RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: At the end of the month, a certain ocean desalination plant’s reservoir contained 30 million gallons of water. This amount is twice the normal level. If this amount represents 75% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?
A.10
B.15
C.20
D.25
Answer: C.20
Explanation: the Q talks of total capacity, normal level, present level, shortage etc..
so it is all about not going wrong in these terms
30 MG= 75% of Total..
total = 30/.75=40MG..
Normal level= 1/2 of 40=20MG..
shortage of normal level=40-20=20MG..
C
Question: The number 42 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A.17
B.10
C.15
D.14
Answer: B.10
Explanation: I think brute force with some common sense should be used to solve this problem.
Write down all perfect squares less than 42: 1, 4, 9, 16, 25, 36.
Now, 42 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 42 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).
We can find that 42 equals to 1+16+25=1^2+4^2+5^2=42 --> 1+5+4=10.
Answer: B.
Question: In one hour, a boat goes 15 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
A.12 kmph
B.13 kmph
C.14 kmph
D.15 kmph
Answer: A.12 kmph
Explanation: Explanation:
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Speed in still water = 1/2(15+9) kmph = 12 kmph.
Answer: Option A
Question: Nitrous oxide (laughing gas) worth Rs 126 per kg and Rs 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 153 per kg, then the price of the third variety per kg will be
A.Rs 169.50
B.Rs 170
C.Rs 175.50
D.Rs 180
Answer: C.Rs 175.50
Explanation: Suppose the quantities of Nitrous oxide worth Rs 126 per kg, Rs 135 per kg and Rs.x per kg purchased are Y, Y and 2Y kg respectively:
(126 Y +135 Y + 2XY )/ 4Y = 153
=> 261 + 2X = 612
=> X= 351/2 = 175.50
Nitrous oxide of the third varity is purchased at the rate of Rs 175.50 per Kg
ANSWER:C
Question: Walking at 25% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
A.8
B.16
C.42
D.48
Answer: A.8
Explanation: speed is inversly proprtional to time
walking at 25% of speed meand 1/4s takes 4t.
It takes 24 minutes extra to cover the distance. then
4t=t+24
3t=24
t=8.
Option A is correct
Question: What is the least integer greater than –4+0.5?
A.–3
B.–1
C.0
D.1
Answer: A.–3
Explanation: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.
First, let's take care of the Arithmetic:
(-4) + (0.5) = -3.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -4 to -3.5).
Next, the question asks for the LEAST integer that is GREATER than -3.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -3.5 is -3.
Final Answer:
A
Question: A train passes a station platform in 28 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.270
B.277
C.240
D.88
Answer: A.270
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 10) m = 150 m.
Let the length of the platform be x meters.
Then, x + 150 / 28 = 15
x + 150 = 420
x = 270 m.
Answer:A
Question: If x and y are negative integers, which of the following statements must be true?
I. (-x)^y is positive.
II. (-x)^(-y) is positive.
III. x^(-y) is positive.
A.None
B.II only
C.I and II
D.I and III
Answer: C.I and II
Explanation: Let's x = -2 and y = -3
I. (-x)^y = (2)^(-3) = 1/(2^3) --> Positive
II. (-x)^(-y) is positive. = 2^3 --> Positive
III. x^(-y) is positive. = -2^3 --> Negative
Answer: C
Question: The average of first 10 odd numbers is?
A.11
B.10
C.18
D.12
Answer: B.10
Explanation: Explanation:
Sum of 10 odd no. = 100
Average = 100/10 = 10
Answer:B
Question: If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
A.27
B.29
C.26
D.40
Answer: D.40
Explanation: 8 = (1*20*R)/100
R = 40%.Answer: D
Question: David completes a piece of work in 5 days, John completes the same work in 9 days. If both of them work together, then the number of days required to complete the work is?
A.3.2 days
B.8 days
C.10 days
D.12 days
Answer: A.3.2 days
Explanation: IfA 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.
That is, the required No. of days = 5 × 9/14= 3.2 days
Answer : A
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
A.4:5
B.9:1
C.2:5
D.3:4
Answer: B.9:1
Explanation: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
ANSWER B
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
A.105
B.120
C.140
D.147
Answer: A.105
Explanation: Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 49t
or 5t+6=7t
or t=3
Distance travelled by car X from the time car Y began traveling until both cars stopped is
35 x 3
= 105 miles
Answer:- A
Question: The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m
A.73889
B.27788
C.73879
D.73800
Answer: D.73800
Explanation: Explanation:
perimeter = total cost / cost per m = 10080 /20 = 504m
side of the square = 504/4 = 126m
breadth of the pavement = 3m
side of inner square = 126 - 6 = 120m
area of the pavement = (126 x126) - (120 x 120) = 246 x 6 sq m
cost of pavement = 246*6*50 = Rs. 73800
Answer: D)
Question: If n is an odd integer, which of the following must also be an odd integer?
A.2n
B.2n^2
C.n^2 + 2n
D.n^2 + 3n
Answer: C.n^2 + 2n
Explanation: (A)	2n = even*odd = even.
(B)	2n^2 = even*odd = even.
(C)	n^2 + 2n = odd + even*odd = odd + even = odd.
(D)	n^2 + 3n = odd + odd*odd = odd + odd = even.
(E)	n^2 + 2n + 3 = odd +even + odd = even.
Answer: C.
Question: An oratorical society consists of six members, and at an upcoming meeting, the members will present a total of four speeches. If no member presents more than two of the four speeches, in how many different orders could the members give speeches?
A.720
B.1080
C.1170
D.1470
Answer: A.720
Explanation: You need to remember that of the 3 people, 1 is going twice and two are going once. Since one of the 3 is going once, there are 3C1 possibilities for the double speaker.
So, to convert your work to the correct answer, you need to multiply:
240 * 3C1 = 240 * 3 = 720. ANS:A
Question: Andrew investe 12 percent of his March earnings. In April he earned 20 percent more than he did in March, and he invested 9 percent of his April earnings. The amount he invested in April was what percent of the amount he invested in March?
A.80%
B.90%
C.100%
D.110%
Answer: B.90%
Explanation: Let Andrew's March earnings be 100 --> Amount invested = 12% of 100 = 12
Andrews April earning = 1.2 * 100 = 120 --> Amount invested = 9% of 120 = 10.8
Amount invested in April = (10.8/12)*100 = (108/120)*100 = 90% of the amount invested in March
Answer: B
Question: Kelly has had 3 pay cuts in her salary in the past 6 months. If the first pay cut was 8%, the second pay cut was 14% and the third was 18%. What will be the percentage decrease, if the salary is decreased in a single shot?
A.35.9%
B.34.12%
C.32.12%
D.35.12%
Answer: D.35.12%
Explanation: Let Rs.100 be initial salary.
Salary After 1st decrease, 8% = 92
Salary After 2nd decrease, 14% = 79.12 i.e. reduced by 14 percent of 92
Salary After 3rd decrease, 18% = 64.88 i.e. reduced by 18 percent of 79.12
So if its decreased in single shot =
i = ( ( b - a ) /b ) * 100
=35.12%
ANSWER:D
Question: An amount of money is to be distributed among P, Q and R in the ratio of 5 : 8 : 12 respectively. If the total share of Q and R is four times that of P, what is definitely P’s share?
A.3,000
B.5,000
C.8,000
D.Data inadequate
Answer: D.Data inadequate
Explanation: P : Q : R = 5 : 8 : 12
Total share of QandR/Share of P=8+12/5=20/5=4
So, we see that no new information has been given in the question and P’s share can’t be determined.
Answer D
Question: Find the 12th term of an arithmetic progression whose first term is 2 and the common difference is 8.
A.45
B.38
C.44
D.90
Answer: D.90
Explanation: n th term of A.P = a +(n-1) *d
= 2+(12-1)*8 , = 2 + 88 = 90.
ANSWER:D
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 2 cm when a man gets on it. The mass of man is
A.12 kg
B.60 kg
C.72 kg
D.120 kg
Answer: D.120 kg
Explanation: Solution
Volume of water displaced	= (3 x 2 x 0.02)m3
= 0.12m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.12×1000) kg
= 120 kg.
Answer D
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
A.A)24.5
B.B)28.5
C.C)30
D.inadequate
Answer: C.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: Option C
Question: At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:85. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?
A.140
B.141
C.142
D.143
Answer: B.141
Explanation: (5/3)*85=141 plus remainder
The answer is B.
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
A.7.5
B.7.4
C.7.9
D.7.2
Answer: D.7.2
Explanation: Net part filled in 1 hour = (1/4 - 1/9) = 5/36
The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.Answer: D
Question: If z is a multiple of 9702, what is the remainder when z^2 is divided by 4?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: 2 is a factor of 9702, so 2 is a factor of z.
Then 2^2 = 4 is a factor of z^2.
Then the remainder when z^2 is divided by 4 is 0.
The answer is A.
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January?
A.391
B.400
C.410
D.423
Answer: B.400
Explanation: Given: January*1.15=December --> January*1.15=460 --> January=460/1.15=400.
Answer: B.
Question: One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 6 robots altogether, if the robots build only one robot at a time?
A.70 min
B.94 min
C.109 min
D.114 min
Answer: D.114 min
Explanation: First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
Now the 4 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 = 5/2
so they complete one robot in 2/5th of an hour, i.e. 24 minutes - (3)
Now the 4 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2+1/2 = 3
so they complete one robot in 1/3th of an hour, i.e. 20 minutes - (4)
And now we have 5 robots
So Total = (1) + (2) + (3) +(4)= 114minutes
Answer - D
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
A.5/21
B.5/28
C.5/22
D.5/25
Answer: A.5/21
Explanation: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21
Answer:A
Question: An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 10000 people who applied for the army and 350 were finally selected, what was the value of N?
A.4
B.5
C.6
D.9
Answer: D.9
Explanation: fastly i reduce 60% till it gets closer to our required 2000 candidates
step(1) 40000 accepted.
step(2) another 40%of 40000=16000 accepted.
here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.
so i would get to second stage of recruitment where 50 % is accepted
step(3) 50% of 16000=8000
step(4) 50% of 8000=4000
Step(5) 50% of 4000=2000
Step(6) 50% of 2000=1000
Step(7) 50% of 1000=500
last step of accepting 70% of 500=350(our target)
total 8 steps required.
Ans D
Question: A class consists of 15 girls and 10 boys. Three students are to be randomly selected. Find the probability that one boy and two girls are picked.
A.21/46
B.21/49
C.21/42
D.26/46
Answer: A.21/46
Explanation: ANSWER: A
Question: In a division, when a student mistook the divisor as 12 instead of 21 and obtained 35 as quotient the remainder is 0 . What is the correct quotient?
A.14
B.18
C.20
D.24
Answer: C.20
Explanation: Let x be the number
x÷12=35, remainder = 0
=> x=35×12
correct quotient
=x21=35×1221=5×123=5×4=20
C
Question: What are the next two numbers in this sequence?
7, 14, 17, 21, 27, 28, 35, 37, ?
A.40
B.41
C.42
D.43
Answer: C.42
Explanation: these are digits which are either multiples of 7 or containing the digit 7.
s0 next numbers are 42
ANSWER:C
Question: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: Explanation:
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20.
Answer: D
Question: Which of the following is a possible length for side AB of triangle ABC if AC = 3 and BC = 9?
I. 6
II. 9 √3
III. 11.5
A.I only
B.II only
C.III only
D.II and III
Answer: C.III only
Explanation: (9-3) < AB < (9+3)
The answer is C.
Question: In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
A.15
B.14
C.21
D.25
Answer: A.15
Explanation: Solution: Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.
Now, according to the question,
nC2 = 105;
Or, n!/[2!*(n-2)!] = 105;
Or, n*(n-1)/2 = 105;
Or, n2-n = 210;
Or, n2-n-210 = 0;
Or, n = 15, -14;
But, we cannot take negative value of n.
So, n = 15 i.e. number of persons in the party = 15.
Answer: Option A
Question: At a certain university, 70% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
A.25
B.37.5
C.50
D.62.5
Answer: C.50
Explanation: answer is 75%
total women = 70%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured = 20%
but question wants to know the percent of men that are tenured
20%/40%=50%
C
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
A.22 kmph
B.77 kmph
C.14 kmph
D.88 kmph
Answer: C.14 kmph
Explanation: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer:C
Question: Which of these must the factor M of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
A.M=1,2 only
B.M=2,3 only
C.M=1,2,3 only
D.M=1,2,3,4 only
Answer: D.M=1,2,3,4 only
Explanation: Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible by 2 x 3 x 4 = 24
only 80 is not divisible. Therefore answer = D
Question: Of the 800 employees in a certain company, 70% have serviced more than 10 years. A number of y of those who have serviced more than 10 years will retire and no fresh employees join in. What is y if the 10 years employees become 60% of the total employees?
A.150
B.200
C.250
D.450
Answer: B.200
Explanation: TOTAL 10 YRS
Original: 800 560
New: 800-y 560-y
560-y = .6 (800 -y)
560-y = 480 - .6y
80 = .4y
800/4 = y
y= 200
Answer: 200	ANSWER:B
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
A.5
B.6
C.8
D.10
Answer: D.10
Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
answer :D
Question: Arun borrowed a sum of money from Jayant at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next six years and 12% per annum for the period beyond ten years. If he pays a total of 12,160 as interest only at the end of 15 years, how much money did he borrow?
A.8000
B.10,000
C.12,000
D.9,000
Answer: A.8000
Explanation: Let the Principal = P
Then P×8×4/100+P×10×6/100+P×12×5/100
= 12160
⇒ 152P = 12160 × 100
or 12160×100/152=8000
Answer A
Question: A car traveled from San Diego to San Francisco at an average speed of 54 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
A.24.
B.32.
C.36.
D.42.
Answer: C.36.
Explanation: Let the time taken be = x
One way distance = 54x
Total distance traveled = 2 * 54x = 108x
Total time taken = x + 2x = 3x
Average speed = 108x/3x = 36
Answer: C
Question: In g is a positive integer smaller than 200 and (14g)/60 is an integer, then g has how many different positive prime factors?
A.2
B.3
C.5
D.6
Answer: B.3
Explanation: 7g/30 tells us that g is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
Question: A monkey start climbing up a tree 21 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
A.15 hrs
B.18 hrs
C.19 hrs
D.17 hrs
Answer: C.19 hrs
Explanation: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 18hrs it wil be 18ft.
But since the height of the tree is 21 ft, so if the monkey hops up the tree in the next hr i.e 19th hr then it reaches at the top of the tree.
hence it takes 19 hrs for monkey to reach at the top
ANSWER:C
Question: A grocery shop has a sale of Rs. 6735, 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.4857
B.4184
C.4012
D.4691
Answer: D.4691
Explanation: Let the sale in the sixth month =x
Then
(6735+6927+6855+7230+6562+x)/6 =6500
=>6735+6927+6855+7230+6562+x =6×6500
=> 34309+x=39000
=> x=39000−34309
=4691
ANSWER:D
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:40 a.m., how long S will the conference last if there are a total of 6 seminars that day?
A.5 hours and 15 minutes
B.5 hours and 20 minutes
C.5 hours and 25 minutes
D.5 hours and 30 minutes
Answer: B.5 hours and 20 minutes
Explanation: Shouldnt the answer be 5 hours 20 mins?
Break = b
Seminar= 10b
9am to 11:40am= 160mins
3s+b=160
30b+b=160
b=160/31
6 seminar will take
6s+2b
=60b+2b
=62b
=62*160/31
=320
S=5 hours 20 mins.B
Question: Mayank Bothra purchased 20 dozens of toys at the rate of 375 Rs per dozen .He sold each one of them at the rate of Rs 33.What was his percentage profit?
A.5.6 %
B.6.5 %
C.7.5 %
D.7.6 %
Answer: A.5.6 %
Explanation: Sol.
Cost = 375 * 20 = 7500
sale price 33 * 20 * 12
= 7920 profit = 420 profit in % = 420/7500 * 100 =5.6 %
Ans: A.
Question: Nine persons went to a hotel for taking their meals. Eight of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine. What was the total money spent by them.
A.Rs. 115
B.Rs. 116
C.Rs. 117
D.Rs. 118
Answer: C.Rs. 117
Explanation: Solution:
Let the average expenditure of all the nine be x.
Then, 12 × 8 + (x + 8) = 9x.
Therefore, x = 13.
Total money spent,
= 9x = Rs.(9 × 13) = Rs.117
Answer: Option C
Question: N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?
A.59
B.49
C.58
D.113
Answer: B.49
Explanation: You have 6 digits: 3, 4, 5, 6, 7, 8
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options?
Try and make a pair with (4** and 5**). Make the 4** number as large as possible and make the 5** number as small as possible.
487 and 536 (difference is 49) or
Try and make a pair with (6** and 7**). Make the 6** number as large as possible and make the 7** number as small as possible. We get 685 and 734 (difference is 49)
B