mathewhe/aqua_rat huggingface dataset:
Question: The average weight of a group of 30 friends decreases by 1 kg when the weight of one of them was removed. If average weight of the group after removing the weight of this one person is 29 kg, what is the weight of their new friend ?
(A) 31 kg
(B) 60 kg
(C) 59 kg
(D) 62 kg
(E) 91 kg
Rationale: let n= weight of one person who was removed from group
original total weight=(30 friends)(30 kg avge)=900kg
(900-n)/(30-1)=29 kg avg.
n=59 kg
Answer = C
Answer: (C) 59 kg
Question: 1/0.025 is equal to
(A) 25.5
(B) 2.5
(C) 40
(D) .25
(E) None of these
Rationale: Explanation:
1/0.025 = (1 * 1000)/25 = 1000/25 = 40
Option C
Answer: (C) 40
Question: In Orange County one fifth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 60.
(B) 42.
(C) 85
(D) 140.
(E) 252.
Rationale: 1/5 mush --> 7/35
1/7 apples -->5/35
We know that we must have a multiple of 35.
D is the only choice that gives us that. 35x4=140
ANSWER:D
Answer: (D) 140.
Question: Amar takes as much time in running 12 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
(A) 600 m
(B) 200 m
(C) 300 m
(D) 400 m
(E) 100 m
Rationale: D
400 m
Distance covered by Amar = 12/4.8 (1.6km) = 2.5(1600) = 400 m
Answer is D
Answer: (D) 400 m
Question: Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and Y. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of Y if J is negative?
(A) -2
(B) Y=0
(C) 1
(D) 2
(E) 5
Rationale: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.
mode of the set is a number which occurs maximum number of time in the set. now, since Y is the mode of the set. therefore Y=0. hence answer is B
Answer: (B) Y=0
Question: A boat having a length 7 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
(A) 140 kg
(B) 60 kg
(C) 72 kg
(D) 96 kg
(E) None of these
Rationale: Explanation:
Volume of water displaced = (7 x 2 x 0.01) m3
= 0.14 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.14 x 1000)kg
= 140 kg.
Answer: A
Answer: (A) 140 kg
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 8 years
(C) 6 years
(D) 5 years
(E) 1 years
Rationale: Let the ages of the 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 youngest child = x = 4 years.
Answer: A
Answer: (A) 4 years
Question: How many differently shaped triangles exist in which no two sides are of the same length, each side is of integral unit length and the perimeter of the triangle is less than 14 units?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation :
Let the lengths of the sides be a, b and c.
Given, Triagle's perimeter < 14
=> a+b+c < 14 ----------(i)
From triangle Inequality theorem,
c < a+b
=> 2c < a+b+c. ----------(ii)
From (i) and (ii), 2c < a+b+c < 14.
=> c < 7 ----------(iii)
=> By similarity, we can say that length of any side must be less than 7.
Keeping these in mind, we can find the following possibilities :-
(2,3,4) (2,4,5) (2,5,6) (3,4,5) (3,4,6)
=> Total 5 possibilities.
Answer : C
Answer: (C) 5
Question: A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 5 volts, what was the smallest possible recording in volts?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: if average of 3 is 5 so sum of 3 should be 15
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 6 and 6
so a has to be 3
B
Answer: (B) 3
Question: What is the difference between the compound interest on Rs.12000 at 26% p.a. for one year when compounded yearly and half yearly?
(A) 399.8
(B) 383.8
(C) 120.8
(D) 202.8
(E) 233.8
Rationale: When compounded annually, interest
= 12000[1 + 26/100]1 - 12000 = Rs.3120
When compounded semi-annually, interest
= 12000[1 + 13/100]2 - 12000 = Rs.3322.80
Required difference = 3322.80 - 3120 = Rs.202.80
Answer: D
Answer: (D) 202.8
Question: A is thrice as good a workman as B and therefore is able to finish a job in 80 days less than B. working together, they can do it in
(A) days
(B) ½ days
(C) days
(D) days
(E) days
Rationale: Explanation:
B = 3A
3A – A =80 days
A = 40days
Then, B = 90 days
(A + B) = 40 × 90/ 120 = 30 days .
Answer: Option D
Answer: (D) days
Question: One boy forgot the last digit of a 7digit telephone no. If he randomly dial the final 3digits after correctly dialing the 1st 4, then what is the chance of dialing the correct no.?
(A) 1/989
(B) 2/890
(C) 1/1000
(D) 3/890
(E) 4/981
Rationale: it is given that last 3 digits are randomly dialed
Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability
= 1/(10)3 = 1/1000
C
Answer: (C) 1/1000
Question: On 4th Jan, 2009 Sunday falls. What day of the week was it on 4th Jan, 2008?
(A) Wednesday
(B) Thursday
(C) Friday
(D) Saturday
(E) Sunday
Rationale: Explanation:
4th Jan 2009 – 4th Jan 2008 = 52 weeks 1 day. So Jan 4th 2008 is behind one day = Saturday
Answer: D
Answer: (D) Saturday
Question: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $35 more than that received by B, find the total amount shared by A, B and C.
(A) $1360
(B) $1250
(C) $1260
(D) $1270
(E) $1280
Rationale: A = 1/3 (B+C) => C = 3A - B ---(1)
B = 2/7 (A+C) => C = 3.5 B - A --(B)
A-B = $35
A = 35+B
(1)===> C = 105+3B - B = 2B+105 ==> 2B-C = -105 ---(3)
(2)===> C = 3.5 B - B-35 = 2.5B-35==>2.5B-C = 35---(4)
from (4) and (3) 0.5B = 140
B = $280
A= $315
C =945-280=$665 Total amount = 315+280+665 = $1260
Answer: C
Answer: (C) $1260
Question: 2/[(1/0.03) + (1/0.37)] = ?
(A) 0.004
(B) 0.05555
(C) 2.775
(D) 3.6036
(E) 36.036
Rationale: Approximate.
1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36
2/36 = .05 something
Answer (B)
Answer: (B) 0.05555
Question: A car has been driven with an average speed of 30 kilometers per hour during the first 30 kilometers of a journey. Upon reaching the 30th kilometer, the car then travels at 45 kilometers per hour for the next 30 kilometers. Find out the average speed of the car if it has not been stopped at all during the journey.
(A)  35
(B)  36
(C)  37.5
(D)  38
(E)  40
Rationale: R * T = D
30 * a = 30 => a=1
45 * b = 30 => b= 2/3
(1*30 + 2/3*90)/5/3 = 36 => B
Answer: (B)  36
Question: The mall charges 40 cents for the first hour of parking and $3 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If Mr.Park parked his car in the mall for 7 hours and 30 minutes, how much is he going to pay?
(A) $6.8
(B) $12.
(C) $13.
(D) $14.5.
(E) $15.
Rationale: 0.40+2*2+1*2+0.40= $6.8
Answer : $6.8
Answer: (A) $6.8
Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs.24. The present worth is
(A) Rs. 480
(B) Rs. 520
(C) Rs. 600
(D) Rs. 960
(E) None
Rationale: Solution
T.D	= (B.G x 100/Rate x Time)
= Rs.(24x100 / 10x 2)
= Rs.120.
P.W	= (100 x T.D/Rate x Time)
= Rs.(100x120 / 10x 2)
= Rs.600.
Answer C
Answer: (C) Rs. 600
Question: Rohit spent 50 percent of his earning last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did John have left over?
(A) 15%
(B) 25%
(C) 35%
(D) 55%
(E) 20%
Rationale: SayRohit's earning last month was $100.
Rohit spent 50 percent of his earning last month on rent --> $50 on rent;
30 percent less than what he spent on rent to purchase a new dishwasher --> $50*0.7=$35 on the dishwasher.
Left over amount 100 - (50 + 35) = $15.
Answer: A.
Answer: (A) 15%
Question: If after 200 grams of water were added to the 30%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 30%-solution was used?
(A) 100 grams
(B) 220 grams
(C) 250 grams
(D) 350 grams
(E) 400 grams
Rationale: The 30% alcohol solution decreases by 1/3 once the 200 grams of water is added so 200/.1 =2000*.05% (2/3 of 30%) is 100 grams, thus answer is A.
Answer: (A) 100 grams
Question: There are 8 letters and corresponding 8 envelopes. If 8 letters are placed into 8 envelopes randomly, find the number of ways that exactly one letter is placed into wrong envelope.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: in 8 letter one letter is placed into wrong envelop means balance 7 are in correct place. so all 7 letters are in correct place means definitely the remaining 8th one is also placed correctly. so ans is 0
ANSWER:A
Answer: (A) 0
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
(A) 187 km
(B) 480 km
(C) 278 km
(D) 297 km
(E) 671 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 4
2x/15 - x/8 = 4 => x = 480 km.
Answer:B
Answer: (B) 480 km
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 9th Ave in the shortest possible time, how many different routes could he take?
(A) 90
(B) 120
(C) 150
(D) 180
(E) 210
Rationale: Bills needs to walk 4 blocks north and 6 blocks east.
One possible solution is NNNNEEEEEE.
There are 10C4 = 210 possible solutions.
The answer is E.
Answer: (E) 210
Question: A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in.
(A) 35 days
(B) 60 days
(C) 79 days
(D) 70 days
(E) 65 days
Rationale: B
60 days
A = 140 days
B = 105 days
1/140 + 1/105 = 7/420 = 1/60
=>60 days
Answer: (B) 60 days
Question: If m is an integer such that (-2)^2m=2^(15-m) then m=?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 2m = 15-m
3m = 15
m = 5
The answer is D.
Answer: (D) 5
Question: Two numbers A and B are such that the sum of 5% of A and 3% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2 : 1
(B) 1 : 2
(C) 7 : 3
(D) 1 : 1
(E) 3 : 2
Rationale: Explanation:
5% of A + 3% of B = 2/3(6% of A + 8% of B)
5A/100 + 3B/100 = 2/3(6A/100+8B/100)
⇒5A + 3B = 2/3(6A + 8B)
⇒15A + 9B = 12A + 16B
⇒ 3A = 7B
⇒ AB = 7/3
⇒ A:B=7:3
Answer: Option C
Answer: (C) 7 : 3
Question: All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?
(A) 25
(B) 20
(C) 35
(D) 45
(E) 55
Rationale: DETAILED SOLUTION
Any multiple of 6 will end in a zero. There are 25 such numbers. Beyond this, we can have zero as the middle digit of a 3-digit number.
This will be the case for numbers from 37 - 41, 73 - 77, 109 - 113 and 145 - 149. There are 20 such numbers.
Overall, there are 45 numbers that have a zero in them.
Correct Answer : D
Answer: (D) 45
Question: Malar and Roja combined will complete a task in 35 days, but Malar alone can complete same work in 60 days. Calculate in how many days Roja can complete this work ?
(A) 85 days
(B) 45 days
(C) 90 days
(D) 84 days
(E) 95 days
Rationale: Malar - 35 days =>1/35
Roja - 60 days =>1/60
Malar one day work = 1/35-1/60
=1/84
==>84 days
ANSWER D
Answer: (D) 84 days
Question: The value of (9x10^8)(5x10^9) is closest to which of the following?
(A) 10^19
(B) 10^15
(C) 10^16
(D) 10^14
(E) 10^12
Rationale: multiplying these we get,
45 x 10^8 x 10^9
= 4.5 x 10^18
which is closer to 10^19
Answer: A
Answer: (A) 10^19
Question: A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $36 to ship a certain package, which of the following was the weight of the package, in pounds?
(A) 15
(B) 17
(C) 19
(D) 21
(E) 23
Rationale: Let the weight of the package be X.
2X + 6= 36
X = 15
The answer is A.
Answer: (A) 15
Question: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 5x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: The big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 2, and 5x – 2 are ALLintegers
For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.
Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers
When x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 2, and 5(3) – 2.
When we evaluate these terms we get: 4, 6, 3, 5 and 13
Rearrange to get: 3, 4, 5, 6, 13. So, when x = 3, we get consecutive integers.
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)
Answer:
C
Answer: (C) 5
Question: If abcd represents a positive four-digit number, where a, b, c and d are one-digit integers, which of the following CANNOT be true?
(A) a + b + c + d = 9
(B) abcd = 9
(C) a – b - c - d = 9
(D) b – a - c - d = 9
(E) a/b/c/d = 9
Rationale: The (thousands place digit, a) cannot be zero, but (hundreds, tens and ones place digits; b, c and d) can be zero.
A is possible
B is possible
C is possible
D is NOT possible
E is possible
Answer: D
Answer: (D) b – a - c - d = 9
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
(A) 587 × 108 miles
(B) 587 × 1010 miles
(C) 587 × 10-10 miles
(D) 587 × 1012 miles
(E) 587 × 10-12 miles
Rationale: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
Answer: (D)
Answer: (D) 587 × 1012 miles
Question: The sum of ages of 5 children born at theintervals of 3 years each is 50 years. what is the age of the youngest child?
(A) 4
(B) 5
(C) 9
(D) 8
(E) 10
Rationale: the age of children x, (x+3), (x+6) , (x+9) and (x+12) years.
x+(x+3)+(x+6)+(x+9)+(x+12)= 50
5x= 20 , x=4. correct answer (A)
Answer: (A) 4
Question: The distance between two villages P and Q is 330 Km. A train starts from P at 8 a.m. and travel towards Q at 60 km/hr. Another train starts from Q at 9 a.m and travels towards P at 75 Km/hr. At what time do they meet?
(A) 11 am
(B) 10 am
(C) 9 am
(D) 12 pm
(E) 11.30 am
Rationale: meet x hrs after 8 a.m.
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
==>60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
ANSWER A
Answer: (A) 11 am
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) 9:1
(B) 3:2
(C) 9:4
(D) 9:2
(E) 9:6
Rationale: 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.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Answer: Option A
Answer: (A) 9:1
Question: Round trip time of 110 meters in a river is 16 min. the velocity of stream is 3m/min. what is the velocity of the person in the still water?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: let speed of boat be x.hence upstream=x-3 and downstream=x+3..so we have
55/x+3 + 55/x-3 = 16...solving we get x=8
ANSWER:C
Answer: (C) 8
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 800 m?
(A) 122.9 m
(B) 170 m.
(C) 122.2 m
(D) 222.9 m
(E) 12289 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 800 m, the number of meters by which A beats C = (800 * 212.5)/1000
= 170 m.
Answer:B
Answer: (B) 170 m.
Question: If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 1/2
(E) 3/5
Rationale: No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 4 = 4C2
Total possible outcomes - 2^4 (each child can be either a girl or a boy)
Probability=2C1*4C2/2^4= 2*4/2*2*2*2=8/16=1/2
Ans=D
Answer: (D) 1/2
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 22 sec
(B) 16 sec
(C) 77 sec
(D) 55 sec
(E) 17 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer:B
Answer: (B) 16 sec
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.80. How much was lent at 5%?
(A) 299
(B) 666
(C) 878
(D) 1000
(E) 1277
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 80
5x/100 + 90 – 6x/100 = 80
x/100 = 10
=> x = 1000
Answer:D
Answer: (D) 1000
Question: If 9a - b = 10b + 70 = -12b - 2a, what is the value of 2a + 22b?
(A) -4
(B) -70
(C) 0
(D) 2
(E) 4
Rationale: This implies 9a - b = 10b + 70, 9a -b = -12b -2a, 10b + 70 = -12b -2a
Manipulating the second equation gives us 10b + 70 = -12b - 2a ==> 2a + 22b = -70
Answer is B
Answer: (B) -70
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
(A) 3209
(B) 3291
(C) 3600
(D) 2997
(E) 2983
Rationale: P = 144(100/5)2 => P
= 3600
Answer: C
Answer: (C) 3600
Question: If the cost price is 25% of selling price. Then what is the profit percent.
(A) 150%
(B) 200%
(C) 300%
(D) 350%
(E) None of these
Rationale: Explanation:
Let the S.P = 100
then C.P. = 25
Profit = 75
Profit% = (75/25) * 100 = 300%. Answer: C
Answer: (C) 300%
Question: Of the 320 people attending a conference, 180 have signed up for the Marketing workshop and 250 have signed up for the Accounting workshop. If 40 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:
(A) 110
(B) 125
(C) 130
(D) 150
(E) 175
Rationale: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:
Total = Gp.1 + Gp.2 - Both + Neither
320 = 180 + 250 - Both + 40
320 = 470 - Both
Both = 150
Final Answer:
D
Answer: (D) 150
Question: Varma can read a book in m minutes. What part of the book can he read in 7 minutes?(m>7)
(A) (k - 8)/k
(B) k/8
(C) 8 + k
(D) k-8
(E) 7/m
Rationale: Option E
Explanation:
Part of the book he can read in 1 minute = 1/3
Part of the book he can read in 7 minutes =7/3.
Answer: (E) 7/m
Question: If positive integer k is divided by 12, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4
(A) None
(B) I
(C) II
(D) III
(E) I and II only
Rationale: k = 12m+2 = 2(6m+1)
I. k + m = 2(6m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Answer: (A) None
Question: If a class of 10 students has six men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
(A) 5!4!
(B) 6!5!
(C) 4!4!
(D) 10!
(E) 10!/5!
Rationale: for no two men to sit together, either all are in even or odd position
fix one at any one position then rest five can be fixed in 5! ways...
also rest six position of women can be fixed in 6!..
total ways 6!5!
B
Answer: (B) 6!5!
Question: Find the remainder when 4*4! + 5*5! + 6*6! +...................+ 19*19! is divided by 64.
(A) 22
(B) 27
(C) 40
(D) 28
(E) 11
Rationale: 8*8! and its subsequent terms are exactly divisible by 64. As highest power of 2 in 64 is 6 and highest power of 2 in 8! is 7 which is greater than 6. So we have to find the remaidner when 4*4! + 5*5! + 6*6! + 7*7! is divided by 64 which is 40.
Elitmus model questions
Answer:C
Answer: (C) 40
Question: G is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of G, and y is the minimum value of the sum of k distinct members of G, what is x + y?
(A)  kn
(B)  kn + k^2
(C)  kn + 2k^2
(D)  2kn – k^2
(E)  2kn
Rationale: Probably the easiest way to solve this question would be to assume some values for n and k.
Say n=3, so G, the set of the first n positive odd numbers would be: G={1, 3, 5};
Say k=1, so X, the maximum value of the sum of K distinct members of G would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of G would simply be 1.
X+Y=5+1=6.
Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.
Answer: E.
Answer: (E)  2kn
Question: A worker is paid Rs.20/- for a full days work. He works 1,1/3,2/3,1/8.3/4 days in a week. What is the total amount paid for that worker ?
(A) 56.5 rupees
(B) 58.5 rupees
(C) 57.5 rupees
(D) 59.5 rupees
(E) 55.5 rupees
Rationale: the total days worked=1+0.333+0.667+0.125+0.75=2.875 days
amount for 2.875 days is(2.875*20) 57.5 rupees
ANSWER:C
Answer: (C) 57.5 rupees
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
(A) 80%
(B) 20%
(C) 28%
(D) 90%
(E) 30%
Rationale: P = (P*5*R)/100
R = 20%
Answer: B
Answer: (B) 20%
Question: There are 15 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 288
(B) 267
(C) 261
(D) 211
(E) 272
Rationale: The total number of stations = 17
From 17 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 17P₂ ways.
17P₂ = 17* 16= 272.
Answer: E
Answer: (E) 272
Question: A person spent Rs. 8,596 from his salary on food and ?7,640 on house rent. After that he was left with 28% of his monthly salary. What is his monthly salary ?
(A) Rs. 21,560
(B) Rs. 22,500
(C) Rs. 22,550
(D) Rs. 23,550
(E) None of these
Rationale: Explanation :
Total money spent on food and 16236 Which is 100 - 28 = 72% of his monthly salary
∴ His salary = 16236x100/72 = 22550
Answer : Option C
Answer: (C) Rs. 22,550
Question: The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 2 students?
(A) 133 years
(B) 177 years
(C) 119 years
(D) 212 years
(E) None
Rationale: Solution
Sum of the ages of 14 students	= (16 x 35) - (14 x 21)
= 560 - 294.
= 266.
∴ Required average	= 266 / 2
= 133 years.
Answer A
Answer: (A) 133 years
Question: The ratio of radius of a circle and the side of a square is 2 : 11. Find the ratio of their areas:
(A) 2 : 1
(B) 4 : 7
(C) 8 : 77
(D) 4 : 121
(E) None
Rationale: radius/side = 2/11
⇒ area of circle/area of square= 4/121
Answer: D
Answer: (D) 4 : 121