RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Robert invests $120,000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Jody invests $120,000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Robert's account, approximately how much more does Jody’s account have?
A.Zero
B.$81.90
C.$819.00
D.$8190.03
Answer: C.$819.00
Explanation: Robert's interest= $120,000*0.12 = $14400 or $1,200 each month.
Jody’s interest, 12%/12 = 1% each month:
For the 1st month = $120,000*0.01 = $1,200;
For the 2nd month = $1,200 + 1% of 1,200 = $1,212, so we would have interest earned on interest (very small amount);
For the 3rd month = $1,212 + 1% of 1,212 = ~$1,224;
For the 4th month = $1,224 + 1% of 1,224 = ~$1,236;
...
For the 12th month = $1,320 + 1% of 1,320 = ~$1,332.
The difference between Robert's interest and Jody's interest = ~(12 + 24 + ... + 132) = $792.
Answer: C.
Question: What two-digit number is less than the sum of the square of its digits by 15 and exceeds their doubled product by 5?
A. 95
B. 99
C. 26
D. 73
Answer: D. 73
Explanation: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -15
Thus 2xy +5 = x^2 + y^2 - 15
x^2 + y^2 -2xy = 16
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 73
Thus the answer is D
Question: The wages of 24 men and 16 women amount to 11600 per day. Half the number of men and 37 women has same money. The daily wages paid to each man is
A.223
B.350
C.31887
D.2797
Answer: B.350
Explanation: 24m + 16w = 11600
12m + 37 w = 11600
Solving we get 12 m = 21w
Substituting in the first equation we get, 42w + 16 w = 11600 ⇒⇒ w = 200
M = 350
Answer:B
Question: If n is an integer from 1 to 96 (inclusive), what is the probability for n*(n+1)*(n+2) being divisible by 8?
A.25%
B.50%
C.62.5%
D.72.5%
Answer: A.25%
Explanation: (A) 25% , to be divisible by 8 the number needs to have 3 2s in it. Only a multiple of 4 can provide that. Number of numbers divisible by 4 = 96/4 = 24. So P(8) = 24/96 = 25% .
Question: 36 workers can reap a field in 6 days. If the work is to be completed in 4 days, the extra workers required are
A.10
B.25
C.18
D.15
Answer: C.18
Explanation: Explanation:
M1D1 = M2D2
36(6)=X(4)
=54
Extra required workers are 54-36=18
Answer: Option C
Question: Ten years ago, P was half of Q's age. If the ratio of their present ages is3:4, what will be the total of their present ages?
A.45
B.40
C.35
D.30
Answer: C.35
Explanation: Let present age of P and Q be
3x and
4x respectively.
Ten years ago, P was half of Q's age
⇒(3x−10)=1(4x−10)/2
⇒6x−20=4x−10
⇒2x=10
⇒x=5
Total of their present ages
3x+4x=7x=7*5=35
ANSWER:C
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 60 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
A.160
B.240
C.330
D.440
Answer: C.330
Explanation: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 60.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*60 = 270.
Total area = 60 + 270 =330.
Answer: C.
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
A.32:21
B.22:21
C.21:32
D.31:21
Answer: C.21:32
Explanation: Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000*6 + 15000*6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000*4 : 50000*4)
Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)
= (20*6 + 15*6) : (30*4 + 50*4)
= (20*3 + 15*3) : (30*2 : 50*2)
= 105:160
= 21:32
Answer is C
Question: N* is defined as 0.5(N+10) for any number N. What is N, if ((N*)*)*=15?
A.20
B.30
C.40
D.50
Answer: D.50
Explanation: N*=0.5(N+10)
(N*)*=0.5(0.5N+5+10)= 0.25N+7.5
((N*)*)*=0.5(0.25N+7.5+10)= 0.125N+8.75
we know that ((N*)*)*=15
0.125N+8.75=15
0.125N=6.25
N= 6250/125= 50
ANSWER:D
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 1800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
A.9000
B.9900
C.10000
D.11000
Answer: C.10000
Explanation: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 1800 ( 18 × 100 = 1800)
100% -------> 10000 votes (100 × 100 = 10000)
C
Question: A man drive his car to the office at 20miles/hr.
After reaching office, he realize that its a new year holiday so he went back home at a speed of 30miles/hr.
Discounting the time spent in the stoppage what was his average speed of his journey ?
A.21
B.20
C.25
D.24
Answer: D.24
Explanation: D
24miles/hr (not 25miles/hr which might be guessed by many)
D : distance traveled
T1 : time of going to office
T2 : time of returning back
Y : Average Speed
D = 20 * T1
T1 = D/20
D = 30 * T2
T2 = D/30
2D = Y(T2 + T1)
2D = Y(D/20 + D/30)
2D = Y(3D/60 + 2D/60)
2D = Y(5D/60)
Y = 120D/5D
=> Y = 24
Question: Pat is now 22 years older than Dan. If in 6 years Pat will be twice as old as Dan, how old will Pat be in 15 years?
A.47
B.49
C.51
D.53
Answer: D.53
Explanation: P=D+22 so D=P-22.
P+6=2(D+6).
P+6=2(P-22+6).
P+6=2P-32.
P=38.
In 15 years, Pat will be 53 years old.
The answer is D.
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
A.299
B.278
C.278
D.480
Answer: D.480
Explanation: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
Answer: D
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur. What is the probability that event A occurs?
A.1/12
B.1/8
C.1/6
D.1/3
Answer: D.1/3
Explanation: Let us say probability of A occurring is a.
Let us say probability of B occurring is b.
a = 2b
Probability (either A or B or both) = 8 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 8*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 8*2b*b
3b-2b^2 = 16b^2
3b = 18b^2
b = 3/18 = 1/6
So, a = 2b = 1/3
ANSWER:D
Question: Calculate the average of first 14 even numbers is?
A.11
B.15
C.16
D.14
Answer: B.15
Explanation: Explanation:
Sum of 14 even numbers = 14 * 15 = 210
Average = 210/14 = 15
Answer: Option B
Question: If 10^(z-1)< 0.000125 <10^z, what is the value of an integer z?
A.-4
B.-3
C.-2
D.3
Answer: B.-3
Explanation: -> Multiply 10^6- > (10^6){10^(z-1)}<125<(10^6)(10^z) -> 125 is bigger than 100
-> (10^6)(10^(z-1))=100 -> 10^(6+z-1)=10^2, z+5=2 -> z=-3
Thus, the answer is B
Question: If x and y are integer, which of the following must also be an integer?
I. xy
II. y
III. y/x
A.I alone
B.II alone
C.III alone
D.I and III
Answer: B.II alone
Explanation: Let's take X = 4and Y = 3
Then X/Y = 4/3 Not an integer.
Y/X = 3/4 Not an integer.
Y alone is 3 which is an integer.
Hence B.
Question: Present ages of souju and tharak are in the ratio of 6:4 respectively. Three years hence, the ratio of their ages will become 12:9 respectively. What is tharak's present age in years?
A.2 years 7 months
B.3 years 2 months
C.3 years 5 months
D.3 years 7 months
Answer: D.3 years 7 months
Explanation: Ratio of the present age of souju and tharak =6:4
Let present age of Souju =6x
Present age of Tharak =4x
After 3 years, ratio of their ages =12:9
⇒(6x+3):(4x+3)=12:9
⇒9(6x+3)=12(4x+3)
⇒54x+27=44x+36
⇒10x=36−27=9
=>x=9/10=0.9
Tharak's present age =4x=4*0.9=3.6=3 years 7 months
ANSWER:D
Question: What is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square?
A.2
B.3
C.5
D.7
Answer: D.7
Explanation: 1008 = 2^4 x 3^2 x 7.
Therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7.
Answer D.
Question: Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 25 grades are D's. What is the number of students in the course?
A. 80
B. 110
C. 160
D. 500
Answer: D. 500
Explanation: We start by creating a variable for the total number of students in the math course. We can say:
T = Total number of students in the math course
Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 25 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:
#A’s + #B’s + #C’s + #D’s = Total number of students in the class
1/5(T) + ¼(T) + ½(T) + 25 = T
We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:
4T + 5T + 10T + 500 = 20T
19T + 500 = 20T
500 = T
There are a total of 500 students in the math class.
Answer is D.
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is
A.0.5909
B.0.5904
C.0.59076
D.0.5907
Answer: B.0.5904
Explanation: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Question: There are 300 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
A.650
B.700
C.750
D.800
Answer: C.750
Explanation: as per question stem 2/5M (Portion of Men employees who are managers) + 200 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+300= 2/5T, or 2/5(T-M)=300, from here we get that T-M=750, that would be total number of female employees and the answer (C)
Question: A car is running at a speed of 90 kmph. What distance will it cover in 15 second?
A.100 m
B.255 m
C.375 m
D.Cannot be determined
Answer: C.375 m
Explanation: Explanation:
Given : Speed = 108 kmph = (90 x (5/18)) m/sec = 25 m/sec
Distance covered in 15 second = (25 x 15) m = 375 m.
ANSWER: C
Question: Two years ago, Claire put $2,000 into a savings account. At the end of the first year, her account had accrued $100 in interest bringing her total balance to $2,100. The next year, her account balance increased by 10%. At the end of the two years, by what percent has Claire's account balance increased from her initial deposit of $2,000 ?
A.10%
B.12%
C.15.5%
D.17%
Answer: C.15.5%
Explanation: investment 2000 dollars
1 st year total gained = 100
total amount end of first year = 2100
second year account increased by 10 % = 2100*0.1 = 210
therefore total amount by second year end = 2310
so total percentage increase in money = (2310-2000)*100/2000 = 15.5 %
Correct Answer C=15.5%
Question: A train ride from Two P to Town Q costs $6.85 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.65. What is the cost of a bus ride from Town P to Town Q?
A.$1.40
B.$2.50
C.$4.10
D.$4.70
Answer: A.$1.40
Explanation: Let x be the cost of a bus ride.
x + (x+685) = 965
2x = 280
x = $1.40
The answer is A.
Question: The sum of two numbers is 120. If the greater number is four times the less, what are the numbers?
A.80
B.84
C.85
D.96
Answer: D.96
Explanation: Let x = the less number
4x = the greater number
The sum of two numbers is 120
x+4x=120
5x=120
x=24
4x=96
Option D
Question: Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq meters.
A.56
B.28
C.99
D.27
Answer: A.56
Explanation: Explanation:
clearly the cow will graze a circular field of area 9856 sq m and
radius equal to the length of the rope.
Let the length of the rope be r mts
{\color{Black} then,\Pi r^{2}=9856\Rightarrow r^{2}=\frac{9856\times 7}{22}=3136\Rightarrow r=56m}
Answer: A) 56m
Question: Which of the following is a parallelogram?
A.120,50,120,50(angle in deg)
B.120,30,130,20(angle in deg)
C.90,90,90,90(angle in deg)
D.a & c
Answer: C.90,90,90,90(angle in deg)
Explanation: sum of adjacent angles is 180 degrees.
ANSWER:C
Question: A man can row 6 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.5.78
B.5.79
C.5.76
D.5.74
Answer: C.5.76
Explanation: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76.Answer: C
Question: What percent is 120 of 90?
A.133 1/3 %
B.134 1/3 %
C.135 1/3 %
D.140 1/3 %
Answer: A.133 1/3 %
Explanation: 120/90 = 4/3
4/3 × 100 = 400/3 = 133 1/3 %
A
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
A.4000
B.345
C.5673
D.6342
Answer: D.6342
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 7 = Rs. 6342
Answer: Option D
Question: Calculate the distance covered by 420 revolutions of a wheel of radius 23.1 cm.
A.609.84 m
B.409.84 m
C.509.84 m
D.109.84 m
Answer: A.609.84 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 420 * 2 * 22/7 * 23.1 = 60984 cm = 609.84 m
ANSWER:A
Question: Sawyer is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be peanut oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Sawyer accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be peanut oil?
A.15/29
B.5/8
C.5/16
D.1/2
Answer: A.15/29
Explanation: peanut oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;
If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are peanut oil --> proportion = 15/29.
Answer: A.
Question: A bag contains 50black pens and 60 white pens. One ball is drawn at random. What is the probability that the ball drawn is black?
A.2/3
B.3/14
C.1/7
D.5/11
Answer: D.5/11
Explanation: total number of pens = 110
number of black pens = 50
drawing a black pens= 50/110 = 5/11
Answer is D
Question: The ratio of the area of a square to that of the square drawn on its diagonal is?
A.1:2
B.2:4
C.3:5
D.4:6
Answer: A.1:2
Explanation: Explanation:
a^2:(a√2)^2
a^2 : 2a^2=1:2
Answer : A
Question: A committee of three people is to be chosen from 3 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
A.12
B.24
C.26
D.30
Answer: A.12
Explanation: One of the approaches:
Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 3 to send only onerepresentativesto the committee: 3C2=3.
But each of these 3 couples can send two persons (husband or wife): 2*2=2^2=4.
Total # of ways: 3C2*2^2=12.
Answer: A.
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
A.60/63
B.125/126
C.1/126
D.8/178
Answer: B.125/126
Explanation: Explanation:
Required probability = 1 - 1/126 = 125/126
ANSWER B
Question: If P(x) = ax^4+bx^3+cx^2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)?
A.48
B.24
C.0
D.50
Answer: A.48
Explanation: Roots are 1,2,3,4
So we can write this
equation As p(x)=
a(x-1)(x-2)(x-3)(x-4).....eq1
Put x=0here we p(0)=48=24a
TheN a=2
Now put a in eq1
And get the answer...
P(5)=a.4.3.2.1=48
ANSWER:A
Question: How many keystrokes are needed to type numbers from 1 to 1000?
A.3001
B.3001
C.2704
D.2890
Answer: B.3001
Explanation: Explanatory Answer
While typing numbers from 1 to 1000, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 900 three-digit numbers: from 100 to 999.
Each of these numbers requires 3 keystrokes.
Therefore, 2700 keystrokes to type the 3-digit numbers.
1000 is a four-digit number which requires 4 keystrokes.
Totally, therefore, one requires 9 + 180 + 2700 + 4 = 2893 keystrokes.
Choice B is the correct answer.
Question: Look at this series: V, VIII, XI, XIV, __, XX, ... What number should fill the blank?
A.IX
B.XXIII
C.XV
D.XVII
Answer: D.XVII
Explanation: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: Option D
Question: If two positive numbers are in the ratio 1/8 : 1/7, then by what percent is the second number more than the first?
A.70%
B.14.28%
C.60%
D.50%
Answer: B.14.28%
Explanation: Given ratio = 1/8 : 1/3 = 3 : 8
Let first number be 7x and the second number be 8x.
The second number is more than first number by 1x.
Required percentage = 1x/7x * 100 = 14.28%.
Answer:B
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
A.Rs.5000
B.Rs.4672
C.Rs.8262
D.Rs.2618
Answer: A.Rs.5000
Explanation: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
Answer:a
Question: How many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {3, 4, 5, 6, 7, 8, 9}
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: Given s=3t
t can take 3
and so s = 9
1 such pairs can be formed.
answer A
Question: find two integers, neither of which ends in a zero, and whose product is exactly 1,00,000
A.64 and 15,625
B.32 and 3,125
C.64 and 15,620
D.64 and 15,635
Answer: B.32 and 3,125
Explanation: 1,00,000=10^5
=10x10x10x10x10
=(2x5)x(2x5)x(2x5)x(2x5)x(2x5)
=(2^5)x(5^5)
= 32x3125
so the numbers are 32 and 3,125
ANSWER:B
Question: How many points (x, y) lie on the line segment between (22, 12 2/3) and (16, 17 2/3) such that x and y are both integers?
A.1
B.5
C.7
D.8
Answer: A.1
Explanation: slope = (17 2/3 - 12 2/3) / (16 - 22) = -5/6
y = mx + b => 12 2/3 = -22*5/6 + b => b = 31
y = -5x/6 + 31
Only integer values work, and the only multiples of 6 between 16 and 22 for x values is 18, thus 1 point.
A
Question: When 12 is divided by the positive integer k, the remainder is 7, for how many different values of k is this true?
A.2
B.3
C.4
D.7
Answer: C.4
Explanation: When 20 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2.
It also means that 18 is completely divisible by k.
Factors of 18 are 1, 2, 3, 6, 9, 18
Out of these, k can be 3, 6, 9 and 18.
Answer (C)
Question: On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 20 miles on Saturday and Sunday, how many miles did Bill run on Sunday?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Let Bill run x on saturday, so he will run x+4 on sunday..
Julia will run 2*(x+4) on sunday..
totai= x+x+4+2x+8=20..
4x+12=20..
x=2..
ans =x+4=2+4=6
Answer B
Question: A worm is at the bottom of a forty foot hole. It can crawl upwards at the rate of four feet in one day, but at night, it slips back three feet. At this rate, how long will it take the worm to crawl out of the hole?
A.33
B.87
C.37
D.28
Answer: C.37
Explanation: Explanation:
For each day worm climb only 4 - 3 = 1feet.
After 36 days worm reach the 36 foot.
Exactly the 37th day worm reach 40 foot and won't slips back.
Answer: C
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
A.833 1/7
B.833 1/3
C.833 1/2
D.833 1/9
Answer: B.833 1/3
Explanation: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: B
Question: You buy a piece of land with an area of √900, how long is one side of the land plot?
A.28
B.29
C.30
D.31
Answer: C.30
Explanation: Try filling the numbers into the answer y x y =
Find the closest to 900.
Answer C
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
A.8
B.9
C.7
D.66
Answer: A.8
Explanation: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer:A
Question: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio R of milk and water in the resultant mixture?
A.17 : 3
B.9 : 1
C.3 : 17
D.5 : 3
Answer: B.9 : 1
Explanation: he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.
Step 1.
When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.
Step 2.
When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.
Shortcut.
We are essentially replacing water in the mixture with pure milk.
Let W_o be the amount of water in the mixture originally = 8 litres.
Let W_r be the amount of water in the mixture after the replacements have taken place.
Then,{W_r}/{W_o}= (1-R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, {W_r}/{W_o} =(1/2)^2  =1/4
Therefore R,W_r ={W_o}/4= 8/4 = 2 litres.B
Question: The price of 3 pens and 6 pencils is Rs. 1500. With the same money one can buy 1 pen and 12 pencils. If one wants to buy 23 pencils, how much shall he have to pay ?
A.2400
B.2300
C.2200
D.2100
Answer: B.2300
Explanation: Let the price of a pen and a pencil be Rs. x and Rs. y respectively.
Then, 3x + 6y = 1500 .... (i)
and x + 12y = 1500 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 500. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 1500 (-)
x + 2y = 500
----------------
10y = 1000
----------------
y = 100
cost of 23 pencils = 23*100 = 2300
Answer : B