2
= (1002 × 45)/(5 × 5) = (10000 × 45)/25 = Rs.18000/-
C
Question: Reena took a loan of Rs. 2000 with simple interest for as many years as the rate of interest. If she paid Rs. 720 as interest at the end of the loan period, what was the rate of interest?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: Let rate = R% and time = R years.
=(2000xRxR)/100 =720
=20Rsquare =720
R Square = 720/20 =36
R= 6
ANSWER :A
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?
A.0
B.12
C.13
D.20
Answer: D.20
Explanation: 12*35=420
420%21=20
ANSWER:D
Question: A fruit seller had some Mangoes. He sells 50% oranges and still has 500 Mangoes. How many Mangoes he had originally?
A.800
B.850
C.900
D.1000
Answer: D.1000
Explanation: He sells 50% of oranges and still there are 500 oranges remaining.
= 50% of oranges = 500
Total oranges x (50/100)= 500
= Total oranges =500×100/50=1000
answer :D
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1600, then what is the smallest possible value of n?
A.6
B.8
C.10
D.12
Answer: C.10
Explanation: 1600=2^6*5^2
2^6 means that n must be at least 8. That is, we need 2, 2*2, 6, and 2*2*2.
5^2 means that n must be at least 10. That is, We need 5 and 10.
The answer is C.
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 50% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
A.2/5
B.4/7
C.10/19
D.7/24
Answer: C.10/19
Explanation: Suppose there are 100 students
Group A : 40% = 40 students
50% drink beer = 20
30% mixed = 12
20% both = 8
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 20+18 =38 and both = 20
thus 20/38 = 10/19
Hence C
Question: From a bunch of eight keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?
A.1/120
B.1/180
C.1/336
D.1/480
Answer: C.1/336
Explanation: The probability is 1/8*1/7*1/6 = 1/336.
The answer is C.
Question: A warehouse had a square floor with area 10,000 sq.meters. A rectangular addition was built along one entire side of the warehouse that increased the floor by one-half as much as the original floor. How many meters did the addition extend beyond the original buildings ?
A.10
B.20
C.50
D.100
Answer: C.50
Explanation: as L*B=10000 ie for square L=B=100m
THEN,
IF A RECTANGULAR ADDITIONALLY WAS BUILT ALONG ONE ENTIRE SIDE IT ENSURES THAT ONE SIDE MUST BE REMAIN SAME AS THE SQUARE
HENCE EQUATION BECOMES
(100+X)100=10000+(1/2)*10000
(100+X)100=15000
X=50
ANSWER:C
Question: A 425 meter long train crosses a platform in 55 seconds while it crosses a signal pole in 40 seconds. What is the length of the platform?
A.155.68
B.160
C.159.38
D.180
Answer: C.159.38
Explanation: Speed = [425 / 40 m/sec = 42.5/4 m/sec.
Let the length of the platform be x meters.
Then, x + 425 / 55= 42.5/4
4(x + 425) = 2337.5 è x =159.38 m. Answer: C
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 85 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
A.50%
B.59%
C.54%
D.55%
Answer: B.59%
Explanation: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
60*0.85=51 Democrats are expected to vote for Candidate A;
40*0.20=8 Republicans are expected to vote for Candidate A.
Thus total of 51+8=59 registered voters are expected to vote for Candidate A, which is 59% of the total number of registered voters.
Answer: B.
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1008?
A.900
B.2217
C.2889
D.2777
Answer: A.900
Explanation: 1008 = P [1 + (5*12/5)/100]
P= 900
Answer: A
Question: A textile manufacturing firm employees 56 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 56 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
A.13000
B.6250
C.10000
D.5000
Answer: B.6250
Explanation: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(55/56)âˆ’150000Ã—(55/56)âˆ’75000.
=>Rs 2,68,750
Decrease in profit
=>2,75,000âˆ’2,68,750
=>Rs. 6,250
Answer : B
Question: A is twice as good a work man as B and together they finish a piece of work in 14 days.The number of days taken by A alone to finish the work is :
A.11
B.21
C.28
D.42
Answer: B.21
Explanation: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.
(A + B)'s 1 day’s work = 1/14
Divide 1/14 in the ratio 2 : 1.
∴ A’s 1 day’s work = (1/14 x2/3)= 1/21
Hence,A alone can finish the work in 21 days.
Answer B
Question: A certain machine produces 550 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 5 days?
A.7,000
B.24,000
C.66,000
D.100,000
Answer: C.66,000
Explanation: Since 5 days consist of 24*5 hours the total is 120 hours.
Since every hour the machine produces 550 units of product P the total product during 120 hours is 120*550=66,000.
Correct Option : C
Question: If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+13 is divided by 41?
A.3
B.18
C.6
D.16
Answer: B.18
Explanation: X can be written as 82K + 5 or X = 5,87,169,etc.
X + 13 = 82K + 5+13= 82K +18 or X + 13 = 18,100, 182 etc.
When divided by 41, we will get the remainder 18.
B
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time?
A.Rs. 52
B.Rs. 51.25
C.Rs. 54.25
D.Rs. 60
Answer: B.Rs. 51.25
Explanation: Simple interest for 2 years = Rs.50 ie. For 1 years Rs. 25. . In the first year the S.I and C.I are
same ie.Rs. 25. So in the 2nd year in C.I calculated for 1 years interest also. So in second years for
Rs.25 interest is 25*5/100 = 1.25 . So total C.P = 51.25.
ANSWER:B
Question: If x^2 – 2y^2 = 2xy, then (x + y)^2 =
A.x^2
B.2x^2-y^2
C.4xy
D.2y^2
Answer: B.2x^2-y^2
Explanation: (x+y)^2 = x^2 + y^2 + 2xy = x^2 + y^2+ x^2-2y^2 = 2x^2-y^2
Correct option : B
Question: Each Machine of type A has 2 steel parts and 3 chrome parts. Each machine of type B has 3 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 40 steel parts and 32 chrome parts, how many machines are in the group
A.12
B.13
C.14
D.15
Answer: A.12
Explanation: Look at the below representation of the problem:
Steel Chrome total
A 2 3 40 >>no. of type A machines=40/5=8
B 3 5 32 >>no. of type B machines=32/8=4
So the answer is 12 i.e A.
Hope its clear .
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
A.7500
B.2878
C.2662
D.2992
Answer: A.7500
Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs. 7500.
Answer: A
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
A.Rs. 14,000
B.Rs. 12,000
C.Rs. 30,000
D.Rs. 40,000
Answer: B.Rs. 12,000
Explanation: Explanation:
[1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
ANSWER IS B
Question: A man buys s cycle for $100 and sells it at a loss of 40%. What is the selling price of the cycle?
A.$50
B.$60
C.$70
D.$80
Answer: B.$60
Explanation: S.P. = 60% of the $100 = 60/100 * 100 = $60
Answer is B
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50
II. 68
III. 90
A.I only
B.III only
C.I and II
D.I only III
Answer: C.I and II
Explanation: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 50 --> 12 + 38 --> Possible
II. 68 --> 30 + 38--> Possible
III. 92 --> Not possible
Answer: C
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $151 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
A.8
B.10
C.12
D.14
Answer: B.10
Explanation: $151 = 29*$5 + 2*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 29, 26, 23, 20,...,2 for a total of 10 combinations.
The answer is B.
Question: In a graduating class of 234 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A.144
B.115
C.113
D.88
Answer: B.115
Explanation: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 234 = 29
Greatest - Smallest is 144-29 = 115
So answer must be B. 115
Question: John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?
A.The average speed is 54 miles per hour.
B.The average speed is 32 miles per hour.
C.The average speed is 44 miles per hour.
D.The average speed is 60 miles per hour.
Answer: A.The average speed is 54 miles per hour.
Explanation: Step 1: The formula for distance is
Distance = Rate × Time
Total distance = 50 × 3 + 60 × 2 = 270
Step 2: Total time = 3 + 2 = 5
Step 3: Using the formula
average speed formula
270/5 = 54
Answer(A)
Question: If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days?
A.71
B.12
C.18
D.11
Answer: D.11
Explanation: Explanation:
Let the required no of binders be X.
Less books , Less binders (Direct Proportion)
More days, Less binders (Indirect proportion)
\inline \fn_jvn \left.\begin{matrix} Books\: 900:600\\ Days\: \: 12:10 \end{matrix}\right\}::18:x
\inline \fn_jvn \therefore \inline \fn_jvn (900\times 12\times x)=(600\times 10\times 18) \inline \fn_jvn \Leftrightarrow x= \inline \fn_jvn \frac{600\times 10\times 18}{900\times 12} = 11
Answer: D
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 21 years replaced by a new boy. The age of the new boy is?
A.14 years 8 months
B.15 years
C.16 years 4 months
D.17 years 8 months
Answer: D.17 years 8 months
Explanation: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 21 years - 3 years 4 months.
= 17 years 8 months.
ANSWER:D
Question: If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?
A.1 day
B.4 days
C.40 days
D.100 days
Answer: D.100 days
Explanation: as
100 cats kill 100 mice in 100 days
1 cats kill 1 mouse in 100 days
then
4 cats kill 4 mice in 100 days
ANSWER:D