RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A student chose a number, multiplied it by 4, then subtracted 138 from the result and got 102. What was the number he chose?
A.60
B.120
C.130
D.140
Answer: A.60
Explanation: Solution:
Let xx be the number he chose, then
4⋅x−138=102
4x=240
x=60
Answer A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.289 m
B.676 m
C.240 m
D.239 m
Answer: C.240 m
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m
= 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540
==> x
= 240 m.
Answer:C
Question: If a is a positive integer then 6^(2a) + (144^a)/(2^(2a)) =
A.2 × 36^a
B.2 / 36^a
C.3 × 36^a
D.2 × 64^a
Answer: A.2 × 36^a
Explanation: 6^(2a) + 144^a/ 2^(2a) = 36^a + 144^a/4^a = 36^a + (144/4)^a = 36^a + 36^a = 2 × 36^a
Answer : A
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
A.30/16
B.30/10
C.30/14
D.30/13
Answer: D.30/13
Explanation: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26 = 30/13 hours. Answer:D
Question: The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit?
A.750
B.800
C.850
D.860
Answer: A.750
Explanation: Let ‘x’ be the CP of the article;
Then 900 – x = 2(x – 450); :. x= 600.
25% of 600 = 150
:. New SP = 600 + 150 = 750
Option 'A'
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 480. The number of hares in the zoo is?
A.40
B.99
C.77
D.66
Answer: A.40
Explanation: 200*2 = 400
480
-----
80
1----2
?----80 = 40
Answer:A
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
A.Rs. 4991
B.Rs. 5991
C.Rs. 6001
D.Rs. 6991
Answer: A.Rs. 4991
Explanation: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer:A
Question: The probability of pulling a black ball out of a glass is 1/X. The probability of pulling a black ball out of a glass and breaking the glass is 1/Y. What is the probability of breaking the glass?
A.1/(XY).
B.Y/X
C.X/Y
D.1/(X+Y).
Answer: C.X/Y
Explanation: pulling a black ball out of a glass and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass = P(a) and Prob of breaking the glass= P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer should be C.
Question: A statue is being carved by a sculptor. The original piece of marble weighed 200 kg. In the first week 20 percent is cut away. In the second week 25 percent of the remainder is cut away. In the third week the statue is completed when 35 percent of the remainder is cut away. What is the weight of the final statue?
A.97.5 kg
B.103 kg
C.108 kg
D.125 kg
Answer: A.97.5 kg
Explanation: A
97.5 kg
250 Ã— 0.8 Ã— 0.75 Ã— 0.65 = 97.5 kg.
Question: A collection of books went on sale, and 2/3 of them were sold for $1.50 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
A.$180
B.$135
C.$108
D.$60
Answer: C.$108
Explanation: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($1.50) or $108. The best answer is therefore C.
Question: At what rate percent on simple interest will Rs.1800 amount to Rs.2000 in 5 years?
A.4 %
B.3 6/7 %
C.2 6/7 %
D.3.47%
Answer: D.3.47%
Explanation: Explanation:
250 = (1800x5xR)/100
R = 3.47%
Answer: Option D
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 25 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
A.36
B.2^4*3
C.24
D.38
Answer: C.24
Explanation: So 24 days
Answer C=24
Question: Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 14 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?
A.12
B.14
C.10
D.11
Answer: B.14
Explanation: Work done by AB in a day = xy respectively.
When A starts:
No. of days when A works = 8No. of days when B works = 6 → 8x + 6y = 1
When B starts:
No. of days when A works = 7No. of days when A works = 7 → 7x + 7y = 1
Solving the above two equations for xy
x = 1/14 y = 1/14
→ Total work done by AB in a day = 1/14 + 1/14 = 2/28= 1/14
→ No. of days to complete the work when both work together =14
Answer: B
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
A.70%
B.60%
C.30%
D.10%
Answer: C.30%
Explanation: Explanation:
Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer C
Question: If 0.12 ÷ x2 = 12, than x = ?
A.0.001
B.0.01
C.0.1
D.1
Answer: C.0.1
Explanation: Explanation:
0.12 ÷ x2 = 12 => 0.12/x2 = 12
=> x2 = 0.12/12 = 0.01
=> x = 0.1
Answer: Option C
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
A.14 days
B.21 days
C.22 days
D.11 days
Answer: D.11 days
Explanation: D
11 days
x/24 + x/30 + x/40 = 1
x = 11 days
Question: From 2008 to 2009, the number of Easter eggs in a certain egg hunt rose 20%, then fell 17% from 2009 to 2010. From 2008 to 2009, the ratio of Easter eggs to Easter bunnies in the same hunt fell 20%, then rose 22% from 2009 to 2010. By what approximate percent did the number of bunnies change over the full period from 2008 to 2010?
A.5% increase
B.2% increase
C.1% decrease
D.3% decrease
Answer: B.2% increase
Explanation: Let the number of Easter eggs be x1 in 2008 and x2 in 2010
Given that it rose 20% in 2009 and then fell 17% in 2010
=>x2 = (0.83)(1.2)x1 ---(1)
Let the number of Easter bunnies be y1 in 2008 and y2 in 2010
Given that the ratio of x to y fell 20% in 2009 and then rose 22% in 2010
=> x2/y2 = (0.8)(1.22)(x1/y1)
=> y1/y2 = (0.8)(1.22)(x1/x2) ----(2)
substituting (1) in (2),
y1/y2 = (0.8)(1.22)/(0.83)(1.2)
=> y2/y1 = (0.83)(1.2)/(0.8)(1.22) = 249/244
% change in y2 from y1 = (y2-y1)*100/y1
= (y2/y1 - 1)*100 = (249/244 - 1)*100
= (5/244)*100 = +2%
It's a 2% increase
Answer option "B"
Question: If Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
A.12x/y
B.12y/x
C.x/(12y)
D.13/(xy)
Answer: A.12x/y
Explanation: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.
Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.
We can find Juan’s rate as follows: Rate = Distance/Time = y yards/12 seconds
Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:
Time = Distance/Rate
Time = x yards/(y yards/12 seconds)
Time = (x yards) x (12 seconds/y yards)
Time = 12x/y seconds
Answer A.
Question: The area of a rectangular field is equal to 500 square meters. Its perimeter is equal to 90 meters. Find the width of this rectangle.
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: L * W = 500 : area , L is the length and W is the width.
2 L + 2 W = 90 : perimeter
L = 45 - w : solve for L
(45 - W) * W = 500 : substitute in the area equation
W = 20 and L = 25
correct answer D
Question: The sum of two numbers is 30 and their product is 1050. What will be the sum of their reciprocals?
A.(1/35)
B.(11/210)
C.(35/4)
D.(75/8)
Answer: A.(1/35)
Explanation: Solution
x+y=30 xy=1050 1/x+1/y=x+y/xy 30/1050 = (1/35).
Answer A
Question: Tough and Tricky questions: Remainders.
1^1 + 2^2 + 3^3 + ... + 10^10+11^11 is divided by 5. What is the remainder?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: a number is divisible by 5, if its last digit is divisible by 5
let's look into the sum of last digits of each term of the given expression
1^1=1
2^2=4
3^3=7
4^4=6
5^5=5
6^6=6
7^7=3
8^8=6
9^9=9
10^10=0
11^11=1
adding all these numbers we get 48 which gives a remainder of 3 when divided by 5. so answer must be 3.
bunuel, can you please confirm the answer of this question.
Yes, the OA is D. Clicked the wrong button when posting. Edited. Thank you.
D
Question: What is 35% of 4/13 of 780?
A.62
B.73
C.84
D.95
Answer: C.84
Explanation: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 780, or 1/9 of 780. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 780 is between 720 and 810, so (1/9)*780 will be between 80 and 90.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The closest answer is 84, so this is the answer to choose.
The answer is C.
Question: If a + b - c = 2d, and if a - b + c =-2e, then a =
A.2(d + e)
B.d – e
C.(d + e)/2
D.d-2e
Answer: B.d – e
Explanation: Add both equations:
a + b - c = 2d
a - b + c =-2e
a+b-c+a-b+c=2d-2e
2a=2d-2e
a=(d-e)
Ans:B
Question: Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.
A.4000
B.5000
C.6000
D.7000
Answer: C.6000
Explanation: Explanation :
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A:B:C =6 x : 4x : x
= 6 : 4 : 1
B's share = 16500 * (4/11) = 1500*4 = 6000. Answer : Option C
Question: A typist uses a sheet measuring 20cm by 30 cm lenghtwise. If a margin of 2 cm is left on each side and a 3 cm margin on the top and bottom, then what is the percentage of page used by the typist?
A.62 %
B.63 %
C.64 %
D.65 %
Answer: C.64 %
Explanation: Area of the sheet=(20*30)cm2= 600 cm2
Area used for typing=([20-4]*[30-6]) cm2 = 384 cm2
Therefore Required Percentage =(384/600)*100 = 64%
Answer C
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre
A.Rs680
B.Rs780
C.Rs880
D.Rs480
Answer: A.Rs680
Explanation: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*80
= 68000p
in Rs =68000/100=Rs680
ANSWER:A
Question: A semicircle has a radius of 12. What is the approximate perimeter of the semicircle?
A.58
B.62
C.66
D.70
Answer: B.62
Explanation: The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*12 + 2*12 which is about 62.
The answer is B.
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 600 resolutions.
A.843.03 m
B.844.03 m
C.845.03 m
D.846.03 m
Answer: B.844.03 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 600 resolutions.
= 600 * 2 * 22/7 * 22.4
= 84403 cm
= 844.03 m
Answer: B
Question: In a room filled with 7 people, 1 people have exactly 1 sibling in the room and 6 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
A.5/21
B.3/7
C.4/21
D.5/7
Answer: C.4/21
Explanation: There are suppose A B C D E F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 6 people who have exactly 2 siblings....(E has F and G as his/her sibling and so on..)
there are now 3 different set of siblings (A and B)
(C and D);(EFG)
Now first selecting 2 people out of 7 is 7C2=21
first sibling pair----(A and B)--selecting 2 people --2C2=1
second sibling pair (C and D)--selecting 2 people--2C2=1
third sibling pair (E F G)--selecting 2 out of 6 --6C2=15
total= 1+1+15=17
but,a/c to formula P(success)-1-p(fail)
here,p(failure)is selecting 2 people who are siblings
=17/21(21 is 7C2)
=1-17/21
=4/21
ANS C
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
A.158 m
B.150 m
C.110 m
D.130 m
Answer: B.150 m
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Question: Two pipes can fill a tank in 12 minutes and 15 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.20
B.22
C.24
D.26
Answer: A.20
Explanation: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/12 + V/15 - V/10 = 3V/60 = V/20 per minute
The tank will be filled in 20 minutes.
The answer is A.
Question: A bag holds 5 red marbles and 5 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?
A.1/6
B.2/5
C.3/10
D.2/9
Answer: D.2/9
Explanation: probability of selecting first red marble = 5/10
probability of selecting second red marble without replacement = 4/9
final probability = 5/10 * 4/9 = 2/9
The correct answer is D.
Question: If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?
A.100.2 miles
B.112.7 miles
C.120.5 miles
D.108.9 miles
Answer: D.108.9 miles
Explanation: We first convert the speed into miles per minute.
66 / 60 = 1.2 miles per minute
We now use the speed and the time to find the distance.
1.2 (miles/minute) * 99 minutes = 108.9 miles
correct answer D
Question: How many pieces of 85 cm length can be cut from a rod of 17 meters long?
A.50
B.40
C.30
D.20
Answer: D.20
Explanation: Number of pieces = 1700/85 = 20
The answer is D.
Question: The midpoints of three of the edges of a cube are
labelled A, B, and C as shown in the diagram. What
is the measure of L ABC ?
A.90o
B.105o
C.120o
D.135o
Answer: C.120o
Explanation: Let D be the point on the base of the cube such that CD is perpendicular to
the base. Let s be the length of the sides of the cube. Then AB = BC = AD =
p
2s/2.
Using the Pythagorean Theorem in 4ADC, we get AC =
p
3s/
p2. By the Law of
Cosines AC2 = AB2 +BC2 −2AB · BC · cos(\ABC). We get cos(\ABC) = −1/2, so
L ABC = 120o.
correct answer C
Question: If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 6?
A.2/3
B.3/8
C.1/2
D.5/8
Answer: A.2/3
Explanation: I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 6 = Integer, therefore we have 48 / 96 numbers divisible by 6
O E O / 6 = Not Integer
We cannot forget multiples of 6 from 1 to 96
We have 16 numbers that are multiple of 8
Therefore, 48/96 + 16/96 = 64/96 = 2/3
answer : A
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
A.720
B.740
C.770
D.780
Answer: A.720
Explanation: 720
Option 'A'
Question: A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:
A.50
B.90
C.80
D.28
Answer: C.80
Explanation: Let C.P. of clock be Rs. x.
Then, C.P. of 90 clocks = Rs. 90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
Answer: Option C
Question: There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that boys and girls sit alternately?
A.1/12!
B.12C6/12!
C.6!6!/12!
D.2∗6!6!/12!
Answer: D.2∗6!6!/12!
Explanation: Total number of ways in which 6 boys and 6 girls can sit in a row = 12!/6!∗6!
Number of ways in which 6 boys and 6 girls can sit alternately = 2 (BGBG..... or GBGB.....)
Probability = 2∗6!∗6!/12!
Answer: D
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
A.87 days
B.20 days
C.16 days
D.19 days
Answer: B.20 days
Explanation: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer:B
Question: A certain country had a total annual expenditure of $7.2 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
A. $ 500
B. $1,000
C. $2,000
D. $3,000
Answer: D. $3,000
Explanation: Total expenditure / Population = per capita expenditure
Hence, (7,2 x 10^11) / 240 000 000 = (7,2 x 10^11) / (2,4 x 10^8) = 3 x 10^(11-8) =
3 x 10^3 = 3000.
Answer is D.
Question: Two employees M and N are paid a total of $583 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
A.$245
B.$255
C.$265
D.$275
Answer: C.$265
Explanation: 1.2N + N = 583
2.2N = 583
N = 265
The answer is C.
Question: Product of two co-prime numbers is 117. Their L.C.M should be:
A.1
B.117
C.116
D.equal to their H.C.F
Answer: B.117
Explanation: H.C.F of co-prime numbers is 1.
So, L.C.M = 117/1 = 117.
ANSWER:B
Question: Brand A coffee costs twice as much as brand B coffee. If a certain blend is 1/2 brand A and 1/2 brand B. what fraction of the cost of the blend is Brand A?
A.a. 1/3
B.b. 2/5
C.3. 1/2
D.4. 2/3
Answer: D.4. 2/3
Explanation: Assume Cost of A= Ca = 200 , Cost of B = Cb=100
The blend contains 0.5 A and 0.55 B ---> Cost of the blend = Cbl = 0.5*200+0.5*100= 150
Thus fraction of A in the blend = 0.5*200/150 = 2/3.
Answer : D
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
=5
Answer:A
Question: Set A = {1, 2, 3, 4, 5, 6, d}
Which of the following possible values for d would cause Set A to have the smallest standard deviation?
A. 1
B. 2.5
C. 3
D. 3.5
Answer: D. 3.5
Explanation: I agree. The mean of the set d=1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.
Answer D.
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in?
A.18
B.12
C.11
D.19
Answer: A.18
Explanation: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/3
6/x = 1/3 => x = 18
So, B takes 9 hours to finish the work.
Answer: A
Question: Three friends Alice, Bond and Charlie divide $1105 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did Charlie receive?
A.$495
B.$510
C.$480
D.$375
Answer: A.$495
Explanation: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 10 : y - 20 : z -15 is 11a : 18a : 24a
When $10, $20 and $15 are removed, we are removing a total of $45 from $1105.
Therefore, 11a + 18a + 24a = 1105 - 45 = 1060
i.e., 53a = 1060
or a = 20.
We know that z - 15 = 24a = 24 * 20 = 480
Therefore, z = 480 + 15 = $495
correct choice is (A)
Question: A man is 30 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
A.28 years
B.22 years
C.23 years
D.24 years
Answer: A.28 years
Explanation: Explanation:
Let's Son age is x, then Father age is x+30.
=> 2(x+2) = (x+30+2)
=> 2x+4 = x+32
=> x = 28 years
Option A
Question: The average weight of A, B and C is 42 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.33 kg
B.31 kg
C.32 kg
D.40 kg
Answer: D.40 kg
Explanation: Let A, B, C represent their respective weights.
Then, we have: A + B + C = (42 x 3) = 126 .... (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 = 40.
B's weight = 40 kg.
D
Question: A and B can do a piece of work in 8 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
A.13 1/3
B.878
C.30
D.88
Answer: A.13 1/3
Explanation: C = 1/5 â€“ 1/8 = 3/40 => 40/3 = 13 1/3 days
Answer: A
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits Q of the larger integer?
A.Q=2
B.Q=5
C.Q=8
D.Q=10
Answer: A.Q=2
Explanation: Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).