mathewhe/aqua_rat huggingface dataset:
Question: At a certain amateur bands rock show the ratio of freaks to nerds (N) to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek?
(A) 1
(B) 1/2
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.
P(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOTAL # of people in the crowd)
=3/6
= 1/2
Answer:
B
Answer: (B) 1/2
Question: What is the product of all the possible values of x if x^2 - 9x + 20?
(A) –29
(B) –12
(C) 12
(D) 20
(E) 168
Rationale: Explanation:
=> y= x^2 - 9x + 20
=> y= (x-4) (x-5)
=> x= 4, y= 5
Product y = (4)(5) = 20
answer option 20
ANSWER:D
Answer: (D) 20
Question: Which of the following number is divisible by 24 ?
(A) 18
(B) 19
(C) 20
(D) 24
(E) 26
Rationale: 24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
3125736 is divisible by (3 x 8), i.e., 24.
D)
Answer: (D) 24
Question: An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 10th member of this sequence?
(A) A)37
(B) B)28
(C) + 13
(D) D)53
(E) + 13
Rationale: Common difference of an arithmetic series is constant.
2p+2-p=4p+3-2p-2
p=1
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Ans:B
Answer: (B) B)28
Question: A one-foot stick is marked in 1/4 and 1/6 portion. How many total markings will there be, including the end points?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: LCM of 24 = 12
1/4 marking are (Table of 3) 0...... 3 ........... 6.......... 9 .......... 12
(Total = 5)
1/6 marking are (Table of 2) 0 ....... 2 ...... 4...... 6........ 8......... 12 ((Total = 6)
Overlapping markings are 0 ........ 6 ......... 12 (Total = 3)
Total markings = 5+6-3 = 8
Answer = A
Answer: (A) 8
Question: Find the odd one out:
125, 106, 87, 76, 65, 58, 53
(A) 33
(B) 87
(C) 26
(D) 18
(E) 222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 87 is the answer.
ANSWER: B
Answer: (B) 87
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 30 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 2/7 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
(A) 5 minutes, 17.6 seconds
(B) 5 minutes, 21.8 seconds
(C) 5 minutes, 23.6 seconds
(D) 5 minutes, 44.44 seconds
(E) 6 minutes, 10.4 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 30 seconds. The only number is 5 minutes, 44.44 seconds.
Another approach:
2/7 close to 20 second when added to the 5 minutes, 30 seconds, it means it passes 5 minute 44.44 seconds
Answer: D
Answer: (D) 5 minutes, 44.44 seconds
Question: In a group of 400 readers who read science fiction or literacy works or both, 250 read science fiction and 230 read literacy works. How many read both science fiction and literacy works?
(A) 70
(B) 80
(C) 90
(D) 100
(E) 110
Rationale: Consider total number of reader n(S U L) = 400
People who read science fiction n(S) = 250
People who read literacy works n(L) = 230
both science fiction and literacy n(S ∩ L) = ?
n(S U L) = n(S)+ n(L) - n(S ∩ L)
400 = 250 + 230 - n(S ∩ L)
n(S ∩ L) = 480 - 400
n(S ∩ L) = 80
SO People read both science fiction and literacy works are 80
ANSWER:B
Answer: (B) 80
Question: Lindsay can paint 1/x of a certain room in 25 minutes. What fraction of the same room can Joseph paint in 25 minutes if the two of them can paint the room in an hour, working together at their respective rates?
(A) 1/7x
(B) 3x/(x – 3)
(C) (3x – 7) / 7x
(D) 1/ (x – 3)
(E) (x – 3) / x
Rationale: Lindsey and Joseph together can paint the room in 1 hour
in 25 mins they can paint 3/7 part of the room.
Lindsay alone paints 1/x part of the room in 25 mins
Take Joseph paints 1/y parts in 25 mins
1/x + 1/y = 3/7
1/y = 3/7 - 1/x = (3x-7)/7x ANs C
Answer: (C) (3x – 7) / 7x
Question: 5 girls and 3 boys are arranged randomly in a row. Find the probability that:
1) there is one boy on each end.
2) There is one girl on each end.
(A) 3/28 & 5/14
(B) 5/28 & 3/14
(C) 5/14 & 3/28
(D) 3/28 & 1/14
(E) 1/28 & 5/14
Rationale: Total # of arrangements is 8!;
1. The # of arrangements where there is one boy on each end is C^2/3∗2∗6! where C^2/3C32 is # of ways to select which 2 boys will be on that positions, *2 # of way to arrange them on that position (A------B and B------A) and 6! is # of arrangements of 6 people left;
P=C^2/3∗2∗6!/8!=3/28
2. The # of arrangements where there is one girl on each end is C^2/5∗2∗7!, where C^2/5 is # of ways to select which 2 girls will be on that positions, *2 # of way to arrange them on that position (A------B and B------A) and 6! is # of arrangements of 6 people left;
P=C^2/5∗2∗6!/8!=5/14
Answer: A.
Answer: (A) 3/28 & 5/14
Question: A Paul's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
(A)  1:2
(B)  4:5
(C)  1:1
(D)  3:2
(E)  5:3
Rationale: A Paul's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y
1997- x1---- y1-- x1+y1
x1= a*x .....(P)
y1= 1.07*y...(Q)
x1+y1/x+y = 1.01
solve using P and Q and find x/y
Answer: (A)  1:2
Question: How many numbers from 29 to 79 are exactly divisible by 11?
(A) 1
(B) 2
(C) 6
(D) 4
(E) 5
Rationale: Numbers=(79/11)-(29/11)
=7-2
=5 numbers
Answer is option E
Answer: (E) 5
Question: . A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 2787
(B) 288
(C) 277
(D) 400
(E) 122
Rationale: Explanation:
2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: (D) 400
Question: On dividing 73 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
(A) A)8
(B) B)15
(C) C)16
(D) D)17
(E) E)18
Rationale: d = (D-R)/Q
= (73 - 1)/9
= 72/9 = 8
A)
Answer: (A) A)8
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 70%
(C) 100%
(D) 120%
(E) None
Rationale: Solution
Let C.P. = Rs. 100.	Then, Profit = Rs.320,
S.P. = 420.
Let C.P. = Rs. 125% of Rs. 100	= Rs.125.
New S.P. = Rs.420.
Profit = Rs. (420 - 125)	= Rs.295.
∴ Required percentage	= (295 / 420 x 100)%
= 1475 / 21%
= 70%.
Answer B
Answer: (B) 70%
Question: A batsman makes a score of 92 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
(A) 36
(B) 39
(C) 42
(D) 44
(E) None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 92 = 17x or x = (92 – 48) = 44.
Answer D
Answer: (D) 44
Question: Using all the letters of the word "PROBLEMS", how many words can be formed, which begin with P and end with S?
(A) 680
(B) 560
(C) 720
(D) 120
(E) 650
Rationale: There are eight letters in the given word.
Consider 8 blanks ....
The first blank and last blank must be filled with P and S all the remaining six blanks can be filled with the remaining 6 letters in 6! ways.
The number of words = 6! = 720.
ANSWER:C
Answer: (C) 720
Question: A bag contains 2 yellow, 5 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 7/12
(B) 5/12
(C) 3/7
(D) 2/7
(E) 5/7
Rationale: Total number of balls = 2 + 5 + 2 = 9
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 9 = 9C2
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 7 (=9-2) balls = 7C2
(∵ There are two blue balls in the total 9 balls. Total number of non-blue balls = 9 - 2 = 7)
P(E) = n(E)/n(S)
=7C2 / 9C2
=7/12
Ans- A
Answer: (A) 7/12
Question: 896.7 – 573.07 – 95.007 = ?
(A) 228.623
(B) 224.777
(C) 233.523
(D) 414.637
(E) None of these
Rationale: Solution
Given expression = 896.7 - (573.07 + 95.007) = 896.7 - 668.077 = 228.623. Answer A
Answer: (A) 228.623
Question: Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 10 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 20 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
(A) 0.1
(B) 0.5
(C) 1
(D) 1.2
(E) 2
Rationale: Option B
20+10t=50t
t=0.5
Answer: (B) 0.5
Question: 20 workers can finish a work in 30 days. After how many days should 5 workers leave the job so the work is completed in 35 days?
(A) 7
(B) 6
(C) 15
(D) 4
(E) 3
Rationale: Work done by 15 workers in 35 days = 15*35=525 men days.
Now, work remaining= 600–525=75 men days and we have 5 workers .
So 5 workers will work for 75/5=15 days.
ANSWER:C
Answer: (C) 15
Question: A triangle has a perimeter 21. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 21
a + 2x = 20.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =8
E
Answer: (E) 8
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) 24
(B) 89
(C) 67
(D) 56
(E) 45
Rationale: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,	(5x + 3/4x + 3)=11/9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6.
Anand's present age = 4x = 24 years.
Answer:A
Answer: (A) 24
Question: A man has Rs. 80 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 7
(B) 2
(C) 13
(D) 15
(E) 10
Rationale: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 80 16x = 80 x = 5.
Hence, total number of notes = 3x = 15.
Answer:D
Answer: (D) 15
Question: Solve for the given equation 121 x 54 =?
(A) 68225
(B) 75625
(C) 76569
(D) 45854
(E) 45858
Rationale: Explanation:
This question can be solved by 2 approaches:
=> Direct Multiplication
=> Numerical Operations
Direct multiplication is quite time consuming and involves a lot of calculations. An easier approach is based on numerical operations.
=> 121 x (10/2)4 = 121 x 10000/16 = 75625
ANSWER: B
Answer: (B) 75625
Question: Find the simple interest on Rs.235 for 3 months at 8 paisa per month?
(A) s.57.8
(B) s.56.4
(C) s.29.3
(D) s.33
(E) s.74
Rationale: Explanation:
I = (235*3*8)/100 = 56.4
Answer: Option B
Answer: (B) s.56.4
Question: If 15% of 30% of 50% of a number is 117, then what is the number?
(A) 5200
(B) 3050
(C) 4400
(D) 4500
(E) None of these
Rationale: Let the number be a
Given, 15/100 * 30/100 * 50/100 * a = 117
=> 3/20 * 3/10 * 1/2 * a = 117
=> a = 10 * 20 * 10 * 2 = 5200.
ANSWER:A
Answer: (A) 5200
Question: Bradley owns x video game cartridges. If Bradley’s total is one-third the total owned by James and four times the total owned by Charles, how many video game cartridges do the three of them own altogether, in terms of x?
(A) (16/3)x
(B) (17/14)x
(C) (13/4)x
(D) (19/12)x
(E) (17/4)x
Rationale: x = Bradley’s total
3x = James’s total
(1/4)x = Charles’s total
Add each total
x + 3x+ (1/4)x = 4x + (1/4)x = = (17/4)x
Answer : E
Answer: (E) (17/4)x
Question: If 9 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A)  10•9•8•7•6•5•4•3•2•1
(B)  10•10
(C)  10•9
(D)  45
(E)  36
Rationale: We got #9 people who shake each other's hands once ==> a pair of 2
9!/7!2! = 9*8/ 2*1 = 36.
Hence answer E.
Answer: (E)  36
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 50 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 50xy
(B) 50y - x
(C) 50x - y
(D) 50y/x
(E) 50x/y
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
50 = d/(x*pi)
d = 50 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (50 * x * pi) / (y*pi) = 50x/y
Answer (E)
Answer: (E) 50x/y
Question: How many 4-letter word with or without meaning can be formed out
of the letters of the word 'LOGARITHMS' if repetition of letters is
not allowed
(A) 2000
(B) 1000
(C) 5040
(D) 5000
(E) 500
Rationale: 'LOGARITHMS' contains 10 different letters
Required number of words
= Number of arrangements of 100 letters taking
4 at a time
= 10P4
= 10 * 9 * 8 * 7
= 5040
ANSWER C
Answer: (C) 5040
Question: Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 9% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 9:3
(B) 9:5
(C) 5:8
(D) 5:4
(E) 9:2
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 9% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 9/100 (6000 - x)
= 540 - 2x/100
=> 540 - 1/50 x = 450
=> x = 4500
Amount lent at 10% = 1500
Required ratio = 4500 : 1500 = 9:3
Answer:A
Answer: (A) 9:3
Question: 200 is what percent of 50?
.
(A) 0.2%
(B) 2%
(C) 5%
(D) 400%
(E) 500%
Rationale: 200= x*50/100
x = 400%
Ans; D
Answer: (D) 400%
Question: If 50 honey bees make 50 grams of honey in 50 days, then 1 honey bee will make 1 gram of honey in how many days?
(A) 1
(B) 3.5
(C) 20
(D) 49
(E) 50
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 50 :: 50 : x
Honey 50 : 1
=> 1 x 50 x x = 50 x 1 x 50
=> x = 50.
Answer : E
Answer: (E) 50
Question: A number is multiplied by 11 and 11 is added to the product. If the resulting number is divisible by 13, the smallest original number is
(A) 6
(B) 12
(C) 22
(D) 52
(E) None
Rationale: Sol.
Let the required number be x.
Then, (11x + 11) = 11(x + 1) is divisible by 13. So, x = 12.
Answer B
Answer: (B) 12
Question: The average of first five multiples of 5 is:
(A) 9
(B) 15
(C) 17
(D) 8
(E) 10
Rationale: Explanation :
(5(1+2+3+4+5)/5
= 5x15/5
= 15
Answer : B
Answer: (B) 15
Question: The sum of the first 92 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?
(A)  5,050
(B)  7,500
(C)  10,500
(D)  11,700
(E)  19,600
Rationale: 101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 92 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 92 positive even integers = 2550
sum of 1st 100 odd numbers = 5050 - 2550 = 2500
so 101+103+.......199 = 92 * 100 + (1+3+5+7+......) = 9200 + 2500 = 11700
D is the answer.
Answer: (D)  11,700
Question: The third proportional to 1 and 3 is?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: (3*3)/1 = 9
ANSWER:A
Answer: (A) 9
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $9,500, what is the bonds face value?
(A)  $6,000
(B)  $6,750
(C)  $7,425
(D)  $7,600
(E)  $9,375
Rationale: Interest = 0.05*face value = 0.04*9,500 --> face value = 0.04*9,500/0.05 = 7,600.
Answer: D.
Answer: (D)  $7,600
Question: One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
(A)  6
(B)  2.5
(C)  9
(D)  11
(E)  13
Rationale: Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4*5=20 seconds it can upload 5*100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds.
Answer: B.
Answer: (B)  2.5
Question: Suresh age after 15 years will be 5 times his age 5 years back, What is the present age of Suresh
(A) 15
(B) 10
(C) 14
(D) 8
(E) 7
Rationale: x+15 = 5(x-5)
<=> 4x = 40 => x = 10
ANSWER B
Answer: (B) 10
Question: The difference between the length and breadth of a rectangle is 60 m. If its perimeter is 300 m, then its area is:
(A) 1520 m2
(B) 2420 m2
(C) 4258 m2
(D) 4725 m2
(E) None
Rationale: EXPLANATION
We have: (l â€“ b) = 60 and 2(l + b) = 300 or (l + b) = 150.
Solving the two equations, we get: l = 105 and b = 45.
Area = (l x b) = (105x 45) m2 = 4725 m2.
Answer D
Answer: (D) 4725 m2
Question: Which of the following are roots of an equation (x^-2)+(4x^-1)-5=0
(A) 1/5 and -1
(B) -1/5 and 1
(C) 1/5 and 1
(D) -1/5 and -1
(E) -5/2 and -1
Rationale: Given: (x^-2) + (4x^-1) - 5 = 0
Rewrite as: 1/(x²) + 4/x - 5 = 0
Remove fractions by multiplying both sides by x² to get: 1 + 4x - 5x² = 0
Rearrange to get: 5x² - 4x - 1 = 0
Factor to get: (5x + 1)(x - 1) = 0
So, EITHER 5x + 1 OR x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If x - 1 = 0, then x = 1
So, the roots (solutions) are -1/5 and 1
The answer is B.
Answer: (B) -1/5 and 1
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 11% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
(A) 70 lbs
(B) 40 lbs
(C) 25 lbs
(D) 50 lbs
(E) 60 lbs
Rationale: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 7% profit
B = # of pounds sold at 11% profit
A+B = 100 pounds
(.07A + .11B)/(A+B) = .10
.07A + .11B = .1A + .1B
.01B = .03A
1B = 3A
1/3 = A/B
So, for every 1 pounds of A, we have 3 pounds of B.
With 100 pounds total, we have 25 pounds of A and 75 pounds of B.
Option C
Answer: (C) 25 lbs
Question: When x is divided by y, the quotient is z with remainder v. Which of the following is equal to v?
(A) yz – x
(B) y/x−z
(C) x – y – z
(D) x – yz
(E) zx – y
Rationale: (x/y)=z(+v)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Answer: (D) x – yz
Question: 84/12/0.8 = ?
(A) 8.17
(B) 7.14
(C) 6.23
(D) 4.35
(E) 8.75
Rationale: E
8.75
? = 84/(12*0.8) = 8.75
Answer: (E) 8.75
Question: A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn?
(A)  188
(B)  258
(C)  376
(D)  470
(E)  517
Rationale: consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn Y= 4 * 94 = 376
correct option - C
Answer: (C)  376
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = f is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-f, -k), then what are the coordinates of the point P?
(A) (-5f, -5k)
(B) (-3f, -3k)
(C) (2f, 2k)
(D) (3f, 3k)
(E) (5f, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-f, -k), so R is at a distance of 2f from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4f and coord (3f,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3f,3k).ans D
Answer: (D) (3f, 3k)
Question: There are 5 red balls, 7 blue balls, 6 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
(A) 10
(B) 23
(C) 43
(D) 40
(E) 24
Rationale: The worst case scenario would be if we pick 4 red balls, 6 blue balls, 5 (?) balls and 8 black balls. In this case we'll have 4+6+5+8=23balls and still won't have all the balls of one color. The next 24rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: E
Answer: (E) 24
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 8 less, he would have made a profit of 10%. The C.P. of the article was
(A) 1600
(B) 1500
(C) 1200
(D) 1388
(E) 1211
Rationale: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 8
=> x = 1600
Answer: A) Rs 1600
Answer: (A) 1600
Question: A students was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?
(A) 3
(B) 7
(C) 17
(D) 31
(E) 38
Rationale: adding all the numbers we get 137+x
GIVEN-(137+x)/12=12
137+x=12*12
x=144-137
x=7
ANSWER:B
Answer: (B) 7
Question: If the class marks in frequency distribution weights of students be 128, 137, 146, 155, 164, 173 and 182 kgs then the first class boundary is
(A) 123.8
(B) 123.7
(C) 123.5
(D) 223.5
(E) 1222.2
Rationale: Sol:
Rule for class boundary is = n1– (n2 – n1)/2.
So here n1 = 128, n2 = 137;
First class boundary = 128 – (137 – 128)/2 = 128 – 4.5 = 123.5
Hence option (C) is correct.
Answer: (C) 123.5
Question: A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 70 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.
(A) 180
(B) 130
(C) 140
(D) 160
(E) 224
Rationale: White:Yellow = x:(x+70) = 8:13 --> 13x = 8x + 560 --> x = 112.
The total # of balls originally x + x = 112 + 112 = 224.
Answer:E.
Answer: (E) 224
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
(A) Rs. 2160
(B) Rs. 3120
(C) Rs. 3972
(D) Rs. 6240
(E) Rs. 5240
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
ANSWER:C
Answer: (C) Rs. 3972
Question: Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 1.5 screws and 4.5 nails?
(A) a. 4
(B) b. 5/2
(C) c. 2
(D) d. 3/2
(E) e. 20/11
Rationale: let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 1.5s and 4.5n= 1.5s+4.5*1.5s=8.25s..
ratio= 15s/8.25s=15/8.25=20/11
E
Answer: (E) e. 20/11