mathewhe/aqua_rat huggingface dataset:
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
(A) 4800
(B) 5760
(C) 2880
(D) 15000
(E) 1440
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
ANSWER:C
Answer: (C) 2880
Question: Driver A passes a milestone at a constant speed of 50 miles per hour. Then, 15 minutes later, Driver B passes the same milestone at a constant speed of 60 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after Driver B passed the gas station did he catch up with Driver A?
(A) 30 min
(B) 45 min
(C) 1 hr 15 min
(D) 2 hrs
(E) 1 hr 30 min
Rationale: When Driver A is at the station, Driver B is 50/4 miles ahead on the highway. (the distance driven in 15 min)
every hour, Driver B drives 10miles more than Mary. how many hours will it takes him to drive 50/4 miles more? the answer is (50/4)/10 = 25/20=1h15min.
Answer C
Answer: (C) 1 hr 15 min
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability E that private Benjamin will be chosen for latrine duty?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: Easier way : Desired probability = 1- 'excluded' probability
In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability E= 1- 3/5 = 2/5. Thus C is the correct answer.
Answer: (C) 2/5
Question: 9!/(9-3)!=?
(A) 336
(B) 346
(C) 356
(D) 366
(E) 504
Rationale: 9!/(9-3)!=9!/6!=9*8*7=504. Hence, the correct answer is E.
Answer: (E) 504
Question: In an election, candidate Douglas won 60 percent of the total vote in Counties X and Y. He won 72 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?
(A) 18%
(B) 30%
(C) 36%
(D) 48%
(E) 54%
Rationale: given voters in ratio 2:1
let X has 200 votersY has 100 voters
for X 72% voted means 72*200=144 votes
combined for XY has 300 voters and voted 60% so total votes =180
balance votes=180-144=36
As Y has 100 voters so 36 votes means 36% of votes required
Ans C
Answer: (C) 36%
Question: The average of a couple was 20Yrs when they were married 8Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 21Yrs now. How old is the
child now ?
(A) 2 Yrs
(B) 4 Yrs
(C) 3 Yrs
(D) 1 Yrs
(E) None of these
Rationale: (a+b-8-8)/2=21;
a+b=58;
a+b+c/3=20;
solving both c=2
ANSWER:A
Answer: (A) 2 Yrs
Question: What is the largest sum of money-all in current coins and no silver dollars-that I could have in my pocket without being able to give change for a dollar, half dollar, quarter, dime, or nickel?
(A) $2.28
(B) $3.31
(C) $1.19
(D) $1.28
(E) $4.18
Rationale: C
$1.19
The largest sum is $1.19, composed of a half dollar, quarter, four dimes, and four pennies.
Answer: (C) $1.19
Question: If a light flashes every 6 seconds, how many times will it flash in 1/5 of an hour?
(A) 81
(B) 101
(C) 121
(D) 141
(E) 161
Rationale: In 1/5 of an hour there are 12*60 = 720 seconds
The number of 6-second intervals = 720/6 = 120
After the first flash, there will be 120 more flashes for a total of 121.
The answer is C.
Answer: (C) 121
Question: The average age of father and his two sons is 32 Years. Five years ago, the average age of the two sons was 14 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?
(A) 45
(B) 46
(C) 47
(D) 60
(E) 49
Rationale: The total present age of father and two sons is 3x32 = 96 yrs
The total present age of sons is (12+5) X 2 = 38Years
so, present age of father is 96 â€“ 36 = 60 yrs
Answer D
Answer: (D) 60
Question: (2^2+4^2+6^2+.....+10^2)=?
(A) 220
(B) 440
(C) 660
(D) 880
(E) 990
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x5)^2
=2^2 x (1^2+2^2+3^2+.......+5^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x5x6x11)
=(4x55)=220
Answer is A
Answer: (A) 220
Question: 50% of all students in a class commute by public transportation. If 20% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists?
I.	15%
II.	40%
III.	70%
(A) I ONLY
(B) II ONLY
(C) III ONLY
(D) I AND II
(E) I AND III
Rationale: 50% Students use public transportation. This means 50% students do not use public transportation. 20% students aspire to be scientists means even if all these students use public transportation, minimum 50% - 20% = 30% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 30% and 50%
Answer : B.
Answer: (B) II ONLY
Question: A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:
(A) 35
(B) 36
(C) 37
(D) 40
(E) 45
Rationale: According to given condition
vt=(v+3)(t-2/3)
vt=(v-2)(t+2/3)
here v is velocity in kmph, t is time in hours and 2/3 is value of 40 min in hour
on solving we will get t=10/3 and and v = 12 so distance = (10/3) * 12 = 40 kms
ANSWER:D
Answer: (D) 40
Question: Each student is given a four-character identification code. The first three characters are selected from the numbers 0 to 9 inclusive, and the last character is selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
(A) 25,700
(B) 26,000
(C) 26,300
(D) 26,600
(E) 26,900
Rationale: The number of possible codes is 10*10*10*26=26,000.
The answer is B.
Answer: (B) 26,000
Question: If the function Q is defined by the formula Q = 5w/(4h(z^2)), by what factor will Q be multiplied if w is quadrupled, h is doubled, and z is tripled?
(A) 1/9
(B) 2/9
(C) 4/9
(D) 3/9
(E) 2/27
Rationale: We just need to find the factor thats all,
w -> quadrupled -> 4w
h-> doubled -> 2h
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
W is in numerator, and h*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B
Answer: (B) 2/9
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 27 m
(B) 24 m
(C) 18 m
(D) 21 m
(E) None of these
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
ANSWER:C
Answer: (C) 18 m
Question: What is the rate percent when the simple interest on Rs.1000 amount to Rs.400 in 4 Years?
(A) 5%
(B) 6%
(C) 2%
(D) 95%
(E) 10%
Rationale: Interest for 4yrs = 400
Interest for 1yr = 100
Interest rate = 100/1000 x 100 = 10%
Answer : E
Answer: (E) 10%
Question: The cricket team of 11members is 24yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
(A) 21
(B) 22
(C) 23
(D) 25
(E) 28
Rationale: Let the average age of the whole team be x years.
11x - (24 + 27) = 9 (x - 1)
=> 11x - 9x = 42
=> 2x = 42
=> x = 21.
So, average age of the team is 21 years.
A
Answer: (A) 21
Question: The measurements obtained for the interior dimensions of a rectangular box are 150 cm by 150 cm by 225cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?
(A) 90,000
(B) 95,000
(C) 93,000
(D) 92,000
(E) 91,000
Rationale: The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*150*225 = 33,750 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 150*1*225 = 33,750 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 150*150*1 = 22,500 cubic centimeters.
So, approximate maximum possible difference is 33,750 + 33,750 + 22,500 = 90,000 cubic centimeters.
Answer: A
Answer: (A) 90,000
Question: Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?
(A) 3/19
(B) 3/12
(C) 3/11
(D) 3/10
(E) 3/14
Rationale: Let Veena paid x,
so Akshitha paid 2x/3 , and Lasya paid 2x,
So total bill paid is given by
x+(2x/3) +2x = 1, we get
i.e. x = 3/11
Answer: C
Answer: (C) 3/11
Question: Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fifth widget, starting with the fifth, and Steven inspects every fourth, starting with the fourth, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?
(A) 66
(B) 68
(C) 70
(D) 64
(E) 72
Rationale: Widgets inspected by Lauren: ((95-5)/5)+1=18+1=19
Widgets inspected by Steven: ((96-4)/4)+1 =23+1 =24
Widgets inspected by both: ((96/12)+1 =9
Total : 19+24 -9=34
hence, widgets not inspected: 98-34=64
Option D
Answer: (D) 64
Question: Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
880/x = 880/1.1x + 10
1.1(880) = 880 + 11x
11x = 88
x = 8
The answer is D.
Answer: (D) 8
Question: In a game of billiards, A can give B 30 points in 50 and he can give C 40 points in 50. How many points can B give C in a game of 100?
(A) 18
(B) 27
(C) 50
(D) 21
(E) 17
Rationale: A scores 50 while B score 20 and C scores 10.
The number of points that C scores when B scores 100 = (100 * 10)/20 = 50.
In a game of 100 points, B gives (100 - 50) = 50 points to C.
Answer: C
Answer: (C) 50
Question: Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9450, find the contribution made by David.
(A) $540
(B) $580
(C) $600
(D) $630
(E) $660
Rationale: Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.
Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.
Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.
Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15
So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9450=$630.
The answer is D.
Answer: (D) $630
Question: If a new town has 250 residents, and the population doubles every 10 years, what will be its population after 75 years?
(A) 6034 residents
(B) 9051 residents
(C) 45255 residents
(D) 15075 residents
(E) 18102 residents
Rationale: 250*2^(75/10)=250*2^7.5=100*181.02=45255
The answer is C.
Answer: (C) 45255 residents
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1260, find the loss %?
(A) 18
(B) 16
(C) 26
(D) 17
(E) 11
Rationale: Explanation:
1500 ---- 240
100 ---- ? => 16%
Answer:B
Answer: (B) 16
Question: The odds in favour of an event A are 3:4.The odds against anotehr independent event B are 7:4. What is the probability that at least one of the events will happen ?
(A) 1/11
(B) 7/11
(C) 6/11
(D) 8/11
(E) None of these
Rationale: Explanation :
The odds in favour of an event A are 3:4.
=> Probability of A = P(A) = 3/(3+4) = 3/7.
The odds against an event B are 7 : 4.
=> Probability of B = P(B) = 4/(7+4) = 4/11.
The probability of occurrence of at least one of the events A and B,
P(A+B) = P(A) + P(B) - P(AB).
=>P(A+B) = P(A) + P(B) - P(A) x P(B).
=> (3/7) + (4/11) - (3/7)(4/11).
=> 7/11.
Hence, the required probability is 7/11.
Answer : B
Answer: (B) 7/11
Question: A car after covering Â½ of a journey of 100 km develops engine trouble and later travels at Â½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
(A) 50 kmph
(B) 40 kmph
(C) 30 kmph
(D) 25 kmph
(E) 35 kmph
Rationale: Explanation:
[50/x + 50/(x/2)] â€“ 100/x = 2
x = 25
ANSWER IS D
Answer: (D) 25 kmph
Question: Each of the integers from 1 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Answer is 6. In the worst case, you could end up drawing 1,2,3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.
D
Answer: (D) 6
Question: Jacob is 12 years old. He is 4 times as old as his brother. How old will Jacob be when he is twice as old?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 18
Rationale: j=12;
j=4b;
b=12/4=3;
twice as old so b=3(now)+(3)=6;
jacob is 12+6=18
ANSWER:E
Answer: (E) 18
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
(A) 3 p.m.
(B) 6 p.m.
(C) 7 p.m.
(D) 4 p.m.
(E) 5 p.m.
Rationale: Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =	37/4 hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
37/720 hrs of this clock =	1/20	hrs of the correct clock.
37/4	hrs of this clock = 1/20 x 720/37 x 37/4 hrs of the correct clock.
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
Answer D
Answer: (D) 4 p.m.
Question: The mean of 1^2,2^2,3^2,4^2,5^2,6^2,7^2 is?
(A) 15
(B) 18
(C) 20
(D) 25
(E) 30
Rationale: 1^2+2^2+3^2+-----+n^2 = n(n+1)(2n+1)/6
1^2+2^2+3^2+-----+7^2 = 7*8*156 = 140
Required average is = 140/7 = 20
Answer is C
Answer: (C) 20
Question: The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference c would have been how much?
(A) 40/3
(B) 40
(C) 120
(D) 360
(E) 420
Rationale: CASE 1:
Deposit = $x;
Rate of increase = r.
Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference c = (x + xr)r - xr = xr^2 = 40.
CASE 2:
Deposit = $x;
Rate of increase = 3r.
Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.
Answer: D.
Answer: (D) 360
Question: A standard Veggiematik machine can chop 32 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 6 minutes?
(A) 36
(B) 54
(C) 288
(D) 108
(E) 324
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 32 Carrots - 4 minutes,
1 standard Veggiematik machine - 8 Carrots - 1 minute,
Now
6 standard Veggiematik machine - ? Carrots - 6 minutes,
Hence = 8X6X6 =288 Carrots
Answer C
Answer: (C) 288
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 11), (x, 11)?
(A) 49
(B) 64
(C) 75
(D) 81
(E) 96
Rationale: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 9.
The area is 9*9 = 81.
The answer is D.
Answer: (D) 81
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 7 * 9 =?
(A) 89
(B) 49
(C) 68
(D) 38
(E) 55
Rationale: C
68
(9 * 7) + 5 = 68
Answer: (C) 68
Question: The ratio of the present ages of a man and his wife is 8 : 7. Which of the following can't be a possible ratio of their ages 45 years ago?
(A) 6: 8
(B) 7: 8
(C) 8:8
(D) 9: 8
(E) 10: 8
Rationale: 8x-45/7x-45 = 9/8
Therefore x=-45
Age cannot be negative.
Answer: D
Answer: (D) 9: 8
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 189m
(B) 180m
(C) 100m
(D) 480m
(E) 1860m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m .Answer: B
Answer: (B) 180m
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 18
(B) 99
(C) 77
(D) 26
(E) 12
Rationale: 9 * 2 = 18 years
Answer: A
Answer: (A) 18
Question: In how many ways can three boys can be seated on five chairs?
(A) 10
(B) 20
(C) 60
(D) 40
(E) 55
Rationale: There are three boys.
The first boy can sit in any of the five chairs (5 ways).
5
Now there are 4 chairs remaining. The second boy can sit in any of the four chairs (4 ways).
5	4
Now there are 3 chairs remaining. The third boy can sit in any of the three chairs (3 ways).
5	4	3
Hence, total number of ways in which 3 boys can be seated on 5 chairs
=5×4×3=60
Ans: C
Answer: (C) 60
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
(A) 0.07
(B) 0.049
(C) 0.7
(D) 0.49
(E) 4.9
Rationale: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*49*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 490/10,000 = 49/1000 = 0.049 ft
The answer is B.
Answer: (B) 0.049
Question: The ratio of the ages of Ragul and Vicky is 3 : 6. The total of their ages is 2.7 decades. The proportion of their ages after 0.3 decades will be
[1 Decade = 10 years]
(A) 4:7
(B) 3:4
(C) 4:5
(D) 7:9
(E) 3:6
Rationale: Let,Ragul’s age = 3A and Vicky’s age = 6A
Then 3A + 6A = 27
A = 3
Ragul’s age = 9 years
and Vicky’s age = 18 years
Proportion of their ages after 3 is = (9 + 3) : (18 + 3)
= 12 : 21
= 4 : 7
Answer : A
Answer: (A) 4:7
Question: If x is an integer, then x(x - 1)(x - l) must be evenly divisible by three when l is any of the following values EXCEPT
(A) -4
(B) -2
(C) -1
(D) 2
(E) 5
Rationale: if we put l=-1 we get:
X(x-1)(X+1) rearrange:(x-1)X(X+1)
so it looks like a sequenc,
if we assume that X =2 and put number from the answer then we get:
(x – 1)x(x – l)
l=5 =1.2.-3
l=2 =1.2.0
l=-1 =1.2.3
l=-4 =1.2.6
but when we put
l=-2 =1.2.4 not satisfied
so,answer is B
Answer: (B) -2
Question: In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 65% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
(A) a) 50%
(B) b) 53%
(C) c) 54%
(D) d) 55%
(E) e) 57%
Rationale: Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=50%
A
Answer: (A) a) 50%
Question: If a#b = ab – b + b^2, then 3#7 =
(A) 2
(B) 63
(C) 15
(D) 21
(E) 35
Rationale: Solution -
Simply substitute 3 and 7 in equation in the place of a and b respectively.
3#7 = 3*7 - 7 + 7^2 = 21 - 7 + 49 = 63. ANS B
Answer: (B) 63
Question: John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
(A) 50
(B) 60
(C) 75
(D) 80
(E) 85
Rationale: (x+x1+...x14)/15 = 40
50
Option A
Answer: (A) 50
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 24 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 20.7
(D) 21.7
(E) 22.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 24 Paise is given as tax
=> Total tax incurred = 24 Paise = Rs.24/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 24/100
⇒ 6(25 −0.3 −x) = 24
⇒ (25 − 0.3 − x) = 4
⇒ x = 25 − 0.3 − 4 = 20.7
C)
Answer: (C) 20.7
Question: A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate =(100 x 3000)/(12500 x 4)%	= 6%
answer :D
Answer: (D) 6%
Question: If a and b are different positive integers and a + b+1 = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
D
Answer: (D) I and II
Question: If P is a prime number greater than 5, what is the remainder when P^2 is divided by 6.
(A) 4
(B) Cannot be determined
(C) 2
(D) 6
(E) 1
Rationale: take square of any prime number
remainder will be 1
Ans E
Answer: (E) 1
Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1. Find the sum
(A) Rs 600
(B) Rs 625
(C) Rs 650
(D) Rs 675
(E) None of these
Rationale: Explanation:
Let the Sum be P
S.I.=P∗4∗2 /100=2P/25
C.I.=P(1+4/100)2−P
=676P/625−P
=51P/625
As, C.I. - S.I = 1
=>51P/625−2P/25=1
=>51P−50P/625=1
P=625
Option B
Answer: (B) Rs 625
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12 m
(B) 111.72 m
(C) 111.15 m
(D) 116.12 m
(E) 111.32 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: (A) 111.12 m
Question: 850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
(A) 17
(B) 138
(C) 60
(D) 38
(E) 12
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 850 = 17
Answer: A
Answer: (A) 17