RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: six family members: 5 grandchildren (3 brothers and 2 sisters) and their 1 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
A.120
B.48
C.1440
D.2880
Answer: B.48
Explanation: Answer: B.
Question: If there are 50 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?
A.1/25
B.2/25
C.3/25
D.4/25
Answer: D.4/25
Explanation: 50 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3
So, 5x=50 ---> x=10
Red marbles = 2*x = 2*10 = 20
Blue marbles = 3*x = 3*10 = 30
Prob to select a red marble = 20/50 = 2/5
Prob to select 2 red marbles with replacement = 2/5*2*5 = 4/25
Hence, answer will be D.
Question: 2y - 2x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?
A.2
B.1
C.0
D.-3
Answer: D.-3
Explanation: Plug in the answer choices in the equation from the question stem.
A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - x = 2x >>> Same, POE
C) y = 0 >>> -x = 0 >>> x can not equal 0
D) y = -1 >>> -2 - 2x = -4x >>> Holds true for x = 1, no need to check E. This is the answer.
Answer D
Question: Sandy buys an old scooter for $900 and spends $300 on its repairs. If Sandy sells the scooter for $1260, what is the gain percent?
A.3%
B.5%
C.7%
D.9%
Answer: B.5%
Explanation: selling price / total cost = 1260/1200 = 1.05
The gain percent is 5%.
The answer is B.
Question: Each of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: The total number in the three clubs is 17+24+22=63.
All 50 students signed up for at least one club.
3 of those students signed up for exactly one more club.
63 - 53 = 10 so 5 students must have signed up for exactly three clubs.
The answer is A.
Question: Working at a constant rate, P can finish a job in 3 hours. Q, also working at a constant rate, can finish the same job in 18 hours. If they work together for 2 hours, how many more minutes will it take P to finish the job, working alone at his constant rate?
A.32
B.36
C.40
D.44
Answer: C.40
Explanation: Each hour they complete 1/3 + 1/18 = 7/18 of the job.
In 2 hours, they complete 2(7/18) = 7/9 of the job.
The time for P to finish is (2/9) / (1/3) = (2/3) hour = 40 minutes
The answer is C.
Question: The average weight of A, B and C is 44 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
A.17 kg
B.28 kg
C.26 kg
D.31 kg
Answer: B.28 kg
Explanation: let d sum of a, b, c is 3*44=132
and sum of a and b s 2*40=80
sum of b and c is 2 *43=86
hence 80+86-132=28
ans=28
ANSWER:B
Question: Which of the following is closest to (120!-119!)/(120!+119!)
A.2
B.2.5
C.3
D.1
Answer: D.1
Explanation: (120!-119!)/(120!+119!)
119! (120-1)/119! (120+1)
119/121 = 1 (approximately)
D is the answer
Question: There are 10 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.156
B.167
C.132
D.352
Answer: C.132
Explanation: The total number of stations = 12
From 12 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 12P₂ ways.
²⁰P₂ = 12 * 11
= 132.
Answer: C
Question: John bought 15 apples for Rs.10 and sold them at the rate of 12 apples for Rs.12. What is the percentage of profit made by him?
A.50 %
B.60 %
C.65 %
D.100 %
Answer: A.50 %
Explanation: Profit % = 15/10 * 12/12 = 1.5 ⇒ 50%.
Answer A
Question: A train passes a station platform in 30 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.150
B.166
C.240
D.157
Answer: A.150
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 30 = 15
x + 300 = 450
x = 150 m.
Answer: A
Question: In an office, totally there are 2800 employees and 25% of the total employees are males. 30% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
A.390
B.490
C.400
D.460
Answer: B.490
Explanation: Number of male employees = 2800* 25/100 = 700
Required number of male employees who are less than 50 years old = 700* (100 - 30)%
= 700* 70/100 = 490.
ANSWER:B
Question: A number is increased by 60% and then decreased by 60%, the final value of the number is ?
A.decrease by 36%
B.decrease by 30%
C.decrease by 32%
D.decrease by 34%
Answer: A.decrease by 36%
Explanation: Here, x = 60 and y = - 60
Therefore, the net % change in value
= ( x + y + xy/100)%
= [60 - 60 + (60 * -60)/100]% or - 36%
Since the sign is negative, there is a decrease in value by 36%.
ANSWER: A
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.12 sec
B.30 sec
C.86 sec
D.16 sec
Answer: B.30 sec
Explanation: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer: B
Question: The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?
A.101!
B.100!
C.99^2(98!)
D.100^2(99!)
Answer: D.100^2(99!)
Explanation: According to this Symbolism question, we're asked to figure out S100 - S99. According to the description of the symbol in the question, we're asked to figure out:
101! - 100!
Both these terms have something in common: 100! so we can factor that out of each piece...
101! - 100!
100!(101 - 1)
Simplifying the parentheses, we get...
100!(100)
Unfortunately, THAT answer isn't listed. We've done the math correctly though, so all we can do is try to convert "our" answer into the format that appears in the answer choices...
100! = (100)(99!) so our answer can be rewritten as...
(100)(99!)(100)
Or....
(100^2)(99!)
ANSWER:D
Question: If books bought at prices ranging from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs 350, what is the greatest possible profit that might be made in selling 15 books ?
A.Rs. 2500
B.Rs. 3000
C.Rs. 3500
D.Rs. 3200
Answer: B.Rs. 3000
Explanation: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 15 books = 150*15 = Rs. 2,250
Maximum selling price of 15 books = 350 *15 = Rs. 5,250
So, maximum profit = 5250 - 2250 = Rs. 3,000
ANSWER : OPTION B
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
A.238
B.227
C.720
D.128
Answer: C.720
Explanation: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer: C
Question: On dividing 23 by a number, the quotient is 4 and the remainder is 3. Find the divisor.
A.1
B.2
C.4
D.5
Answer: D.5
Explanation: d = (D-R)/Q
= (23 - 3)/4
= 20/4 = 5
D
Question: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 4-percent solution?
A.35
B.33 1/3
C.21
D.16 2/3
Answer: C.21
Explanation: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 4-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 4% of the solution. Set up an inequality and solve for x:
1.5/x = 1/4
x = 6
Since you need a 15L solution, you must evaporate 21 of the original 50L solution to get a 4% solution.
Answer is C.
Question: If CRY is coded as MRYC then how will GET be coded?
A.MTEG
B.MGET
C.MEGT
D.METG
Answer: D.METG
Explanation: CRY=M+RYC
GET=M+ETG
METG
ANSWER:D
Question: A and B walk around a circular track. They start at 8 a.m from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9 a.m
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: Explanation:
Relative speed = (2+3) =5 rounds per hour
So, they cross each other 5 times in an hour hence, they cross 5 times before 9 a.m
Answer: Option A
Question: Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
A.2(26)^3
B.26(26)^2
C.27(26)^2
D.26(26)^3
Answer: C.27(26)^2
Explanation: 26^2+26^3 = 26^2(1+26)=27*26^2
The answer is C.
Question: A train is 360 meter long is running at a speed of 72 km/hour. In what time will it pass a bridge of 140 meter length?
A.27 seconds
B.29 seconds
C.25 seconds
D.11 seconds
Answer: C.25 seconds
Explanation: Speed = 72 Km/hr = 72*(5/18) m/sec = 20 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/20) = 25 seconds
Answer:C
Question: A and B together can do a work In 3 days. A alone can do it in 12 days. What time B will take to do the work alone?
A.4 days
B.8 days
C.12 days
D.10 days
Answer: A.4 days
Explanation: Explanation:
A and B 1day's work = 1/3
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/3 - (1/12) = 4 Days
Answer: Option A
Question: If 10 crates have 95 apples each and how many apples more is required in order to make 100 apples in each crate?
A.5
B.10
C.15
D.50
Answer: D.50
Explanation: Each crate requires 5 apples and totally there are 10 crates so required apples = 10 * 5 = 50
Answer: D
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,160 ?
A.$12
B.$14
C.$11.5
D.$17
Answer: C.$11.5
Explanation: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,160, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,160 --> (5+x)(20-x)=116 --> x=0.75 or x=14.25 --> price=10+$2*0.75=$11.5 or price=10+$2*14.25=$38.5.
Answer: C.
Question: The sum of ages of 5 children born 1 years different each is 30 years. What is the age of the Elder child?
A.8
B.9
C.10
D.16
Answer: A.8
Explanation: Let the ages of children be x, (x + 1), (x + 2), (x + 3) and (x + 4) years.
Then, x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 30
5x = 20
x = 4.
x+4= 4+4= 8
Answer : A
Question: The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
A.A)8:9
B.B)3:5
C.C)4:3
D.inadequate
Answer: A.A)8:9
Explanation: Let P's age and Q's age be 6x and 8x years respectively.
Then, 8x - 6x = 4 => x =2
Required ratio = (6x + 4) : (7x + 4)
16 : 18 = 8:9
ANSWER:A
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A.1/2
B.10/21
C.9/11
D.7/11
Answer: B.10/21
Explanation: Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)=5C2/7C2=(5×42×1)/(7×62×1)=5×4/7×6=10/21
Answer is B
Question: Running at the same constant rate, 6 identical machines can produce a total of 240 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A. 648
B. 1,800
C. 1,600
D. 10,800
Answer: C. 1,600
Explanation: 6 machines produce 240 bottles per minute;
1 machine produces 240/6=40 bottles per minute;
10 machines produce 40*10=400 bottles per minute;
In 4 minutes 10 machines produce 400*4=1,600 bottles.
Answer: C.
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
A.2996 sq m
B.2897 sq m
C.4312 sq m
D.2768 sq m
Answer: C.4312 sq m
Explanation: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7)
= 4312 sq m
Answer:C
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
A.3 1/5 Km
B.2 1/5 Km
C.3 Km
D.4 Km
Answer: A.3 1/5 Km
Explanation: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A)
Question: If p is a natural number and p! ends with q trailing zeros, then the number of zeros that (5p)! ends with will be
A.a) (p+q) trailing zeros
B.b) (5p+y) trailing zeros
C.c) (5p+5y) trailing zeros
D.d) (p+5y) trailing zeros
Answer: A.a) (p+q) trailing zeros
Explanation: Let p = 1. p! = 1! = 1, which means q= 0
(5p)! = 5! = 120, trailing zeros = 1
1 = 1 + 0 = p + q
Answer (A).
Question: If a is an odd integer, which of the following must be an even integer?
A.a^4−a+1
B.(a^4−a)(a+1/a)
C.a^4−a^3+a^2+2a
D.(a^3+a^2+a)^2
Answer: B.(a^4−a)(a+1/a)
Explanation: Let assume a be 1..
A. 1-1+1..odd
B.(1-1)(2) = 0.. even
C.1-1+1+2..odd
D.1+1+1..odd
E.None
Ans: option B.
Question: How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.23 sec
B.30 sec
C.27 sec
D.48 sec
Answer: D.48 sec
Explanation: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 800 * 3/50
= 48 sec.
Answer:D
Question: Let the function R(n) represent the product of the first n prime numbers, where n > 0. If x = R(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
A.ii only
B.iii only
C.i and ii only
D.i and iii only
Answer: D.i and iii only
Explanation: R(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of R(n). Thus, R(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Question: Two sets of 3 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A.4
B.7
C.6
D.12
Answer: C.6
Explanation: A=(2,3,4), sum of this=9
B=(4,5,6), sum of this=15,
The differenct between 15-9=6
Hence,6 is the answer i.e.C
Question: In how much time will a train of length 110 m, moving at 36 kmph cross an electric pole?
A.sec
B.sec
C.sec
D.sec
Answer: D.sec
Explanation: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 110/10 = 11 sec.
Answer:D
Question: A motorboat, whose speed in 15 km/hr in sƟll water goes 30 km downstream and comes back in a
total of 4 hours 30 minutes. The speed of the stream (in km/hr) is
A.2 km/hr
B.3 km/hr
C.4 km/hr
D.5 km/hr
Answer: D.5 km/hr
Explanation: Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr
So we know from quesƟon that it took 4(1/2)hrs to travel back to same point.
So,
3015+x−3015−x=412=>900225−x2=92=>9x2=225=>x=5km/hr
Answer: D
Question: If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
A.1
B.7
C.3
D.14
Answer: B.7
Explanation: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)7:1
(webs) 1:7}::x:7
⇒7×1×7=1×7 × x
⇒x=7
Answer: Option B
Question: Ram professes to sell his goods at the cost price but he made use of 950 grms instead of a kg, what is the gain percent?
A.5 15/19%
B.3 15/19%
C.4 15/19%
D.6 15/19%
Answer: A.5 15/19%
Explanation: 950 --- 50
50 --- ? =>
=50/950 *100
= 5 15/19%
Answer: A
Question: If x^3 = y^2 > z, which of the statements could be true?
I. x < y < z
II. x < z < y
III. y < x < z
A.I only
B.III only
C.I and II only
D.II and III only
Answer: C.I and II only
Explanation: Given : x^3 = y^2 > z
x^3 = y^2 is possible only when 9^3=27^2=729
I. x < y < z is true for x=9, y=27, z=30 i.e. Answers can only be Options A, C or E
II. x < z < y is true for x=9, y=27, z=10 i.e. Answers can only be Options C or E
III. y < x < z is not true for x=9, y=27
Answer: option C
Question: If f(x) = x^3/(x^5 - 1), what is f(1/x) in terms of f(x)?
A.-f(x)
B.1/f(x)
C.2/f(x)
D.3/f(x)
Answer: A.-f(x)
Explanation: If x = 2 then f(x) = 8/31 and f(1/x) = -8/31 which is equal to -f(x)
answer A
Question: If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
A.1/2
B.1
C.-1/2
D.-1
Answer: B.1
Explanation: When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.
Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p
=> x = (p + q - r + p - q + r + q + r - p) / (r + q + p)
=> x = (r + q + p) / (r + q + p) = 1
p + q + r is non-zero.
ANSWER:B
Question: Income of A is 25% more than the income of B. What is the income of B in terms of income of A?
A.80%
B.75%
C.78.66%
D.71.25%
Answer: A.80%
Explanation: Explanation:
One of the most basic questions.
Let income of B be 100. Income of A is 25% more than income of B which means Income of A becomes 125
Now income of B in terms of A = 100/125 *100 = 80%
ANSWER A
Question: A sum of money at simple interest amounts to Rs. 1717 in 1 year and to Rs. 1734 in 2 years. The sum is:
A.Rs. 1200
B.Rs. 1690
C.Rs. 1600
D.Rs. 1700
Answer: D.Rs. 1700
Explanation: S.I. for 1 year = Rs. (1734 - 1717) = Rs. 17.
Principal = Rs. (1717 - 17) = Rs. 1700.
Answer: Option D
Question: Two pipes A and B can fill a cistern in 12 and 24 minutes respectively, and a third pipe C can empty it in 36 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.10 2/7 min
B.10 1/8 min
C.11 1/7 min
D.12 8/7 min
Answer: A.10 2/7 min
Explanation: 1/12 + 1/24 - 1/36
= 7/72
72/7 = 10 2/7
Answer:A
Question: The Guests at a football banquet consumed a total of 323 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
A.160
B.161
C.162
D.163
Answer: C.162
Explanation: To minimize one quantity maximize other.
161*2 (max possible amount of food a guest could consume) = 322 pounds, so there must be more than 161 guests, next integer is 162.
Answer: C.
Question: If 20 % of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.
A.11 1/9
B.10 1/9
C.12
D.15
Answer: A.11 1/9
Explanation: Use algebra :
0.2/A + 0.8/B = 20
1/A + 4/B = 100
0.8/A + 0.2/B = 30
4/A+ 1/B = 150
15/B = 250
B = 3/50 work per day
A = 3/100 work per day
Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days
Answer (A)
Question: Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share twice, no apples were left.How many apples were there?
A.62
B.63
C.64
D.65
Answer: B.63
Explanation: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 6 times. So answer is (2^6)-1=63.
ANSWER:B
Question: The percentage profit earned by selling an article for Rs. 1520 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
A.3000
B.1230
C.1750
D.5600
Answer: C.1750
Explanation: C.P. be Rs. x.
Then, (1520 - x)/x * 100 = (x - 1280)/x * 100
1520 - x = x - 1280
2x = 2800 => x = 1400
Required S.P. = 125 % of Rs. 1400 = 125/100 * 1400 = Rs. 1750.
ANSWER C
Question: Jeremy bought 2Q steaks for P dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?
A.50RP/Q.
B.50QR/P.
C.25RQ/P.
D.25RP/Q.
Answer: D.25RP/Q.
Explanation: Jeremy bought 2Q steaks for P dollars, so 1 steak = P/2Q
Jerome buys R steaks for a 50% discount: r* (P/4Q)
in cents the answer will be : r* (100 P/4Q)= 25 RP/ Q=D
Question: There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?
A.80
B.140
C.120
D.100
Answer: C.120
Explanation: Let the number of persons in building P = p
and the number of persons in building Q = q
If 15 persons are sent from P to Q,
then the number of persons in each building is the same
=> p-15 = q+15
=> p - q = 30 ----(Equation 1)
If 20 persons are sent from Q to P,
then the number of persons in P is double the number of persons in Q
=> 2(q - 20) = (p + 20)
=> 2q - 40 = p + 20
=> 2q - p = 60 ----(Equation 2)
(Equation 1) + (Equation 2)=> q = 90
From Equation 1, p = 30 + q = 30 + 90 = 120
i.e., Building P has 120 persons
Answer : Option C
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 9 cans so that at least one red and at least one blue cans to remain the refrigerator.
A.460
B.175
C.493
D.455
Answer: B.175
Explanation: Ways to pick 3 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 3 can out of 12 - ways to pick 3 red out of 7 red - ways to pick 3 blue out of 5 blue
12C3âˆ’7C3âˆ’5C3=220âˆ’35âˆ’10=175
ANSWER:B
Question: In Country S, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
A. 50% decrease
B. 30% decrease
C. 15% decrease
D. 30% increase
Answer: B. 30% decrease
Explanation: In Country S 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B