RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The ages of Nishi and vinnee are in the ratio of 6: 5 respectively. After 9 yr the ratio of their ages will be 9: 8. What is the difference in their ages?
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: Answer:C
Question: Susan has four apples. How many ways can she eat one or more apples?
A.15
B.44
C.38
D.12
Answer: A.15
Explanation: Susan can eat one or more of four apples
= > 2 ^ 4 -1 = 15
A
Question: A completes a work in 8 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?
A.6 days
B.11 days
C.21 days
D.22 days
Answer: A.6 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 8 Ã— 24/ 32 = 6 days.
Option 'A'
Question: In a certain country ½ of 7 = 3. Assuming the same proportion, what would be the value of 1/3 of 21 ?
A.7
B.6
C.3
D.4
Answer: B.6
Explanation: B
6
Question: What is the difference between 62% of 150 nd 20% of 250.
A.16
B.17
C.43
D.19
Answer: C.43
Explanation: (62/100) * 150 â€“ (20/100) * 250
93 - 50 = 43
Answer: C
Question: For what values of k will the pair of equations 6x + 8y = 24 and kx + 12y = 30 does not have a unique solution?
A.12
B.9
C.3
D.7.5
Answer: B.9
Explanation: we have 2 equations
1. 6x + 8y = 24 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
Question: T and F represent two distinct digits. If the number 457T89F is divisible by 36, what is the value of (T+F)?
A.a) 9
B.b) 3
C.c) 12
D.d) 6
Answer: B.b) 3
Explanation: A no. divisible by 36 means it is div by 49 .
to be div by 4 last 2 digits to be multiple of 4 So, F could be either 2 or 6 only
similarly for a number to be div by 9 its sum must be multiple of 9 first. filtering we find T could be either 1,4,7 only.
To be divisible by 9 only 1 works .(if we choose f=6 then T have to be 6 but as per condition TF are distinct) So
T=1
F=2
Ans:- 3.B
Question: A man swims downstream 30 km and upstream 12 km taking 3 hours each time, what is the speed of the man in still water?
A.8
B.7
C.5
D.2
Answer: B.7
Explanation: 30 --- 3 DS = 10
? ---- 1
12 ---- 3 US = 4
? ---- 1 M = ?
M = (10 + 4)/2 = 7
Answer:B
Question: When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder?
A.11
B.13
C.15
D.Data inadequate
Answer: D.Data inadequate
Explanation: Number= (31 * Q)+ 29. Given data is inadequate.
Answer: D
Question: There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
A.14/19
B.14/18
C.14/11
D.14/13
Answer: A.14/19
Explanation: If rearrangement is not allowed, then actual probability of picking up a red ball = 12(10)+12(0)=1212(10)+12(0)=12
As we are allowed to move the balls, we keep only 1 red in the first box, and shirt the remaining 9 to the second.
So = 12×(1)+12×91/9=14/19
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. a-b is positive integer
II. ab is an even integer
III. (a+b+c)/2 is an integer
A.II only
B.I only
C.III only
D.II,III only
Answer: D.II,III only
Explanation: a<b, a-b is negative.
odd* even or even * even = even
1+2+3 =6/2=3 is an integer
Answer : D
Question: During the first two weeks of April, the total rainfall in Springdale was 30 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of April?
A.12
B.15
C.16
D.18
Answer: D.18
Explanation: Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.
2.5x = 30
x = 12
The rainfall during the second week was 1.5 * 12 = 18 inches
The answer is D.
Question: What is the maximum number of pieces of birthday cake of size 4” by 4” that can be cut from a cake 16” by 16”?
A.5
B.4
C.16
D.20
Answer: C.16
Explanation: The prompt is essentially asking for the maximum number of 4x 4 squares that can be cut from a larger 16 by 16 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 4 'pieces' each, we have (4)(4) = 16 total smaller squares (at maximum).
C
Question: At Atira's party there were five times as many females as males. There were three times as many adults as children. Which of the following could NOT be the number of people at the party?
A.384
B.258
C.216
D.120
Answer: B.258
Explanation: we have to work on the info and understand what that info takes us to...
1) there were five times as many females as males At Atira's party..
this means F=5M.. so total number=6M..
2) There were three times as many adults as children..
A=3C...
or total = 4C..
so the total is 4C or 6M..
since C and M have to be positive integers, we can say for sure that Total is a multiple of 4 and 6..
or Total is multiple of LCM of 4,6..
LCM of 4,6= 12..
lets see which number is not multiple of 12..
A. 384...12*32
B. 258... no
C. 216....12*18
D. 120....12*10
E. 72......12*6..
so B is our answer..
Question: A sum was put at simple interest at a certain rate for 4 years Had it been put at 2% higher rate, it would have fetched 56 more. Find the sum.
A.500
B.600
C.700
D.800
Answer: C.700
Explanation: Difference in S.I. = P×T/100(R1−R2)
⇒ 56 = P×4×2/100(∵ R1 - R2 = 2)
⇒ P = 56×100/4×2=700
Answer C
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.40 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
A.399
B.272
C.932.4
D.277
Answer: C.932.4
Explanation: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1.4 = 932.4 Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
A.12/459
B.12/489
C.12/455
D.12/454
Answer: C.12/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer: C
Question: There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?
A.1/n!
B.n/n!
C.1/n^y
D.1/n^(y-1)
Answer: D.1/n^(y-1)
Explanation: The simplest way to look at it is to assume that the first traveler picks a place. All the remaining travelers (given as y-1) now need to pick the same place for vacation.
As a result the probability is equivalent to (1/n) for each traveler to pick that same spot as the original traveler, which has to happen (y-1) times.
P=1n∗1n∗...∗1nP=1n∗1n∗...∗1n (y-1) times
P=1n(y−1)
The answer is D: 1/n^(y-1).
Question: 1/7 of 133 of 46% of 924 = ?
A.7075
B.8025
C.8075
D.9025
Answer: C.8075
Explanation: Explanation :
? = 1/7 x 133 x 46/100 x 924
= 8075.76 = 8075
Answer : Option C
Question: Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?
A.8 hours and 24minutes.
B.6 hours and 45 minutes.
C.3 hours and 60 minutes.
D.4 hours and 30 minutes.
Answer: D.4 hours and 30 minutes.
Explanation: The time it takes Kim to walk 18 kilometers is equal to
18 / 4 = 4.5 hours = 4 hours + 0.5 ? 60 minutes
= 4 hours and 30 minutes.
correct answer D
Question: In a bag there are a certain number of blue balls and white balls. The probability of picking up exactly 1 white ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of blue balls to white balls in the bag
A.1:1
B.1:2
C.1:5
D.1:4
Answer: A.1:1
Explanation: since the probability of drawing a white ball out of two picks is 1/2.
the ratio of the white ball to blue balls should be 1:1
Answer : A
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women?
A.T=18/35
B.16/35
C.14/35
D.13/35
Answer: A.T=18/35
Explanation: METHOD- 1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 16 minutes, how much time will she spend doing yoga? (rounded to minutes)
A.10 min.
B.41 min.
C.27 min.
D.23 min.
Answer: C.27 min.
Explanation: The ratio is 2:3 = gym:ride, so (16)(3/2) = 24 minutes at the gym, and 24 + 16 = 40 minutes exercise, so (2/3)(40) = 27 minutes yoga.
Answer: C
Question: The probability of two events A and B are0.25 and 0.40 respectively. The probability that both A and B occur is 0.20. The probability that neither A nor B occur is _________
A.0.45
B.0.4
C.0.55
D.0.05
Answer: C.0.55
Explanation: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.25+.40-.20
=.45
but the probability of neither A nor B=1-.45
=0.55
ANSWER:C
Question: A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 3/7, and the probability of selecting a blue paper clip is 1/7. What is the probability of selecting a silver paper clip?
A. 1/12
B. 1/2
C. 3/7
D. 3/4
Answer: C. 3/7
Explanation: Prob of Red = 3/7
Prob of Blue = 1/7
Prob of Silver = ?
P(Silver) = 1 - P(Red) - P(Blue) ==> 1-1/7-3/7 = 3/7
Ans: C
Question: The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?
A.3
B.1
C.0
D.19
Answer: C.0
Explanation: Average of 20 numbers = 0
Sum of 20 numbers / 20=0
=> Sum of 20 numbers = 0
Hence at the most, there can be 19 positive numbers.
(Such that if the sum of these 19 positive numbers is x, 20th number will be -X)
ANSWER:C
Question: Three sets of 90, 50 and 70 students appeared for an examination and the pass percentage was 50, 90 and 70 respectively. the pass percentage of the whole set is
A.69.19%
B.66.19%
C.66.29%
D.65.19%
Answer: B.66.19%
Explanation: Explanation:
total passed student =45+45+49=139
139 is 66.19% of210
ANSWER:B
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.2000
B.3377
C.2997
D.26790
Answer: A.2000
Explanation: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Question: Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 24624, how much amount per month would he have spent on clothes and transport?
A.4038
B.8076
C.2052
D.4845.6
Answer: C.2052
Explanation: ∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
∵ Amount, spent on clothes and transport
= 24624⁄12 = 2052
Answer C
Question: If 3 girls can do 3 times of a particular work in 3 days, then, 7 girls can do 7 times of that work in
A.3 days
B.4 days
C.5 days
D.7 days
Answer: A.3 days
Explanation: That is, 1 girl can do one time of the work in 3 days.
Therefore, 7 girls can do 7 times work in the same 3 days itself.
A)
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
A.40
B.80
C.120
D.200
Answer: A.40
Explanation: EXPLANATION
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Answer A
Question: For every $10 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
A.1 : 4 : 400
B.1 : 4 : 100
C.20 : 4 : 1
D.100 : 4 : 1
Answer: B.1 : 4 : 100
Explanation: B.........M........Y
10.....0,20......Y
B.........4........1
What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:
B.........M........Y
100.....2.........Y
B........40......10
Then I multiplied every row by 40 (the LCM of 2 and 40), which led me to this:
B.........M........Y
1000...40.......10
Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:4:100
ANS B
Question: A train running at the speed of 40 km/hr crosses a pole in 27 seconds. What is the length of the train?
A.250
B.300
C.350
D.400
Answer: B.300
Explanation: Speed=(40 * 5/18) m/sec = (100/9) m/sec Length of the train = (Speed x Time) = (100/9 *29 ) m
= 300 m.
Answer: B
Question: From a certain number of people who attended an interview, y people were selected. If instead, y+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of y if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?
A.6
B.10
C.5
D.2
Answer: D.2
Explanation: At least 2 interviews a day, so minimum 8 interviews in four days. Thus at least a total of 8 candidates should be there.
Let, total candidates = n
according to the question,
nCx = nC(y+2)
or, nCn-y = nCy+2 [nCr = nCn-r]
or, n-y = y+2
so, n = 2y+2
Remember total least number should be 8? So below 8 we can't expect anything.
Put y=2, then n=6 that is unacceptable.
so y is not equal to 2 .
Answer:D
Question: A set of numbers has the property that for any number x in the set, x+3 is also in the set. If -3 is in the set, which of the following must also be in the set
1. -6
2. 0
3. 6
A.1 only
B.2 only
C.1 and 2 only
D.2 and 3 only
Answer: D.2 and 3 only
Explanation: If X is in the set than X+ 3 is also in the set
If -3 in the set than
-3+3= 0 is also in the set
Since + 3 is Present, 3 + 3= 6 Is also present in the set .
Therefore Answer: D
Question: A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 5 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?
A. $198
B. $228
C. $220
D. $230
Answer: B. $228
Explanation: Wholesale cost of video recorder = 200 $
Video recorder was priced at 20 percent above 200 = 240 $
% discount given by store employee = 5
Emlpoyee paid = .95 * 240 = 228 $
Answer B
Question: Eight years ago, Ajay's age was 4/3 times that of Vijay. Eight years hence, Ajay's age will be 6/5 times that of Vijay. What is the present age of Ajay?
A.11
B.40
C.38
D.27
Answer: B.40
Explanation: Explanation:
Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.
A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)
3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8
V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8
=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8
=> 10 - 20/3 = 10/12 A - 9/12 A
=> 10/3 = A/12 => A = 40.
Answer: B
Question: A bus started its journey from Mumbai and reached Pune in 30 min with its average speed of 60 km/hr. If the average speed of the bus is increased by 10 km/hr, how much time will it take to cover the same distance?
A.28 min 30 sec
B.25 min 42 sec
C.25 min 40 sec
D.25 min 43 sec
Answer: B.25 min 42 sec
Explanation: Sol. Distance between Ramgarh and Devgarh =(60*30/60=30
Average speed of the bus is increased by 10 km/hr then the
speed of the bus = 70km/hr
Required time = 30*60/70= 25min 42sec
B
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?
A.8 kmph
B.10 kmph
C.12 kmph
D.14 kmph
Answer: C.12 kmph
Explanation: Let the distance travelled by x km.
Then,	x	-	x	= 2
10	15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60	hrs	= 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60	kmph.	= 12 kmph.
5
C
Question: John has a certain number of marbles in his pocket. He is able to divide his marbles equally to five of his friend but while trying to divide that same amount of marbles to seven of his other friend he found out that some marbles are left out. What could be the number of marbles that John have?
A.70
B.21
C.50
D.35
Answer: C.50
Explanation: since John was able to divide his marble equally to 5 of his friend but not to 7 of his friend so the total marbles that he has should be divisible by 5 but not by 7.
75, 35 and 105 are all divisible by 5 and 7--- ruled out
we are now left with 21 and 50, here 21 is again divisible by 7-- wrong again.
The answer has to be 50. [ divisible by 5 but not by 7 ]
answer: (C)
Question: What is the perimeter, in meters, of a rectangular garden 8 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
A.48
B.56
C.64
D.76
Answer: C.64
Explanation: Say Length of garden is L meters.
Then (L*8) = 16 * 12 [Given area is same. Area= L * B]
Therefore L works out to 24 meters.
Perimeter of Garden = 2* (24+8) = 64 meter.
Answer is C
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 40, the dividend is?
A.3320
B.4040
C.4330
D.4334
Answer: B.4040
Explanation: Divisor = (5 * 40) = 200
= 10 * Quotient = Divisor
=> Quotient = 200/10 = 20
Dividend = (Divisor * Quotient) + Remainder
Dividend = (200 * 20) + 40 = 4040
B
Question: A can do a piece of work in 15 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
A.15
B.10
C.12
D.11
Answer: C.12
Explanation: 2/15 + 4/15 + x/20 = 1
x = 12 Answer: C
Question: If |5x−6|=|x+20|, which of the following could be a value of x?
A.6
B.-7/3
C.−13/3
D.-6
Answer: D.-6
Explanation: 5x - 6 = -x + 20 or 5x - 6 = x - 20
6x = 26 or 4x = -24
x = 13/3 or x = -6
Answer: D
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be
A.12 years
B.20 years
C.25 years
D.28 years
Answer: B.20 years
Explanation: Solution
Let the present ages of son and father be x and (60 - x) years respectively.
Then,	(60 - x) - 6 = 5(x - 6)
= 54 - x = 5x - 30
‹=›6x = 84
‹=›x= 14.
∴Son's age after 6 years = (x + 6) = 20 years.
Answer B
Question: If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it?
A.8
B.24
C.32
D.56
Answer: C.32
Explanation: let AABBCCDD is the group with same letter representing a sibling pair.
total # ways to select 3 from 8 is 8C3=56
Qtn: committee of 3 NOT having siblings in it = Total (56) - committee of 3 with siblings in it
committee of 3 with siblings = select 2As and one from rem. 6. This can be done in 4 ways as 4 different letters A,B,C and D
= 4 * (2C2*6C1) = 24
Hence Answer = 56-24 = 32
ANS:C
Question: A rower can row 7 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
A.3.19
B.3.28
C.3.35
D.3.43
Answer: D.3.43
Explanation: Let x be the distance to Big Rock.
time = x/6 + x/8 = 1
x = 48/14 = 3.43 km
The answer is D.
Question: What is the 6th digit to the right of the decimal point in the decimal equivalent of 16/45?
A.5
B.12
C.2
D.35
Answer: A.5
Explanation: 16/45 = 0.3555....
35 is non-terminating repeating decimal.
The 22nd digit to the right of decimal point will be 5.
Answer A
Question: Meera purchased two three items from a shop. Total price for three items is Rs.8200/- She have given Rs. 10000/- What is the balance amount meera got?
A.1800
B.1200
C.1650
D.800
Answer: A.1800
Explanation: Total cost of Items : 8200/-
amount Paid : 10000/-
Balance receivable : 10000- 8200 = 1800/-
Answer is A
Question: When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number?
A.228
B.103
C.286
D.122
Answer: B.103
Explanation: Explanation:
Let the number be x
x2 - 732 = 5280
x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609
= 10000 + 2(100)(3) + 32 = (100 + 3)2
x = 100 + 3 = 103.
Answer: B
Question: Sunil invested $ 2600 fir 3 years and $ 1200 for 5 years at the same rate of Simple Interest. If the total interest from these investments is $ 930, what is the rate of interest?
A.2 3/4%
B.5 1/3%
C.5 1/2%
D.6 3/4%
Answer: D.6 3/4%
Explanation: (2600x3xR)/100+(1200x5xR)/100=930
138R=930
R= 6 3/4%
Answer is D
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 10 cans so that at least one red and at least one blue cans to remain the refrigerator.
A.460
B.490
C.493
D.35
Answer: D.35
Explanation: Ways to pick 2 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 2 can out of 12 - ways to pick 2 red out of 7 red - ways to pick 2 blue out of 5 blue
12C2âˆ’7C2âˆ’5C2=66âˆ’21âˆ’10=35
ANSWER:D
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
A.3 years
B.4 years
C.6 years
D.7 years
Answer: B.4 years
Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
B)
Question: When divided by 5, x has a remainder of 3 and y has a remainder of 1. Which of the following could be the remainder when x + y is divided by 10?
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: x = 5k+3 and y = 5j+1
x+y = 5(j+k) + 4
When divided by 10, the remainder is either 4 or 9.
The answer is D.
Question: If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 5), what is the value of x?
A.7
B.11
C.13
D.15
Answer: A.7
Explanation: (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 5)
2^x - 2^(x-2) = 3. 2^5
Hence x = 7.
Answer is A
Question: How many words can be formed by using all letters of the word “QUADRIC”
A.1200
B.5040
C.4050
D.3440
Answer: B.5040
Explanation: The word QUADRIC contains 7 different letters.
Required number of words = 7p7 = 7! = (7x6x5x4x3x2x1) = 5040
Answer B.
Question: Venus travels around the sun at a speed of approximately 21.9 miles per second. The approximate speed is how many miles per hour?
A.64,420
B.78,840
C.83,160
D.88,970
Answer: B.78,840
Explanation: 21.9 * 3600 = 78,840
The answer is B.
Question: What is the ratio of 3/7 to the product 2*(7/3)?
A.3:7
B.9:98
C.3:21
D.1:7
Answer: B.9:98
Explanation: 3/7 / 14/3 = 9/98...
IMO option B.