RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A can do a job in 3 days less time than B. A works at it alone for 4 days and then B takes over and completes it. If altogether 14 days were required to finish the job, how many days would each of them take alone to finish it?
A.17 days, 20 days
B.12 days, 15 days
C.13 days, 16 days
D.14 days, 11 days
Answer: B.12 days, 15 days
Explanation: Let B can finish the work in x days.
Then A can finish the work in (x – 3) days.
B’s one day’s work = 1⁄xth work.
A’s one day’s work = 1⁄(x - 3)th work.
A’s 4 days’ work = 4⁄(x - 3)th work.
Remaining work = 1 - 4⁄(x - 3) = x−7 /x−3
The remaining work done by B in 14 – 4 = 10 days.
Now, in 10 days, work done by B = x−7/x−3th work.
∴ in 1 day, work done by B = 110(x−7/x−3) th work.
and 1/10(x−7/x−3)=1/x
⇒ x = 15 days
∴ B → 15 days and A → 12 days
Answer B
Question: The average weight of a group of boys is 20 kg. After a boy of weight 25 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
A.7.0
B.5.0
C.6.0
D.4.0
Answer: D.4.0
Explanation: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 25 kg joins the group, total weight of boys = 20x + 25
So 20x + 25 = 21(x + 1) = > x = 4.
Answer: D
Question: A military garrison in a wild frontier has 600 men who have provisions to last 20 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
A.13 1/3
B.9 1/3
C.11 3/3
D.12 1/2
Answer: B.9 1/3
Explanation: Total provisions=600*20*7=84000
Provisions used for in 6 weeks=6*7*600=25200
remaining provisions=58800
remaining provisions need to be split between 900(600+300) people.
Number of provisions per person= 58800/900
we need to find the answer in terms of weeks=(58800/900)/7=9 1/3
Answer:B
Question: Two trains of length 60 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
A.10 sec
B.32 sec
C.17 sec
D.20 sec
Answer: C.17 sec
Explanation: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 60 + 280 = 400 m.
The time required = d/s = 340/20 = 20 sec.
Answer:C
Question: Tough and Tricky questions: Functions.
Let a be a positive integer. Let n#a equal n^(2a) . Then (2#3) + (3#2) – (3#3) is equal to
A.64
B.82
C.-584
D.512
Answer: C.-584
Explanation: Answer:
2^6 + 3^4 - 3^6 = -584
ANs C
Question: Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 500 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?
A.1:40 PM
B.1:50 PM
C.2:05 PM
D.2:10 PM
Answer: C.2:05 PM
Explanation: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.
Now, total words typed by Bobby would be 500+60t and we want that number to be 200 less than 80t: 500+60t=80t-200 --> t=35.
1:30 PM + 35 minutes = 2:05 PM.
Answer: C.
Question: How many of the positive divisors of 120 are also multiples of 4 not including 120?
A.3.
B.4.
C.5.
D.7.
Answer: C.5.
Explanation: Given to find the positive divisors of 120 and condition is that divisors have to be multiple of 4 but not including 120.
Consider factors of 120
4 * 30
6 * 20
15 * 8
24 * 5
60 * 2
Total we get 5 different ways and all are part of 4.
Answer:C is correct option.
Question: Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 81 hours and 9 hours respectively. The ratio of their speeds is
A.1 : 2
B.2 : 3
C.1 : 3
D.4 : 5
Answer: C.1 : 3
Explanation: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √9 : √81
= 3 : 9. => 1 : 3
Answer C
Question: In a group of cows and hens, the number of legs are 20 more than twice the number of heads. The number of cows is
A.5
B.7
C.10
D.12
Answer: C.10
Explanation: Explanation:
Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 20
4x + 2y = 2x + 2y + 20
2x = 20
x = 10
Answer: C
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
A.172
B.268
C.215
D.257
Answer: C.215
Explanation: Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 216 - 1 =215.
Answer: C
Question: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 40 pints of Perfect Pink paint?
A.9
B.16
C.21
D.25 1/3
Answer: C.21
Explanation: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
40 pints will require 9/17 * 40= 21 pints..
C
Question: The proportion of the ages of Pooja and Charlie is 2 : 5, After 8 years, their ages will be in the proportion of 1 : 2. Then what is the variance in their current ages?
A.36 years
B.28 years
C.24 years
D.19 years
Answer: C.24 years
Explanation: C
24 years
Let Pooja’s age = 2A
and Charlie’s age = 5A
(2A + 8)/(5A+8)= (1/2)
=> 2 (2A + 8) = 5A + 8
=> A = 8
Pooja’s age = 16 years
and Charlie’s age = 40 years
variance of their ages = 24 years.
Question: The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 50 minutes after it was poured was how many degrees Fahrenheit?
A.63.75
B.75
C.80
D.85
Answer: A.63.75
Explanation: Answer: B
The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 50 minutes after it was poured is:
F = 120 ( 2 ^ -50/10) + 60
F = 120 * 1/ 32 + 60
F = 15/4 + 60
F = 255/4=63.75
A
Question: A man can row 9 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.98
B.9.98
C.9.06
D.9.87
Answer: C.9.06
Explanation: M = 9
S = 1.2
DS = 7.2
US = 10.8
x/10.8 + x/7.8 = 1
x = 4.53
D = 4.53 * 2 = 9.06
Answer:C
Question: Two employees X and Y are paid a total of Rs. 560 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A.s.254
B.s.284
C.s.290
D.s.304
Answer: A.s.254
Explanation: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 560
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 560
⇒ y[12/10 + 1] = 560
⇒ 22y/10 = 560
⇒ 22y = 5600
⇒ y = 5600/22 = Rs.254 (Approx)
A)
Question: 1480 men have provisions for 14 days. If 460 more men join them, for how many days will the provisions last now?
A.9.9
B.8.0
C.12.5
D.12.2
Answer: A.9.9
Explanation: 1480*13 = 1940*x
x = 9.9
Answer:A
Question: Given a certain number (Q), find Q given that 1 is 5% of 25% of Q?
A.80
B.60
C.95
D.100
Answer: A.80
Explanation: Using elimination method to pick the correct option it will be discovered that option A i.e 80 is the correct option because 25% of 80 is 20 and 5% of 20 is 1.
ANSWER:A
Question: Ravi purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
A.23%
B.1.2%
C.5.6%
D.34.1%
Answer: C.5.6%
Explanation: C
C.P. of 1 toy = 375/12 = Rs. 31.25
S.P of 1 toy = Rs. 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
A.4/5 km
B.4/6 km
C.4/9 km
D.4/1 km
Answer: A.4/5 km
Explanation: x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
Question: Rebecca's annual income is $20,and Jimmy's annual income is $10,. By how much must Rebecca's annual income increase so that it constitutes 55% of Rebecca and Jimmy's combined income?
A.8
B.9
C.7.77
D.10
Answer: C.7.77
Explanation: total rebecca = x+20; total = x+20+10
x+20/x+30 = 55/100 therefore x =7.77
C
Question: How many positive integers arethere from 0 to 1000 that leave a remainder of 3 on division by 7 & a remainder of 2 on division by 4?
A.30
B.36
C.38
D.42
Answer: B.36
Explanation: Number should be of the form 7n + 3 and 4m + 2.
The LCM of 7 and 4 is 28. So, let us see what are the possible remainders when we divide this number by 28.
A number of the form 7n + 3 can be written as 28K + 3 or 28k + 10 or 28 + 17 or 28k + 24.
A number of the form 4m + 2 can be written as 28l + 2, 28l + 6, 28l + 10, 28l + 14, 28l + 18, 28l + 22, 28l + 26.
For a detailed discussion on how we get to this, look at this post.
Within these, the only common term is 28K + 10.
The numbers in this sequence are 10, 38, 66.....990.
We still need to figure out how many numbers are there in this sequence. We are going in steps of 28, so let us see if we can write these numbers in terms of 28p + r.
10 = 28 * 0 + 10
38 = 28 * 1 + 10
66 = 28 * 2 + 10
94 = 28 * 3 + 10
...........................
990 = 28 * 35 + 10
There are 36 numbers in this sequence.
Correct Answer: 36
B
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
A.5/6
B.5/9
C.2/9
D.5/7
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 =5/9.
Answer:B
Question: A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of C square inches. Which of the following equations must be true?
A.2W^2 + PW + 2C = 0
B.2W^2 − PW + 2C = 0
C.2W^2 − PW − 2C = 0
D.W^2 + PW + C = 0
Answer: B.2W^2 − PW + 2C = 0
Explanation: P = 2(L+W)-----------------1)
C= LW------------------------2)
option A is not possible why ?? because all the terms are positive.
lets try option B , put value of P and A from 1 and 2 we have,
2W^2-2(L+W)W + 2(LW)
2W^2 - 2LW - 2W^2 + 2LW=0.
hence answer is B.
Question: If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms R in the sequence are smaller than the average
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: Let the sequence have N terms starting 18*K
--> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.
The sum of the sequence is
---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).
So the average is
153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).
On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).
By *), **) we have K=2, N=14.
Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms R which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C.
Question: Which expression is the greatest?
A.3252/3257
B.3456/3461
C.3591/3596
D.3346/3351
Answer: C.3591/3596
Explanation: Let 3252/3257 be the original fraction.
Notice that it is a positive Proper fraction.
Hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one.
Hence we just have to pick the number that adds the greatest value to both the numerator and the denominator.
Options can be re-written as (x-5)x => 1-(5/x)
A) 1- (5/3257)
B) 1- (5/3461)
C) 1- (5/3596)
D) 1- (5/3351)
E) 1- (5/3458)
ANSWER:C
Question: If the mode of Set D is equal to the median of Set D, Set D could be
A.[0, 1, 2, 2, 3, 4, 5, 6]
B.[2, 2, 5, 7, 9]
C.[x, x+1, x+2, x+2, x+3, x+3]
D.[10, 102, 105, 105]
Answer: C.[x, x+1, x+2, x+2, x+3, x+3]
Explanation: Correct Answer: (C)
Set D could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set C is equal to the median of set C.
Question: The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 2 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?
A.1:2
B.2:3
C.3:4
D.4:5
Answer: C.3:4
Explanation: 5B = 7C and so B = 7C/5
7A = 2B and so A = 2B/7 = 2C/5
A+B = 2C/5 + 7C/5 = 9C/5
B+C = 7C/5 + C = 12C/5
The ratio of A+B:B+C = 9:12 = 3:4
The answer is C.
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. y = 0
II. x = 0
III. x = -y
A.I only
B.II only
C.III only
D.I and III only
Answer: B.II only
Explanation: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer B
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.50
B.23
C.26
D.28
Answer: A.50
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Question: A man can row with a speed of 40 kmph in still water. If the stream flows at 8 kmph, then the speed in downstream is?
A.48
B.28
C.32
D.82
Answer: A.48
Explanation: M = 40
S = 8
DS = 40 + 8 = 48 .Answer:A
Question: In a race, Mohan beats Sohan by 40m and Sohan beats Rohan by 80m. Mohan beats Rohan by 104m. Find the length of the race (in m).
A.50
B.100
C.150
D.200
Answer: D.200
Explanation: length of race = 200 mtrs
length of race = 40*80/(40+80-104) = 40*80/16 = 200 m
ANSWER:D
Question: 80 is what percent of 160?
A.35%
B.40%
C.45%
D.50%
Answer: D.50%
Explanation: 80/160×100=50% ANSWER : D
Question: In a business, A and C invested amounts in the ratio 2 : 1, and B also invest some amount . If Rs 180000 was their profit, B receive 48000, what was the investment ratio between A and B?
A.4 : 9
B.5 : 8
C.7 : 11
D.4 : 7
Answer: A.4 : 9
Explanation: Explanation :
Assume that investment of C = x
Then, investment of A =2x
A receive 48000
Then C will receive = 48000/2 = 24000
And B receive = 180000 - (24000+48000) = 108000
Ratio of investment between A and B = 48000 : 108000 = 4 : 9
Answer : Option A
Question: If (1/2)^16 (1/81)^k = 1/18^16, then k =
A.8
B.12
C.16
D.24
Answer: A.8
Explanation: I'm going to focus on denominator only..
(2^16) . ((3^4)^k = 18^16
(2^16) . ((3^4k) = (2. 3^2)^16
(2^16) . ((3^4k) = (2^24) . (3^2)^16
hence
4k =32
k = 8
answer A
I hope it's quite clear
Question: If log	a/b	+	log	b/a= log (a + b), then:
A.a + b = 1
B.a - b = 1
C.a = b
D.a2 - b2 = 1
Answer: A.a + b = 1
Explanation: Explanation:
log	a/b	+ log	b/a= log (a + b)
=>log (a + b) = log a/b	x	b/a = log 1.
So, a + b = 1.
ANSWER IS A
Question: Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=2/3, what is the ratio of rectangle A’s area to rectangle B’s area?
A.4/9
B.2/3
C.3/2
D.9/2
Answer: A.4/9
Explanation: The area of rectangle A is ab.
c=3a/2 and d=3b/2.
The area of rectangle B is cd=9ab/4.
The ratio of rectangle A's area to rectangle B's area is ab / (9ab/4) = 4/9.
The answer is A.
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
A.9/41
B.3/42
C.9/42
D.7/41
Answer: C.9/42
Explanation: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Question: Seven carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if six of the carpenters work together at their respective rates ?
A.11/15
B.3/5
C.11/30
D.47/70
Answer: D.47/70
Explanation: Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(6/7) = ?
47/70 or (D)
Question: If f(a)=6a+6, what is the value of (f(2a)+f(a)) ?
A.2a-4
B.8a-7
C.10a+12
D.12a+12
Answer: C.10a+12
Explanation: f(a)=6a+6
f(2a)= 8a+6
(f(2a)+f(a)) = 8a+6+2a+6 = 10a+12
Answer is C
Question: If x = 6 and y = −2, what is the value of (x − 2y)^y?
A.−100
B.0.01
C.0.25
D.4
Answer: B.0.01
Explanation: (x−2 y)^y=(6−2(−2))^−2 = 1/(6+4)^2= 1/100 = 0.01
ANSWER:B
Question: An aeroplane covers a certain distance at a speed of 120 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
A.520
B.620
C.820
D.740
Answer: A.520
Explanation: Distance = (120 x 5) = 600 km.
Speed = Distance/Time
Speed = 600/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = (600 x 3/5) km/hr = 360 km/hr
Answer A) 360 Km/hr
Question: A boy needs to deliver three different newspaper to three different house. The problem is that he doesn't know which newspaper belong to which house. Find the probability that the boy only got one house with the wrong newspaper.
A.0
B.1/3
C.2/3
D.4/27
Answer: A.0
Explanation: This one is a trick question. There are three house and three different newspapers. If he only got one wrong delivery, it means that he got the other two house correct. This is not possible because there are only three newspaper. If there are two correct delivery made the remaining one must also be correct. So the possibility of getting o my one of the delivery made wrong is impossible ore 0
Answer: A
Question: Find the total number of prime factors in the expression (4)^11 x (7)^7 x (11)^2
A.31
B.22
C.25
D.27
Answer: A.31
Explanation: (4)^11x (7)^7 x (11)^2
= (2 x 2)^11 x (7)^7 x (11)^2
= 2^11 x 2^11 x7^7x 11^2
= 2^22 x 7^7 x11^2
Total number of prime factors = (22 + 7 + 2) =31.
Answer is A.
Question: If ‘n‘ integers taken at random and multiplied together, then what is the probability that the last digit of the product is 1, 3, 7 or 9 ?
A.(2/5)^n
B.(1/5)^n
C.(3/5)^n
D.(4/5)^n
Answer: A.(2/5)^n
Explanation: Last digit may be 0,1,2,3,4,5,6,7,8,9 = 10
condition is 1,3,7,9 = 4
and n random no. so
probability is 4^n/10^n=(4/10)^n=(2/5)^n
ANSWER:A
Question: A man sold 18 toys for Rs. 18900, gaining thereby the cost price of 3 toy find the cost price of a toy
A.s. 600
B.s. 800
C.s.500
D.s.900
Answer: D.s.900
Explanation: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 18900.
Gain = SP â€“ CP
3X = 18900 â€“ 18X
21X = 18900
X = Rs. 900.
ANSWER : OPTION D
Question: the sum of the ages of 5 children born at the intervals of 3 year each is 40 year. what is the age of the eldest child ?
A.14 year
B.8 year
C.10 year
D.None of these
Answer: A.14 year
Explanation: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 40 â‡” 5 x = 10 â‡” x= 2.
âˆ´ Age of the youngest child = x + 12= 2 + 12 = 14 years. Answer A
Question: Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $914800, how many months will it take Joan to pay back her mortgage?
A.6
B.8
C.10
D.9
Answer: D.9
Explanation: Joan starts off with 100 $ .. which is to be tripled every month
Her monthly payments look like this :
100 , 300 , 900 , 2700 ......... Upto 914800
This can be re written as :
100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 9148
So we have 1 , 3 , 9 , 27 ..... 914800 in GP
We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)
Therefore to find the Sum of n terms of a GP we use this formula :
Sn = a (1-r^n) / 1 -r
Using this and plugging in the information we get ...
9148 = 1 - 3^n / 1-3 ; 1-3^n / -2
Cross multiplying we get
9148 x -2 = 1- 3^n
- 19682 = 1 - 3^n
- 19682 = - 3 ^n
19683 = 3 ^n (negatives cancel out)
19863 can also be re written as 3 ^ 9
Therefore ; 3 ^9 = 3 ^n
Thus n = 9 (D)
Question: If A and B get profits of Rs.18,000 and Rs.15,000 respectively at the end of year then ratio of their investments are
A.6 : 5
B.1:4
C.3:2
D.2:3
Answer: A.6 : 5
Explanation: Ratio = 18000/15000 = 6 : 5
Answer : A
Question: The value of P, when 4864 x 9P2 is divisible by 12, is
A.2
B.5
C.8
D.NOne of these
Answer: D.NOne of these
Explanation: Sol.
Since 4864 is divisible by 4, So 9P2 must be divisible by 3.
∴ (11 + 9) must be divisible by 3.
∴ Least value of P is 1.
Answer D
Question: Nine men went to a theater. Eight of them spent Rs.3 each over their tickets and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
A.29
B.29.25
C.31
D.31.23
Answer: B.29.25
Explanation: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25
B
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
A.200/7years
B.222/7years
C.225/7years
D.245/7years
Answer: B.222/7years
Explanation: Multiply avg age of grand parents, parents and grand childrens with respectively to the no of persons in the family.
i.e,
Total Age of the family => (67*2)+(35*2)+(3*6)=222
Total no of persons in family = 7
Now the avg age of the family = 222/7 years
ANSWER:B
Question: Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?
A.5/11!
B.7/8!
C.5/9!
D.15/21!
Answer: A.5/11!
Explanation: Two dices are thrown ! So we may get 1+1 or 1+2 ... or 1+6.. or 2+6 or 3+6 etc
Therefore the total different sum values we can get are :2,3,4,5,6,7,8,9,10,11,12[Sample space] ----------------(1)
Out of these values, 5 numbers are primes i.e.2,3,5,7,11[Favorable events] --------------------(2)
From (1)(2)
The answer is5/11!!
Ans: A
Question: From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 9, what is the probability that the 2 numbers included the number 5?
A.1/2
B.2/5
C.3/10
D.3/5
Answer: A.1/2
Explanation: We know that the sum of two numbers picked was 9. So, there could be the following cases:
(3, 6);
(6, 3);
(4, 5);
(5, 4);
Total of 4 cases out of which 2 have 5, thus the probability is 2/4=1/2.
Ans A
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
A.33
B.20
C.88
D.77
Answer: B.20
Explanation: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer:B