RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If -1 < h < 1, which of the following has the greatest value?
A.a) 1-h
B.b) 1+h
C.c) 1+h^2
D.d) 1-1/h
Answer: C.c) 1+h^2
Explanation: easiest way of solving this would be to substitute a value.
lets say h= - 1/2
a) 3/2
b) 1/2
c) 5/4
d) 3
e) - 3
the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.
Answer is C.
Question: The H.C.F. and L.C.M. of two numbers are 11 and 5040 respectively If one of the numbers is 144, find the other number
A.400
B.256
C.385
D.420
Answer: C.385
Explanation: Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 11 * 5040
x = (11*5040)/144 = 385
Option C
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
A.17 cm2
B.30 cm2
C.18 cm2
D.19 cm2
Answer: B.30 cm2
Explanation: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle
= 6 * 5
= 30 cm2
Answer: B
Question: A candidate got 40% of the votes polled and he lost to his rival by 2000 votes. How many votes were cast?
A.10000
B.2028
C.2775
D.5496
Answer: A.10000
Explanation: 40%-----------L
60%-----------W
------------------
20%----------2000
100%---------? => 10000
Answer:A
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
A.Rs.16537.76
B.Rs.16537.98
C.Rs.16537.50
D.Rs.16537.56
Answer: C.Rs.16537.50
Explanation: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20)
= Rs.16537.50
Answer: C
Question: How many seconds will a 900 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
A.48
B.36
C.54
D.11
Answer: C.54
Explanation: Explanation:
Here distance d = 900 mts
speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s
time t = = 54 sec.
Answer: C
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 400 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
A.240
B.246
C.252
D.292
Answer: D.292
Explanation: Number of newborns that can die in first month = 1/10 * 400 = 40
Survived = 360
Number of newborns that can die in second month = 1/10 * 360 = 36
Survived = 324
Number of newborns that can die in third month = 1/10 * 324 = 32
Survived = 292
Answer:D
Question: Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^5
A.26
B.32
C.25
D.27
Answer: B.32
Explanation: (4)^11x (7)^5 x (11)^5
= (2 x 2)^11 x (7)^5 x (11)^5
= 2^11 x 2^11 x7^5x 11^5
= 2^22 x 7^5 x11^5
Total number of prime factors = (22 + 5 + 5) = 32.
Answer is 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.1232?
A.1000
B.2217
C.1100
D.2777
Answer: C.1100
Explanation: 1232 = P [1 + (5*12/5)/100]
P= 1100
Answer: C
Question: The average of 11 numbers is 10.5. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
A.9
B.9.2
C.10
D.15.9
Answer: D.15.9
Explanation: Explanation:
1 to 11 = 11 * 10.5 = 115.5
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 115.5 = 15.9
6th number = 15.9
D)
Question: The length of a rectangle is twice the breadth. If the area is 128 cm2, determine the length and the breadth.
A.b=2,l=9
B.b=8,l=16
C.b=9,l=9
D.b=4,l=14
Answer: B.b=8,l=16
Explanation: We are given length l=2b and l×b=128
∴2b×b=128
2b^2=128
b^2=64
b=±8
But breadth must be positive, therefore b=8 cm, and l=2b=16 cm.
Answer is B.
Question: A train 125 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.49
B.50
C.12
D.13
Answer: B.50
Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: Option B
Question: The length of the bridge, which a train 140 m long and traveling at 45 km/hr can cross in 30 sec is?
A.235
B.240
C.245
D.250
Answer: A.235
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (140 + x)/30 = 25/2
x = 235 m.
Answer: Option A
Question: A painting at an art gallery is framed such that the area of the square frame is 1/5 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 6, what is the area of the painting inside the frame?
A.10
B.15
C.30
D.40
Answer: B.15
Explanation: Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b
Area of painting = a^2 and we know that the area of the frame is (1/5) of that of the painting so
Area of frame = (1/5) * a^2
Area of Frame + Painting = a^2 + (1/5)*a^2 = (6/5)*a^2 which is equal to b^2
Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2
so, b * sqrt2 = 6
so, b = 3 * sqrt2
b^2 = 18
we know that b^2 = (6/5)*a^2
so, a^2 = (5/6)*b^2 = (5/6)*18 = 15
And area of painting = a^2 = 40
So, answer will be B.
Question: 0.41 + 21.4 + 6.3 + 280=?
A.708.71
B.408.71
C.508.71
D.308.71
Answer: D.308.71
Explanation: Add 280.00+
21.40+
6.30+
0.41=
308.71
correct answer D
Question: How many different ways can you select a pilot and a co pilot if you have 80 people to choose from?
A. 199
B. 200
C. 398
D. 6320
Answer: D. 6320
Explanation: You are not just choosing two from 80. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (80C2) x 2 = 6320.
Ans D
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
A.422
B.476
C.429
D.428
Answer: B.476
Explanation: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x '
= 476
Answer:B
Question: There are 4 copies of 5 different scales. In how many ways can they be arranged on a shelf?
A.20!/4!
B.20!/5(4!)
C.20!/(4!)^5
D.20!
Answer: C.20!/(4!)^5
Explanation: There are 4 copies of 5 different scales.20!/((4!)^5)
Answer - C
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.5%
B.28%
C.27%
D.40%
Answer: A.5%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 70
2/3 SP1 = 70
SP1 = 105
100 --- 5 => 5%
Answer:A
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
A.12
B.19
C.60
D.180
Answer: D.180
Explanation: 5C3 * 4C2 * 3C2 = 10*6*3 = 180.
Answer: D
Question: Look at this series: 40, 44, 48, __, 52, 56, 40, 60, ... What number should fill the blank?
A.60
B.50
C.40
D.46
Answer: C.40
Explanation: C
40
In this series, 4 is added to the previous number; the number 40 is inserted as every third number.
Question: A shopkeeper sold an article for 360 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’?
A.25%
B.30%
C.23%
D.50%
Answer: D.50%
Explanation: Cost price = 360×100/120= 300
S.P. at no discount = 360×100/80 = 450
∴ % profit = 150×100/300 = 50 %
Answer D
Question: A sum of Rs.4000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
A.2888
B.3120
C.2877
D.2600
Answer: D.2600
Explanation: Let A be the amount received at the end of the three years.
A = 4000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.6600
So the interest = 6600 - 4000 = Rs.2600
Answer: D
Question: The difference between two angles of a triangle is 24o. The average of the same two angles is 54o. Which one of the following is the value of the greatest angle of the triangle
A.45o
B.45o
C.66o
D.72o
Answer: D.72o
Explanation: Solution:
Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24o.
=> a – b = 24.
Since the average of the two angles is 54o, we have (a+b)/2 =54.
Solving for b in the first equation yields b=a–24, and substituting this into the second equation yields,
[{a+(a−24)}/2] =54
2a−24 = 54*2
2a−24 = 108
2a = 108 +24
2a =132
a =66
Also,
b=a−24=66−24=42.
Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is
180o, a+b+c =180.
Putting the previous results into the equation yields 66+42+c =180.
Solving for c yields c =72
Hence, the greatest of the three angles a, b and c is c, which equ
Answer: Option D
Question: The ratio of red boxes to blue boxes in a certain warehouse is 20 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
A.37
B.74
C.111
D.90
Answer: D.90
Explanation: Ratio = R/B = 20/25 or R = 20/25 B -----------(1)
2R/B+150 = 20/25*1/2 = 2/5 or we can say that 10R=2B+300 -------------(2)
solving (1) and (2) we get
B=50 and R = 40
so total boxes is B + R = 50+40=90
Hence D. 90 is the correct answer
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
A.Sunday
B.Saturday
C.Friday
D.Wednesday
Answer: C.Friday
Explanation: On 31st December, 2005 it was Saturday.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
Answeer:C
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost Q for a course at the gym's highest level?
A.$175
B.$245
C.$425
D.$675
Answer: A.$175
Explanation: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost Q of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Question: One fourth of one third of two fifth of a number is 25. What will be40% of that number
A.140
B.300
C.180
D.200
Answer: B.300
Explanation: Explanation:
(1/4) * (1/3) * (2/5) * x = 25 then x = 25 * 30 = 750
40% of 250 = 300
Answer: Option B
Question: The banker’s gain on a certain sum due 1½ years hence is 3/25 of the banker’s discount. The rate percent is :
A.3 1/3 %
B.6 1/6 %
C.9 1/9 %
D.9 1/6 %
Answer: C.9 1/9 %
Explanation: Sol.
Let B.D. = Re 1. Then, B.G. = Re 3/25.
∴ T.D. = (B.D. - B.G.) = Re[1 - 3/25] = Re 22/25.
Sum = [1 * 22/25 / 1 - 22/25] = Rs. 22/3.
S.I. on Rs. 22/3 for 1 ½ years is Re 1.
∴ Rate = [100 * 1 / 22/3 * 3/2] % = 9 9/1%.
Answer C
Question: Solution Y is 30 percent liquid O and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid O?
A.30%
B.33 1/3%
C.37 1/2%
D.40%
Answer: C.37 1/2%
Explanation: Answer:C
Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid O and 70% water, and then I was able to get the answer. That was a bit tricky and nice question=C
Question: Find the compound interest on $20000 in 2years at 4% per annum, the interest being compounded half-yearly?
A.$645.56
B.$1648.64
C.$954.26
D.$745.69
Answer: B.$1648.64
Explanation: Principle = $20000
Rate = 2% half yearly = 4 half years
Amount = 20000*(1 + 2/100)^4 = 20000 * 51/50 * 51/50 * 51/50 * 51/50
= $21648.64
C.I. = 21648.64-20000 = $1648.64
Answer is B
Question: Riya and Priya set on a journey. Riya moves eastward at a speed of 18kmph and Priya moves westward at a speed of 24 kmph.How far will be priya from Riya after 15 minutes
A.25kms
B.11kms
C.50kms
D.30kms
Answer: B.11kms
Explanation: total eastward distance= 18kmph*1/4hr=4.5 km
total westward distance= 24kmph*1/4hr=6 km
total distn betn them= 4.5+6=10.5m
ans 11km
ANSWER:B
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
A.16%
B.16.66%
C.22%
D.24%
Answer: B.16.66%
Explanation: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Question: Given a Number 123456, from this number put any three values in numerator and remaining three are in denominator. So how many values you can make from this number less than 1/5.
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: 123/645 ,123/654 ,124/635 ,124/653
,125/634 ,125/643 ,
ans is 6.
ANSWER:C
Question: In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
A.20 m
B.25 m
C.22 m
D.9 m
Answer: C.22 m
Explanation: Distance covered by B in 9 sec. =	110/45 x 9	m = 22 m.
A beats B by 20 metres.
Answer: Option C
Question: 4, 12, 48, 240, (...)
A.1440
B.10080
C.6200
D.10020
Answer: A.1440
Explanation: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6,
Answer : Option A
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
A.8279
B.2890
C.2800
D.2730
Answer: C.2800
Explanation: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Answer: C
Question: What number should be added to each of the numbers 8, 21, 13 and 31 so that the resulting numbers, in this order form a proportion?
A.2
B.3
C.5
D.7
Answer: C.5
Explanation: Explanation :
(8+x)/(21+x) = (13+x)/(31+x)
Then, (8 + x)(31 + x) = (13 + x)(21 + x)
or39x + 248 = 34x + 273 or 5x=25 or x = 5.
Answer : C
Question: In a contest, a bowl contains 7 keys, one of which will open a treasure chest and Six of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Sita is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
A.1/8
B.1/9
C.2/7
D.3/19
Answer: C.2/7
Explanation: The total possibilities existing while withdrawing two keys are: 7C2 = 21
For Sita to win, 6 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,6)
P = 6/21= 2/7
Option C
Question: How many ways can six friends be arranged around a circular dinner table?
A.16
B.48
C.96
D.120
Answer: D.120
Explanation: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (6 - 1)! = 5! = 120.
Answer: D.
Question: On planet Jupiter the people use a certain number system to the base ‘n’ (n > 2), Jerk, a resident of the planet, one day received twice his daily wage because the digits of this wage, which was a 2 digit number, were reversed. If the value of ‘n’ is the least possible value there the decimal representation of the difference between Jerk’s correct wage for the day is
A.8
B.9
C.10
D.11
Answer: A.8
Explanation: Sol:
Let the base of the number system be n and the two digit number be ab
given 2(ab)n = (ba)n
⇒⇒ nb + a = 2na + 2b
⇒⇒ a(2n - 1) = b(n - 2)
⇒a/b= n−2 /2n−1
Now the maximum possible value of a or b is (n - 1) (base n) for n = 3 we get
a/b=1/5 which is not possible as in base 3, 5 won't exist.
Similarly, for n = 4
but for n = 5
We get a/b=3/9 i.e.1/3
a = 1, b = 3 is the only number possible when n is the least possible.
The correct wage = (13)5=(8)10
The actual wage paid = (31)5=(16)10
So difference = 8
Answer A
Question: A man bought 40 shares of Rs. 60 at 6 discount, the rate of dividend being 12 1/2%The rate of interest obtained is
A.13.89%
B.15.5%
C.14%
D.14.25%
Answer: A.13.89%
Explanation: Explanation :
Face Value of a share = Rs.60
He bought each share at Rs.60 - Rs.6 = Rs.54
Number of shares = 40
Dividend = 12 1/2%=25/2%
Dividend per share = 60×25/2×100=Rs.7.5
Total dividend = (40 × 7.5)
ie, He got a dividend of (40 × 7.5) for an investment of Rs.(40 × 54)
Interest obtained = 40×7.5×100/40×54=13.89%
Answer : Option A
Question: The average age 12 monkeys in a tree is 16 years. Out of these, the average age of 6 monkeys is 18 years and that of the other 6 monkeys is 13 years. The age of the 12th monkey is?
A.10
B.9
C.4
D.6
Answer: D.6
Explanation: Age of the 12th monkey= 12*16 - (6*18+6*13) = 192-186= 6 years
Answer is D
Question: In the following number sequence how many such even numbers are there which are exactly divisible by its immediate preceding number but not exactly divisible by its immediate following number?
3 8 4 1 5 7 2 8 3 4 8 9 3 9 4 2 1 5 8 2
A.Two
B.Three
C.Four
D.More than four
Answer: B.Three
Explanation: correct answer is a
283,489
ANSWER:B
Question: If (68-a)(68-b)(68-c)(68-d)(68-e)=725
then a+b+c+d=?
A.231
B.231
C.233
D.234
Answer: B.231
Explanation: we will first break 725 in prime factor=(5*5*29*1*1) a/c to whatever factors is here
then we we will compare like
(68-63)(68-63)(68-39)(68-67)(68-67)i.e.5*5*29*1*1
a=63
b=63
c=39
d=67
and now sum is =a+ b+ c+ d=232
ANSWER:B
Question: What should come in place of question mark(?) in the following equation?
8597 – ? = 7429 – 4358
A.5706
B.5526
C.5426
D.5626
Answer: B.5526
Explanation: 8597 – ? = 7429 – 4358
∴ ? = 5526
Answer B
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability E that the integer drawn is divisible by 8?
* A solution will be posted in two days.
A.1/6
B.1/3
C.1/2
D.2/3
Answer: D.2/3
Explanation: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,E= two out of three can be divided and the answer is D.
Question: Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for s dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?
A.x/(y - s)
B.x/(s - y)
C.x
D.x/s
Answer: B.x/(s - y)
Explanation: Two ways...
1) let t be the total number, so cost = t*y+x and selling price=t*s..
No profit no loss....t*y+x=t*s.....T=x/(s-y)...
B
Question: 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
A.16 vans
B.26 vans
C.12 vans
D.17 vans
Answer: A.16 vans
Explanation: To find the number of vans, we divide 123 by 8.
123 / 8 = 15 and remainder = 3
So 15 vans are needed to transport 15 x 8 = 120 girls, and 1 van is needed to transport the 3 remaining girls. A total of 16 vans are needed.
correct answer A
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12500 after a year?
A.3630
B.2881
C.2887
D.3750
Answer: D.3750
Explanation: 6300:4200:10500
3:2:5
3/10 * 12100 = 3750.Answer: D
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
A.971
B.973
C.268
D.646
Answer: D.646
Explanation: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Question: The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
A.6535
B.6532
C.6725
D.6874
Answer: C.6725
Explanation: C
6725
CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725
Question: A discount of 10 percent on an order of goods followed by a discount of 40 percent amounts to
A.the same as one 46 percent discount
B.the same as one 40 percent discount
C.the same as one 36 percent discount
D.the same as one 30 percent discount
Answer: A.the same as one 46 percent discount
Explanation: 0.9*0.6*x=0.54x from initial value, meaning 0.46 or 46% discount
A
Question: A foreign language club at Washington Middle School consists of n students, 3/5 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German?
A.2n/5
B.n/3
C.4n/75
D.2n/15
Answer: C.4n/75
Explanation: 3/5 of the students are boys, thus 2/5 of the students are girls.
1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French.
Thus 1/5 of 2/3 = 2/15 of the girls study German.
Since girls comprise 2/5 of the students, then 2/5*2/15=4/75 are girls who study German.
The answer is C.
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 7, or 8. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
A.1/625
B.2/625
C.50/625
D.75/625
Answer: C.50/625
Explanation: I think most of the answers are missing a point. Let me try to put it across:
Total number of possible numbers are : 5x5 = 25
Correct number =1
Case 1: When he gets it right in first attempt: P(E1) = 1/25
Case 2: He gets 1st attempt wrong and second right:
When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24
Thus, P(E2) = 24/25 x 1/24
=1/25
Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (C) is therefore right as most of you mentioned but the method employed was wrong.
Question: The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?
A.X.
B.X/2.
C.2X/3
D.X/3
Answer: A.X.
Explanation: Given the value of stock is X dollars.
Then on Sunday the stock's value is increased by half i.e. X + X/2 = 3X/2 ( this is the new value)
Then on Monday its value dropped by 1/3 of new value = 1/3(3X/2) = 3X/6
Then 3X/2 - 3X/6 = 6X/6 = 6. (new value - 1/3 value)
Ans: A is correct option..
Question: Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?
A.35.5mph
B.37.5mph
C.38.5mph
D.39.5mph
Answer: B.37.5mph
Explanation: 3 hours of his journey at 60 mph means 180 miles in 3 hours
5 hours at 24 mph speed means 120 miles in 5 hours. In total 300 miles in 8 hours.
Average Speed is ((3*60)+(5*24))/8 = 37.5mph
ANSWER:B