mathewhe/aqua_rat huggingface dataset:
Question: Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?
(A) 1 pm
(B) 2 pm
(C) 3 pm
(D) 4 pm
(E) 5 pm
Rationale: Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the Printer were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
A
Answer: (A) 1 pm
Question: Of the three- digit integers greater than 700, how many have two digits T that are equal to each other and the remaining digit different from the other two?
(A) 90
(B) 82
(C) 80
(D) 45
(E) 36
Rationale: three-digit integers greater than 700: 701 to 999, inclusive.
possible values for hundreds-digit--> 7,8,9
possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9
when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999
when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999
when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700
T=27+27+26 = 80
Answer: C
Answer: (C) 80
Question: Find the number of divisors of 1728.?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: 1728= 2^6 * 3^3
Hence the Number of factors = (6+1) x (3+1) = 7 x 4 = 28.
We know that if a number represented in standard form (a^m *b^n) , then the number of factors Is given by (m+1)(n+1).
Answer is 28
ANSWER:C
Answer: (C) 28
Question: Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $400, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
(A) 12000
(B) 13000
(C) 14000
(D) 15000
(E) 16000
Rationale: The average price of 25 products is $1,200 means that the total price of 25 products is 25*1,200=$30,000.
Next, since exactly 10 of the products sell for less than $1,000, then let's make these 10 items to be at $400 each (min possible).
Now, the remaining 14 items cannot be priced less than $1,000, thus the minimum possible price of each of these 14 items is $1,000.
Thus the minimum possible value of 24 products is 10*400+14*1,000=$18,000.
Therefore, the greatest possible selling price of the most expensive product is $30,000-$18,000=$12,000.
Answer: A.
Answer: (A) 12000
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
(A) 7
(B) 5
(C) 8
(D) 6
(E) 4
Rationale: Explanation:
33 + 43 + 53 = a3 => a = 6
Answer: Option D
Answer: (D) 6
Question: A teacher prepares a test. She gives 8 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 5 questions have 3 choices and the last 3 have 4 choices.
(A) 6255
(B) 5280
(C) 5192
(D) 5100
(E) 5144
Rationale: Two cases.
First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices
5C2 * 3C2 ways to select the questions
3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions
= 10 * 3 * 3 * 3 * 4 * 4
= 4320
Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices
5C1 * 3C3 ways to select the questions
3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions
= 5 * 1 * 3 * 4 * 4 * 4
= 960
Total = 4320 + 960
=5280
B
Answer: (B) 5280
Question: What is the units digit of the product of the first 15 odd numbers?
(A) 0
(B) 5
(C) 1
(D) 2
(E) 3
Rationale: 1*3*5*7 ................... will end up in 5 in the units place
Answer : B
Answer: (B) 5
Question: If s,u, and v are positive integers and s=2u+2v, which of the following must be true?
i. s=u
ii. u is not equal to v
iii. s > v
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III
Rationale: Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.
Given: s=2u+2v --> s/2=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's may be necessarily true,
Answer: A
Answer: (A) None
Question: If n divided by 9 has a remainder of 8, what is the remainder when 2 times n is divided by 9?
(A) 1
(B) 7
(C) 3
(D) 5
(E) 6
Rationale: As per question => N=9P+8 for some integer p
hence 2N => 18Q + 16
But again, 16 can be divided by 9 to get remainder 7 for some integer Q
hence B
Answer: (B) 7
Question: On a certain scale of intensity, each increment of 20 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 125?
(A) 40
(B) 100
(C) 400
(D) 1000
(E) 10 000
Rationale: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 165 it'll be 10*10*10*10*x=400*x.
Answer: B.
Answer: (B) 100
Question: The present value of a bill due at the end of 2 years is Rs.1250. If the bill were due at the end of 2 years and 11 months, its present worth would be Rs.1200. Find the rate of interest and the sum.
(A) rs.1175
(B) rs.1375
(C) rs.1475
(D) rs.1575
(E) None of these
Rationale: Explanation:
PW=100xAmount/100+(Rx T)
Answer: B
Answer: (B) rs.1375
Question: A five-character password consists of one letter of the alphabet and four different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 5,040
(B) 18,720
(C) 262,000
(D) 137,440
(E) 262,080
Rationale: 4 character password: DLDD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
Next digit can be chosen in 8 ways.
Next digit can be chosen in 8 ways.
This gives us 10*26*9*8*7 ways
Now, the letter can also be DDLDD so there will be another 10*9*26*8*7 ways
Total = 10*26*9*8*7*2 = 262,080 ways
E
Answer: (E) 262,080
Question: Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59 Then find the seventh result?
(A) 120
(B) 123
(C) 125
(D) 128
(E) 130
Rationale: 125
Option 'C'
Answer: (C) 125
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $195 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
(A) 17,010
(B) 2,100
(C) 1,890
(D) 1,950
(E) 210
Rationale: 10% ---- 195 millions
for 100% => ( 195 * 100% )/10% = 1950.
Option D.
Answer: (D) 1,950
Question: How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?
(A) 10,300
(B) 10,030
(C) 1,353
(D) 1,352
(E) 1,339
Rationale: There is one number in hundred with 1 in th tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 324,700 and 458,600 is 458,600-324,700=133,900 - one number per each hundred gives 133,900/100=1,339 numbers.
Answer: E
Answer: (E) 1,339
Question: A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 13, 5
(B) 15, 2
(C) 15, 5
(D) 14, 5
(E) 12, 5
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 20--- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 5.
Answer:C
Answer: (C) 15, 5
Question: A 24 month project had a total budget of $60,000. After eleven months, the project had spent $26,300. At this point, how much was the project under budget?
(A) $800
(B) $1000
(C) $1200
(D) $1400
(E) $1600
Rationale: Each month, the project should spend $60,000 / 24 = $2500.
In 11 months, the project should spend 11*$2500=$27,500.
The project is under budget by $27,500 - $26,300 = $1200.
The answer is C.
Answer: (C) $1200
Question: At a loading dock, each worker on the night crew loaded 1/2 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/7
Rationale: Method: X = No. of boxes loaded by day crew.
Boxes by night crew = 1/2 * 4/5 X = 2/5 X
% loaded by day crew = X/(X + 2/5X) = 5/7
Answer E
Answer: (E) 5/7
Question: Of the science books in a certain supply room, 60 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 334
Rationale: I solve it using the tough luck technique:
According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.
80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=110>80
Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books
What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.
We picked:
60 Botany Books
65 Zoology Books
50 Geology Books
Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!
Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick
79*2+1 books
Because, we could have picked the books in following order;
1st book picked: Physics
2nd book picked: Chemistry
3rd book picked: Physics
Thus, Total= 60+65+50+79*2+1=175+1+158=334
Ans:E
Answer: (E) 334
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 2:5. The first number is:
(A) A)33
(B) B)98
(C) C)34
(D) D)35
(E) E)62
Rationale: (3x-9):(5x-9) = 2:5
x = 11 => 3x = 33
Answer:A
Answer: (A) A)33
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 15% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is:
(A) 4000
(B) 24000
(C) 8000
(D) 10000
(E) None of these
Rationale: Total expenditure = 40 + 25 + 15 + 15 = 95%
Saving = (100 - 95) = 5%
5/100 × Salary = 1200, Salary = 24000 Rs.
Answer:B
Answer: (B) 24000
Question: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 20 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
(A)  4
(B)  5
(C)  6
(D)  16
(E)  24
Rationale: Total work = 4*20 machine hrs
Time taken = 4* 20 /5 => 16 hours...
Thus all five machines, operating simultaneously will take ( 20 - 16 ) 4 hours..
Answer will be (A) 4
Answer: (A)  4
Question: Four years ago, the average age of a family of 4 members was 21 years.A baby having been born,the average age of the family is the same today.The present age of the baby?
(A) 5 years
(B) 7 years
(C) 2 years
(D) 3 years
(E) 6 years
Rationale: Total age of the 4 members, 4 years ago = (21*4)= 84 years.
Total age of the 4 members now =( 84+ 4*4) years =100 years.
Total age of the 5 members now = (21*5) = 105 years.
Age of the baby is = 105- 100= 5 years
Answer :A
Answer: (A) 5 years
Question: How many 1/10s are there in 37 1/2?
(A) 375
(B) 475
(C) 500
(D) 670
(E) 700
Rationale: Required number = (75/2)/(1/10)
= (75/2 x 10/1)
= 375.
ANSWER:A
Answer: (A) 375
Question: a light flashes every 5seconds, how many times will it flash in ? of an hour?
(A) 720
(B) 600
(C) 650
(D) 700
(E) 750
Rationale: 1flash=5sec
for 1 min=12flashes
so for 1 hour=12*60=720 flashes.
ANSWER:A
Answer: (A) 720
Question: RADIO X sells cheap radios for commercial use by buying surplus supplies. A surplus bag of 100 diodes costs $2.00. A surplus bag of diodes, on average, has 10% faulty diodes (the faulty diodes are thrown away, and the remaining diodes are used in production). It takes 5 diodes to make 1 circuit board. If it takes 3 circuit boards to make a radio, how much money is needed to buy diodes to make x number of radios, in dollars?
(A) x/3
(B) 3x
(C) 2x/3
(D) x
(E) 3x/4
Rationale: Initial cost for 1 bag of diodes = $2, but ONLY 100(1 - 0.1) = 90 are used. So the cost for 90 diodes = $2. The number of diodes for making a radio is (3 circuit boards)(5 diodes) = 15 diodes. So, the cost for diodes to make a radio is $2(15/90) = $1/3.
$x/3 =cost of diodes to make x number of radios.
Answer is A
Answer: (A) x/3
Question: A Positive number which when added to 999 given a sum which is greater than when it is multiplied by 999. Which of the following could be the value of the positive integer?
(A) 5
(B) 3
(C) 1
(D) 2
(E) 4
Rationale: Explanation:
Let the positive integer = x
Then, 999 + x > 999x
By trial and error, when x = 1,
1000 > 999
So, the required positive integer is 1,
1000 > 999
So, the required positive integer is 1.
Answer: Option C
Answer: (C) 1
Question: X starts a business with Rs.77000. Y joins in the business after 5 months with Rs.42000. What will be the ratio in which they should share the profit at the end of the year?
(A) 21:23
(B) 23:45
(C) 22:7
(D) 25:29
(E) None of these
Rationale: Explanation :
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 77000 * 12: 42000 * 7
= 77 * 12: 42 * 7
= 11*2: 7
= 22:7.
Answer : Option C
Answer: (C) 22:7
Question: A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds in passing him. The speed of the train was
(A) 25.2 km/hr
(B) 32.4 km/hr
(C) 50.4 km/hr
(D) 75.6 km/hr.
(E) None of these
Rationale: Explanation:
Let the train’s length be L m.
L/9=(L+84)/21
21 L = 9L +756
12L= 756
L=63 m
Speed = 63 /9 = 7 m/s = 7 x 18/5 = 25.2 Km/hr.
Answer A
Answer: (A) 25.2 km/hr
Question: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
(A) 20 kmph
(B) 30 kmph
(C) 87 kmph
(D) 99 kmph
(E) 77 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance
= 40 * 3x = 120x km
He covered 2/3 * 120x = 80x km in 1/3 * 3x
= x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed
= 40x/2x = 20 kmph.
Answer:A
Answer: (A) 20 kmph
Question: When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?
(A) 9
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: The given number =7y86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(9+y) = divisible by 11
14 � y = divisible by 11.
Y must be 3, to make given number divisible by 11.
C
Answer: (C) 11
Question: A certain city with a population of 108,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 10,700
(B) b) 10,800
(C) c) 9,000
(D) d) 11,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 108k
x = 9,000
Answer : C
Answer: (C) c) 9,000
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is seven times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 1:1
(B) 2:3
(C) 3:2
(D) 9:4
(E) 63:8
Rationale: Water:soap = 3:2
Soap:Salt=21:2
=> For 21 soap, salt = 2
=> For 2 Soap, salt = (2/21)*2 = 4/21
So, water:soap:salt = 3:2:4/21 = 63:42:4
After open container, water:soap:salt = 31.5:42:4
So, water:salt = 31.5:4 = 63:8
E
Answer: (E) 63:8
Question: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
(A) 6
(B) 7
(C) 9
(D) 5
(E) 3
Rationale: 4/10 + 9/x = 1 => x = 15
1/10 + 1/15 = 1/6 => 6 days
Answer: A
Answer: (A) 6
Question: Set A: 3, r, 8, 10
Set B: 4, g, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of g – r?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: So we have even no. of elements in the Set
So median is the average of Middle two numbers
(r+8)/2= (g+9)/2
g - r= -1
Answer B
Answer: (B) -1
Question: A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?
(A) 3 : 9
(B) 3 : 7
(C) 3 : 8
(D) 3 : 4
(E) 3 : 1
Rationale: Since S # 1/t
S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4
Answer:D
Answer: (D) 3 : 4
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
(A) 6
(B) 9
(C) 12
(D) 18
(E) 19
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: (C) 12
Question: What is the sum of all consecutive integers from 10 to 100, inclusive?
(A) 4550
(B) 4950
(C) 5005
(D) 5500
(E) 5555
Rationale: SUM= n/2(Starting number+ Ending number)
n: total numbers between the starting no. and ending no.
n= 100-10+1= 91
SUM= (91/2)*(10+100)
= 91*55
=5005
Hence, answer C
Answer: (C) 5005
Question: How many three digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 11?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: A number is divisible by 11 when Difference of Sums of even place digits and odd place digits is either zero or a multiple of 11.
i.e. a 3-Digit Number abc will be divisible by 11 if (a+c) - b = 0 or multiple of 11
@b=1, a+c should be 1 or 12 i.e. (a,c) can be (5, 7), (7, 5) --- 2 cases
@b=2, a+c should be 2 or 13 i.e. (a,c) can be (6, 7), (7, 6) ---- 2 cases
@b=3, a+c should be 3 or 14 i.e. (a,c) can be (1, 2), (2, 1) ---- 2 cases
@b=4, a+c should be 4 or 15 i.e. (a,c) can be (1, 3), (3, 1) ---- 2 cases
@b=5, a+c should be 5 or 16 i.e. (a,c) can be (1, 4), (2, 3), (3, 2), (4, 1) ---- 4 cases
@b=6, a+c should be 6 or 17 i.e. (a,c) can be (1, 5), (2, 4), (4, 2), (5, 1) ---- 4 cases
@b=7, a+c should be 7 or 18 i.e. (a,c) can be (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) ---- 6 cases
Total Cases = 2+2+2+2+4+4+6 = 22 cases
Answer: option E
Answer: (E) 22
Question: A boat having a length 5 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is
(A) 12 kg
(B) 60 kg
(C) 72 kg
(D) 96 kg
(E) None
Rationale: Solution
Volume of water displaced	= (5 x 3 x 0.01)m3
= 0.15m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.15×1000) kg
= 150 kg.
Answer E
Answer: (E) None
Question: An article is bought for Rs.800 and sold for Rs.1200, find the loss percent?
(A) 55%
(B) 25.25%
(C) 33.33%
(D) 45%
(E) 50%
Rationale: 800 ---- 400
400 ---- ? => 50%
Answer: E
Answer: (E) 50%
Question: Average age of 7 members of a family is 29 years. If present age of the youngest member is 5 year, find average age of the remaining members at the time of birth of the youngest member.
(A) 28
(B) 37
(C) 29
(D) 237
(E) 212
Rationale: Average age (present) of 7 members = 29 years
5 years ago, average age of 7 members was 29 - 5 = 24 years.
Since, the youngest member was not born 5 years ago.
Therefore, Average age of remaining 6 members is increased by 246246 = 4 years.
Therefore, 5 years ago, average age of 6 members was 24 + 4 = 28 years.
Answer:A
Answer: (A) 28
Question: What is the probability of finding exactly 33 multiples of 3 when 100 consecutive
natural nos are selected?
(A) 1/3
(B) 2/3
(C) 1
(D) 2
(E) none of these
Rationale: out of 3x,3x+1,3x+2 as starting numbers,
Only case when starting no. is 3x we'll get 34 multiples of 3.
ANSWER:B
Answer: (B) 2/3
Question: What is the probability that a three digit number is divisible by 7?
(A) 1/7
(B) 127/900
(C) 32/225
(D) 129/900
(E) 1/8
Rationale: Total 3 digit integers which are divisible by 7 :
(994-105)/7+1 = 128
The total number of 3 digit integers = (999-100)+1 = 900
The required probability : 128/900 = 32/225
answer:C.
Answer: (C) 32/225
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:
(A) 5324
(B) 5334
(C) 5336
(D) 5356
(E) 5400
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336.
C
Answer: (C) 5336
Question: How much space, in cubic units, is left vacant when maximum number of 5x5x5 cubes are fitted in a rectangular box measuring 10x15x18 ?
(A) 50
(B) 150
(C) 250
(D) 350
(E) 450
Rationale: No of cubes that can be accommodated in box = (10*15*18)/(5*5*5)
15*10 in numerator can be perfectly divided by 5*5 in denominator.
side with length 18 can't be perfectly divided by 5 and hence is the limiting factor. Closet multiple of 5 less that 18 is 15. so vacant area in cube =
=15*10*(18-15)
=15*10*3
=450
Ans - E
Answer: (E) 450
Question: If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?
(A) -22.5
(B) 16
(C) -10.5
(D) -17.5
(E) None
Rationale: Explanatory Answer
We know that the product of the roots of a quadratic equation ax2 + bx + c = 0 is
In the given equation, x2 + mx + 24 = 0, the product of the roots = = 24.
The question states that one of the roots of this equation = 1.5.
If x1 and x2 are the roots of the given quadratic equation and let x1 = 1.5.
Therefore, x2 == 16.
In the given equation, m is the co-efficient of the x term.
We know that the sum of the roots of the quadratic equation ax2 + bx + c = 0 is = -m
Sum of the roots = 16 + 1. 5 = 17 = -17.5.
Therefore, the value of m = -17.5
Answer D
Answer: (D) -17.5
Question: If the wheel is 8 cm then the number of revolutions to cover a distance of 948 cm is?
(A) 11
(B) 14
(C) 14
(D) 12
(E) 19
Rationale: 2 * 22/7 * 8 * x = 948 => x = 18.9
Answer: E
Answer: (E) 19
Question: When toys are grouped into 12 and 18, always 3 toys remain ungrouped. What is the minimum number of toys to be added so that when they are grouped into 7, no toys will remain ungrouped ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: T= 12a+3 = 18b + 3
2a=3b --> min (a,b) = (3,2)
So minimum number of toys --> 12*3+3 = 39
When toys are grouped into 7, 4 will remain ungrouped so in order to make another group of 7 toys -->
7-4 = 3 toys at least to be added.
ANSWER: D
Answer: (D) 3
Question: The expenditure of a businessman increase consistently by 10% per year. If his present expenditure is Rs. 20000 then what will his expenditure be after 2 years ?
(A) 24500
(B) 24400
(C) 24300
(D) 24200
(E) 24100
Rationale: Explanation :
Expenditure = 20000 x 1.1 x 1.1 = 24200
Answer : Option D
Answer: (D) 24200