RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A Locomo's train rails across an open track at 250 kilometers per hour. A regular passenger train travels at 68% of the Locomo's train speed. If the two trains start moving from the same station at the same time, how much time longer will it take the passenger train than the Locomo's to travel 850 kilometers?
A.1 hour and 24 minutes.
B.1 hour and 36 minutes.
C.2 hours and 24 minutes.
D.2 hours and 36 minutes.
Answer: B.1 hour and 36 minutes.
Explanation: Difference in time = time taken by passenger train- time taken by Locomo's train
850/(250*68) *100 - 850/250
850 (100/ 250*68 - 1/250)
850*32/ (250*68)
1.6 hrs or 1 hr and 36 mins
B is the answer
Question: At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
A.1/3
B.1/4
C.3/8
D.2/9
Answer: D.2/9
Explanation: Males who did not arrive on time are 1/4*2/3 = 1/6 of the attendees.
Females who did not arrive on time are 1/6*1/3 = 1/18 of the attendees.
The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9
The answer is D.
Question: Four friends, Peter, John, Quincy, and Andrew, are pooling their money to buy a $1200 item. Peter has twice as much money as John. Quincy has $20 more than Peter. Andrew has 15% more than Quincy. If they put all their money together and spend the $1200, they will have $11 left. How much money does Peter have?
A.$320
B.$160
C.$200
D.$410
Answer: A.$320
Explanation: P= 2J ; Q= P+20 ; A= 1.15(Q)
P+J+Q+R-1200=11
P+0.5P+P+20+1.15(P+20) = 1211
P+0.5P+P+20+1.15P+23=1211
P+0.5P+P+1.15P+43=1211
P+0.5P+P+1.15P=1168
3.65P=1168
P=320
Answer:A
Question: If log 27 = 1.431, then the value of log 9 is:
A.0.934
B.0.945
C.0.954
D.0.958
Answer: C.0.954
Explanation: Explanation:
log 27 = 1.431
=log (33 ) = 1.431
=3 log 3 = 1.431
=log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
ANSWER IS C
Question: Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics?
A.7/12
B.4/9
C.5/9
D.1/4
Answer: C.5/9
Explanation: Lets pick smart numbers. Total number of students: 12
Biology (1/2): 6
Chemistry (1/3): 4
Physics (1/6): 2
After leaving school
Biology: 4
Chemistry: 4
Physics: 1
New Total number of students: 9
Biology and Physics: 5
Answer 5/9 or C
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Dollar 5400 interest only for the period. The principal amount borrowed by him was:
A.$ 18000
B.$ 13000
C.$ 14000
D.$ 15000
Answer: D.$ 15000
Explanation: D
$ 15000
Principal = Dollar (100 x 5400)/(12x3) = $ 15000.
Question: The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s?
A.23 1/2%
B.23 1/1%
C.23 1/3%
D.23 1/8%
Answer: C.23 1/3%
Explanation: y=100	x=130
130---------30
100---------? => 23 1/3%
Answer: C
Question: A can do a work in 8 days. B can do the same work in 16 days. If both A & B are working together in how many days they will finish the work?
A.3 days
B.16/3 days
C.3/4 days
D.9/12 days
Answer: B.16/3 days
Explanation: A rate = 1/8
B rate = 1/16
(A+B) rate = (1/8)+(1/16) = 3/16
A & B finish the work in 16/3days
correct option is B
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 10sec, then the speed of each train is?
A.30
B.108
C.36
D.25
Answer: B.108
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/10 => x = 30
Speed of each train = 30 m/sec.
= 30 * 18/5 =108km/hr.
Answer: Option B
Question: Julie drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 80 miles per hour. On the trip back she drives an average speed of 40 miles per hour. What is her approximate average speed for the round trip in miles per hour?
A.40
B.48.3
C.53.33
D.61.7
Answer: C.53.33
Explanation: Average speed = total distance/total time
Here distance to Julie's sister house and back is same as she takes the same route.
D = 80T1 and D=40T2
Therefore, T1 = D/80 and T2 = D/40
T1+T2 = 3d/80
Therefore, average speed = 2d/3d/80
=2d * 80/3d
Answer is 53.3 Since, the options are far away we need not solve till the decimal points
So correct answer is option C
Question: 4 dices are thrown at the same time. What is the probability of getting ONLY 2 dices showing the same face?
A.4/9
B.5/9
C.11/18
D.7/9
Answer: B.5/9
Explanation: Probability of getting two same faces: 1 and 1/6
For other two faces, probabilities: 5/6 and 4/6 respectively.
The dice combinations can be arranged in 4!/2! ways
Total probability = 1*1/6*5/6*4/6*4!/2! = 5/9
Answer:B
Question: 250 hundred multiples of seven are chosen at random, and 250 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
A.25.5%
B.26%
C.30%
D.25%
Answer: D.25%
Explanation: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....
Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.
So approx. 50 % of the 250 multiples are odd i.e 125 multiples.
--> Similalrly, for 8 multiples are:8,16,24...
All are even so 0 % are odd.
Total odd= (125+0)/(250+250)= 125/500=1/4 = 25%
Answer D
Question: A man sells an article at 5% loss. Had he sold it for Rs.60 more he could have gained 10%. What is the cost price of the article?
A.Rs.200/-
B.Rs.400/-
C.Rs.450/-
D.Rs.500/-
Answer: B.Rs.400/-
Explanation: Short cut method:
Loss =====> 5 %
Profit ====> 10 %
~
----------------
15 % ---------> Rs.60/-
100 % --------> Rs.400/-
Option B)
Question: If N is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT
A.z - w = 3(y - x)
B.N is divisible by 8
C.The average of w, x, y, and z is odd
D.N is divisible by 4
Answer: B.N is divisible by 8
Explanation: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.
N = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12
Focus on the easiest options first. You see that N is not divisible by 8. Answer (B)
Question: by combining number of small cubes, a larger cube is produced. the ratio between volume of larger cube and small cube is 1000:8 then how many small cubes are required to produce a larger cube?
A.100
B.2
C.5
D.125
Answer: D.125
Explanation: the ratio is a13:a23=1000:8
then number small cubes requiered is 1000/8=125
so the answre is D
Question: If 6Pr = 360 and If 6Cr = 15, find r ?
A.5
B.6
C.4
D.3
Answer: C.4
Explanation: Solution:
nPr = nCr�r!
6Pr = 15 *r!
360 =15 *r!
r! =360 /15 =24
r! = 4*3*2*1
=> r! =4!
Therefore, r = 4.
Answer: Option C
Question: Area of square with side x is equal to the area of a triangle with base x . The altitude of the triangle is
A.x/2
B.x
C.2x
D.4x
Answer: C.2x
Explanation: x^2 =1/2 Ãƒâ€” x Ãƒâ€” h or h = 2x^2/x = 2x
Answer : C
Question: The number of bacteria in a petri dish increased by 20 percent every 2 hours. If there were 72 million bacteria in the dish at 6: 00 p.m., at what time were there 50 million bacteria in the dish?
A.6: 00 p.m.
B.8: 00 p.m.
C.2: 00 p.m.
D.8: 00 a.m.
Answer: C.2: 00 p.m.
Explanation: Given:
he number of bacteria in a petri dish increased by 20 percent every 2 hours
There were 72 million bacteria in the dish at 6: 00 p.m
Since the bacteria is increasing by 20% every 2 hours, this means that the number is multiplied by 1.2 every 2 hours.
Required: At what time were there 50 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 50 million and 72 million.
50 * (1.2)^n = 72
(12/10)^n = 72/50 = 144/100 = (12/10)^2
Hence n = 2 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 4
Subtracting 4 hours from 6 PM, we get 2 PM as the answer.
Option C
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
A.1/6
B.1/7
C.1/5
D.1/9
Answer: C.1/5
Explanation: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $3,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
A.$21,700
B.$19,500
C.$20,200
D.$20,400
Answer: A.$21,700
Explanation: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 1500
Net price of the car in 02 = 18700 + 3000 = $21700
Correct Option: A
Question: The average mark of a class of thirty six students is 72. If three students whose marks are 32,28 and 34 are removed , then find the approximate average mark of the remaining students of the class.
A.71
B.74
C.57
D.76
Answer: D.76
Explanation: Exp. Total mark of 36 students = 72*36 = 2592,
Total mark after the removal of 3 students = 2592 –(32 +28+34 )
= 2592 – 94 = 2498
Approximate average mark = 2498/(36-3) = 2498/ 33 = 76
Answer: D
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A.18%
B.23%
C.44%
D.65%
Answer: C.44%
Explanation: g%
= 20 + 20 + (20*20)/100
= 44%
Answer:C
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least four ingredients? (Also assume that each bin can hold one and only one blend.)
A. 1
B. 4
C. 7
D. 11
Answer: A. 1
Explanation: We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 4 ingredients...
4 ingredient blends:
ABCD
Total blends = 1
A
Question: The sum of first five prime numbers is?
A.12
B.23
C.24
D.28
Answer: D.28
Explanation: Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
D
Question: If x^2 + y^2 = 18 and xy = 3, then (x − y)^2 =
A.8
B.11
C.14
D.12
Answer: D.12
Explanation: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 18-2*3=12..
Answer D
Question: How many words can be formed by using all letters of the word ‘ILLINOIS’ ?
A.40230
B.40320
C.30420
D.20340
Answer: B.40320
Explanation: Solution
The word ILLINOIS contains 8 different letters.
Required number of words = 8P8 = 8 ! = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 40320
Answer B
Question: The maximum numbers of students among them 561 toys and 510 pencils can be distributed in such a way that each student gets the same number of toys and same number of pencils is
A.91
B.910
C.1001
D.51
Answer: D.51
Explanation: olution
Required number of students.
= H.C.F of 561 and 510.
â€¹=â€º 51.
Answer D
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 15% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
A.11.7%
B.12.5%
C.15%
D.22%
Answer: A.11.7%
Explanation: Answer is A.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 10%+0,15X
id est X = 11,7%
Question: Find the odd man out.
6, 9, 15, 21, 24, 28, 30
A.28
B.27
C.26
D.98
Answer: A.28
Explanation: Explanation:
Each of the numbers except 28, is a multiple of 3.
Answer: A) 28
Question: How many numbers between 0 and 1470 have a prime tens digit and a prime units digit?
A.228
B.236
C.244
D.252
Answer: B.236
Explanation: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.
From 0 to 1400, there 16*14 = 224 such numbers.
From 1401 to 1470, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.
The total number is then 224+12 = 236
The answer is B.
Question: A box contains 20 machine parts, 5 of them being standard. A worker takes out 3 parts at random. Find the probability that at least 1 of 3 turns out to be standard.
A.137/228
B.13/228
C.91/228
D.41/228
Answer: A.137/228
Explanation: Explanation :
Let, E ≡ at least 1 of the 3 parts turns out to be standard.
P(E) = 1 - P(none is standard)
= 1 - (15C3 / 20C3 ).
= 1 - (15 x 14 x 13) / ( 20 x 19 x 18).
= 137/228.
Answer : A
Question: In a class of 42 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
A.1
B.5
C.8
D.13
Answer: A.1
Explanation: Total # of students = 42
Avg # of books per student = 2
Total # of books = 42*2 = 84
# of student borrowed at least 3 books = 42-2-12-10 =18
# of books borrowed by above 18 students =84-(12*1)+(10*2) = 52
Considering that 17 out of above 18 students borrowed only 3 books, # of books borrowed = 17*3 = 51
So maximum # of books borrowed by any single student = 52-51 = 1
Option A
Question: In 19 years time the combined ages of my three brothers will be 94. What will it be in nine years time?
A.45
B.62
C.82
D.97
Answer: C.82
Explanation: C
82
Combined age in 9 years time will 94 – (3 x (13 – 9))
94 – 12 = 82.
Question: The population of City A for each of three years is shown in the table above. If the population grew by m percent from 1970 to 1980 and n percent from 1980 to 1990, then m exceeds n by how much?
A.37.5
B.20
C.17.5
D.15
Answer: C.17.5
Explanation: 70 - 80
m = (55-40)/40 = 3/8
80 - 90
n = (66-55)/55 = 1/5
m - n
3/8 - 1/5 = 7/40 = 17.5%
ANSWER:C
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A.6 minutes
B.8 minutes
C.5 minutes
D.2 minutes
Answer: B.8 minutes
Explanation: Required time =12*24/12+12=12*24/36
=24/3=8 minutes
ANSWER:B
Question: A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 7 adults have their meal, find the total number of children that can be catered with the remaining food.
A.33
B.54
C.81
D.17
Answer: C.81
Explanation: Explanation:
As there is meal for 70 adults and 7 have their meal, the meal left can be catered to 63 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 63 adults = 81 children
Hence, the meal can be catered to 81 children.
ANSWER: C
Question: The length of a rectangular landscape is 12 times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/4rd of the total landscape. What is the length of the landscape?
A.90
B.120
C.240
D.180
Answer: C.240
Explanation: Sol. x *12x = 4 * 1200
x = 20
Length = 12 * 20 = 240
C
Question: The compound ratio of 2:3, 3:2 and 4:5?
A.1:9
B.1:7
C.1:2
D.4:5
Answer: D.4:5
Explanation: 2/3 * 3/2 * 4/5
= 4/5
=4:5
Answer: D
Question: A person lent a certain sum of money at 6% per annum at simple interest and in 8 years the interest amounted to $520 less than the sum lent. What was the sum lent?
A.800
B.1000
C.1200
D.1400
Answer: B.1000
Explanation: P - 520 = (P*6*8)/100
P = 1000
The answer is B.
Question: After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.4 cubic inches, what is the original volume of the cubic ice, in cubic inches?
A.2.5
B.3.0
C.4.0
D.6.4
Answer: D.6.4
Explanation: Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.4
x = 6.4
Alternate solution: Try to backsolve.
Initial volume = 6.4
After one hour --> (1/4)6.4 = 1.6
After two hours --> (1/4)1.6 = 0.4
Answer: D
Question: Lucy deposited $62500 in an investment fund that provided 24 percent annual return compounded half yearly.If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $10400?
A.0.5
B.2
C.12
D.6
Answer: C.12
Explanation: A = P + I = 62500 + 10400 = 72900
72900 = 62500(1 + 24/2*100)^(2t)
(676/625) = (112/100)^(2t)
(27/25)^2 = (27/25)^2t
t = 1yrs = 12 months
Answer: C
Question: How much time will a train of length 280 m moving at a speed of 72 kmph take to cross another train of length 360 m, moving at 36 kmph in the same direction?
A.50
B.99
C.64
D.76
Answer: C.64
Explanation: The distance to be covered = Sum of their lengths = 280 + 360 = 640 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 640/10 = 64 sec.
Answer:C
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
A.3630
B.4000
C.4200
D.4400
Answer: A.3630
Explanation: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 = 3630
A)
Question: 862.68 âˆ’ 4.5 + 108.98 = ? âˆ’ 2132.54
A.6078.58
B.5225.9
C.6258.58
D.6088.58
Answer: D.6088.58
Explanation: Option 'D'
Question: Mrs. Rodger got a weekly raise of $165. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
A.$204
B.$231
C.$156
D.$165
Answer: D.$165
Explanation: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 165.
So after completing the 1st week she will get $ (x+165).
Similarly after completing the 2nd week she will get $ (x + 165) + $ 165.
= $ (x + 165 + 165)
= $ (x + 330)
So in this way end of every week her salary will increase by $ 165.
D
Question: Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
A.6400
B.6500
C.7200
D.7500
Answer: A.6400
Explanation: Explanation :
Let the investment in scheme A be Rs.x
and the investment in scheme B be Rs.(13900 - x)
We know that SI = PRT/100
Simple Interest for Rs.x in 2 years at 14% p.a. = x×14×2/100=28x/100
Simple Interest for Rs.(13900 - x) in 2 years at 11% p.a. = (13900−x)×11×2/100
=22(13900−x)/100
Total interest = Rs.3508
28x/100+22(13900−x)/100=3508
28x+305800−22x=350800
6x=45000
x=45000/6=7500
Investment in scheme B = 13900 - 7500 = Rs.6400
Answer : Option A
Question: The average age of 15 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
A.22
B.37
C.99
D.38
Answer: B.37
Explanation: total age increased = (15 * 2) years = 30 years.
Sum of ages of two new men = (21 + 23 + 30) years = 74 years
Average age of two new men = (74/2) years = 37 years.
Answer: B
Question: A company pays project contractors a rate ofadollars for the first hour andbdollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 4 and 8 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
A.Per month, with savings of $(3a + 3b)
B.Per month, with savings of $(3a - 3b)
C.The two options would cost an equal amount.
D.Per project, with savings of $(3a + 3b)
Answer: B.Per month, with savings of $(3a - 3b)
Explanation: Per Project, company will pay as follows:
For 4 hours work = a+3b
For 8 hours work = a+7b
Total = 2a+10b
Per Month, company will pay for 12 hours work = a+11b
Total per contract - total per month
4a+8b - (a+11b)
3a-3b
Since a>b Amount 4a+8b(per contract amount) > a+11b (per project amount) by 3a-3b.
Hence per month payment will be cheaper by 3a-3b .
OA B
Question: It takes six minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video?
A.13.8
B.14.1
C.14.4
D.14.6
Answer: C.14.4
Explanation: The laptop can load the video at a rate of 1/15 of the video per second.
The phone can load the video at a rate of 1/(60*6) = 1/360 of the video per second.
The combined rate is 1/15 + 1/360 = 25/360 of the video per second.
The time required to load the video is 360/25 = 14.4 seconds.
The answer is C.
Question: In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
A.45
B.56
C.47
D.57
Answer: C.47
Explanation: Explanation: With all the talk of doubling and halves, your brain jumps to the conclusion that to solve the problem of when the lily patch covers half the lake, all you have to do is divide the number of days it took to fill the lake (48) in half. It's understandable but wrong.
The problem says that the patch DOUBLES in size every day, which means that on any day, the lily patch was half the size the day before. So if the patch reaches the entire size of the lake on the 48th day, it means the lily pad was half the size of the lake on day 47.
correct answer is C)47
Question: The sum of two numbers is 16 and the sum of their squares is 113. Find the
numbers.
A.1 and 2
B.4 and 5
C.7 and 8
D.2 and 3
Answer: C.7 and 8
Explanation: Let the numbers be x and (15 - x).
Then, x2 + (15 - x)2 = 113 =>	x2 + 225 + X2 - 30x = 113
=> 2x2 - 30x + 112 = 0 => x2 - 15x + 56 = 0
=> (x - 7) (x - 8) = 0 => x = 7 or x = 8.
So, the numbers are 7 and 8.
Answer is C
Question: In how many ways can the letters of the word 'LEADER' be arranged?
A.90
B.180
C.360
D.60
Answer: C.360
Explanation: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Therefore, Required number of ways = 6!/(1!)(2!)(1!)(1!)(1!)= 360.
Answer is C.
Question: If x and y are integers and x=50y + 49, which of the following must be odd?
A.xy
B.x + y
C.x + 4y
D.3x-1
Answer: C.x + 4y
Explanation: x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.
A: odd * even = even ; odd*odd= odd ->not true
B: odd + odd = even ; odd+even = odd -> not true
C: odd + 4*odd = odd ; odd + 2*even = odd -> TRUE, stop here.
D&E -- EVEN
Answer C
Question: In a test, sixty percent students passed in Maths and 65% in History, 40% passed in both of these subjects. If 90 students failed in maths and history both, then what is the total number of students?
A.600
B.650
C.700
D.750
Answer: A.600
Explanation: Explanation :
Solution: let the total number of students be x.
Number passed in one or both is given by : n( A U B) = n(A)+n(B) -n( A ^ B).
= 60% of x+65% of x-40% of x
= (60/100 * x + 65/100 * x - 40/100 * x)
= 85x/100 = 17x/20.
Failed in both = (x - 17x/20) = 3x/20.
.'. 3x/20 =90
x = 90*20/3 = 600.
Answer : A