divelab/Sys2Bench huggingface dataset:
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 221, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
Options:
A)22
B)33
C)39
D)77
E)88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 221 => .1x + 3/4x = 221 => x = 260
260 - 221 = pure gala = 39.
Answer C
Answer: C
Question: If a and b,c are both even numbers, which of the following is an even number?
Options:
A)a + b+c
B)a + b +c+ 1
C)abc+1
D)abc + 3
E)NOne
Rationale: Sol.
Sum of 3 even numbers is always even.
Answer A
Answer: A
Question: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 12 such machines to perform the same job?
Options:
A)6 hours
B)8.75 hours
C)12 hours
D)4 hours
E)16 hours
Rationale: Let each machine do 1 unit of work for 1 hour
8 machines --> 8 units of work in 1 hour
For 6 hours = 8*6 = 48 Units of total work is done.
Now this 48 Units of total work must be done by 3 machines
12 units of work(12 machines) ---> 1 hour
for 48 Units of work
12*4 ---> 1*4 hours
D 4 hours
Answer: D
Question: Which of the following is a prime number? ?
Options:
A)33
B)81
C)83
D)93
E)10
Rationale: C
83
Clearly, 83 is a prime number.
Answer: C
Question: Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?
Options:
A)120cc
B)360cc
C)450cc
D)589C
E)478cc
Rationale: Explanation:
r1 = x r2 = 3x
Π * x2 * h = 40
Π9 x2h = 40 * 9 = 360cc
Answer: B
Answer: B
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 25 minutes, and 2nd puncture do the same tyre flat in 15 minutes.Both started their work, After 4 minutes the puncture 2 has mechanic close the leak.Then how many minutes 1st puncture required to flat the remaining air of the tyre?
Options:
A)5 minutes
B)2 minutes
C)3.25 minutes
D)2.25 minutes
E)1.72 minutes
Rationale: First take LCM of (25,15) = 75; Total work = 75; 1st puncture make the tyre flat in one minutes = 75/25 = 3 ; 2nd's puncture make the tyre flat in one minutes =75/15 = 5 ; both can flat the tyre in= 3+5 = 8 min; Total work completed in 4 min = 8*4=32; remaining work is = 75 - 32 = 43; remaining work completed by 1st puncture in = 43/25= 1.72 min.
Answer = E
Answer: E
Question: How many W ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles?
Options:
A)120
B)240
C)360
D)540
E)720
Rationale: Jason can select his seat in 2 Ways (two aisles)
His 1st of 4 friends have 5 seats to select =>
His 2nd of remaining 3 friends will have 4 seat to chose from...and so on
Total ways W=> 2*5*4*3*2*1 = 240.B
Answer: B
Question: Mary works in a restaurant a maximum of 60 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
Options:
A)300
B)420
C)560
D)320
E)400
Rationale: Mary receives $8(20)=$160 for the first 20 hours.
For the 40 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(40)=$400.
The total amount is $160+$400 = $560
Answer C 560.
Answer: C
Question: A locker consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)200
B)215
C)220
D)223
E)224
Rationale: 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
B
Answer: B
Question: A server generates random passwords of 3 letters followed by 3 digits. How many different passwords are possible if letters and digits can be repeated?
Options:
A)26 × 3 × 10 × 4
B)26³ x 1000
C)26³ × 10 000 × 9 × 9 × 9 × 9
D)26 × 25 × 24 × 10 000
E)26 × 25 × 24 x 23 x 21 x 20
Rationale: OFFICIAL SOLUTION:
(B) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 for the three digits. The number of passwords generated is 26 × 26 × 26 × 10 × 10 × 10 = 26³ × 1000.
The correct answer is choice (B).
Answer: B
Question: What is the decimal equivalent of (1/10)^2?
Options:
A)0.0016
B)0.0625
C)0.16
D)0.25
E)0.01
Rationale: (1/10)² = (1/10)(1/10)= 1/100
APPROACH #1: use long division to divide 100 into 1 to get 1/100 = 0.01
E
Answer: E
Question: Find the surface area of a cuboid 12 m long, 10 m broad and 18 m high
Options:
A)868 sq.cm
B)1200 sq.cm
C)1032 sq.cm
D)1302 sq.cm
E)None of these
Rationale: Explanation:
Surface area = [2 (12 x 10 + 10 x 18 + 12 x 18)] cm2 = (2 x 516)cm2 = 1032 cm2.
Answer: C
Answer: C
Question: Find the cost of fencing around a circular field of diameter 70 m at the rate of Rs.1 a meter?
Options:
A)288
B)132
C)220
D)592
E)261
Rationale: 2 * 22/7 * 35 = 220
220* 1 = Rs.220
Answer: C
Answer: C
Question: If a > 0 and x is m percent of y, then, in terms of a, y is what percent of x?
Options:
A)a) 100a
B)b) 1/100a
C)c) 1/a
D)d) 10/a
E)e) 10,000/a
Rationale: x= a/100 * y
So y= 100/a * x
So y= (10000/a)/100 * x
E
Answer: E
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is a Multiple of 5
II. P is a multiple of 17
III. P is a multiple of 19
Options:
A)I only
B)II only
C)III only
D)None of the above
E)All of the above
Rationale: The correct answer is A.
Answer: A
Question: Find the value of 72519 x 9999 = m?
Options:
A)246574453
B)345657673
C)455767868
D)725117481
E)876674564
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: How many of the integers between 20 and 80 are even ?
Options:
A)21
B)30
C)11
D)10
E)9
Rationale: Number start between 20 to 80 is 60 numbers
half of them is even..which is 30
ANSWER:B
Answer: B
Question: A person tosses an unbiased coin. When head turns up, he gets Rs.8 and tail turns up he loses Rs.4. If 3 coins are tossed, what is probability that the gets a profit of Rs.12?
Options:
A)3/8
B)5/8
C)3/4
D)1/8
E)1/4
Rationale: When a person tosses two heads and one tail, he will get Rs.12. When three coins are tossed, total outcomes = 23 = 8. Favourable out comes i.e, two heads and one tail is = {HHT, HTH, THH} = 3ways. Therefore, required probability = 3/8.
ANSWER:A
Answer: A
Question: A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.
Options:
A)20 Days
B)22 Days
C)21.5 Days
D)22.5 Days
E)23.5 Days
Rationale: If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day= 1/90
Amount of work A can do in 1 day = 3 × (1/90) = 1/30
Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45
=> A and B together can do the work in 45/2 days = 22 ½ days
Answer is D.
Answer: D
Question: A man walks West 10 miles, then turns right towards North and walks another 10 miles. How far is he from the place he started walking.
Options:
A)11.11
B)10
C)14.14
D)16.15
E)1
Rationale: As we can see the man moves in configuration of a right angle triangle. The man has walked on the sides and now we need to calculate the length of the hypotenuse which is the distance of the man from the starting point to his current location.
Since we know the length of two sides, we can find the length of hypotenuse.
As per pythagoras:
a^2+b^2=c^2
a = 10
b = 10
10^2 + 10^2 = c^2
100+100 = c^2
200 = c^2
c= squareroot 200
c=14.14 miles
Ans:C
Answer: C
Question: One pack of cake mix is being stirred before being poured into two separate baking trays. The first tray can hold a certain amount of cups of the mix while the other holds 20 cups less than the first. If the total number of cups poured is 500, how many cups of batter does the second tray hold?
Options:
A)250
B)260
C)500
D)280
E)240
Rationale: Tray one as t1 and tray two as t2.
T2= T1-20 cups as equation a.
t1+t2=500 cups in total as equation b.
substitute equation a into equation b, resulting in t1 +( t1-20)=500
transpose like terms, 2*t1=500 + 20
(2*t1)/2=520/2
t1=260, thus t2 is t1 less 20 cups, which is 240 cups.
Answer is E.
Answer: E
Question: If -1 < x < 0, which of the following must be true? I. x^8 < x^3 II. x^4 < 1 – x III. x^3 < x^2
Options:
A)III only
B)II only
C)I only
D)I,II,III only
E)II,III only
Rationale: Answer : D
Answer: D
Question: An investor bought two shares of stock, which he sold for $60 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:
Options:
A)a profit of $10
B)a profit of $5
C)a loss of $5
D)a loss of $10
E)neither a profit nor a loss
Rationale: The cost of the first stock was 60/1.2=50, so the profit from it is 10.
The cost of the second stock was 60/0.8=75, so loss from it is 15.
Overall the loss is $5.
The answer is C.
Answer: C
Question: Working alone, machine X can manufacture 1,000 nails in 15 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
Options:
A)3 9/17
B)5 1/3
C)7
D)7 1/2
E)8 4/7
Rationale: rate of machine x = 1000/15
(1000/15 + y)5=1000
y=200-200/3=400/3
400/3 * t = 1000
t=7 1/2
D. 7 1/2
Answer: D
Question: John makes $60 a week from his job. He earns a raise andnow makes $75 a week. What is the % increase?
Options:
A)16.12%
B)25%
C)16.56%
D)17.66%
E)18.1%
Rationale: Increase = (15/60)*100 = (1/4)*100 = 25%.
B
Answer: B
Question: Company K's earnings were $12 million last year. If this year's earnings are projected to be 150 percent greater than last year's earnings, what are Company K's projected earnings this year?
Options:
A)$13.5 million
B)$15 million
C)$18 million
D)$27 million
E)$30 million
Rationale: 150 percent greater is (1 + 150/100) = 2.5 times greater (the same way as 10% greater is (1+10/100)=1.1 times greater or the same way as 100% greater is (1+100/100)=2 times greater or the same way as 5% greater is (1+5/100)=1.05 times greater).
Earnings this year = 12*2.5 = 30.
Answer: E.
Answer: E
Question: For 1rs 6p interest
wat will be for 2000rs?
Options:
A)45Rs
B)150Rs
C)140Rs
D)120Rs
E)48Rs
Rationale: For 1rs , 6p interest
for 2000rs, x
x= 2000/1 * 6p ==> 12000 paise
To express in rs, 12000/100 = 120rs
ANSWER:D
Answer: D
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what R percent of the list price is the lowest possible sale price?
Options:
A)20
B)25
C)30
D)40
E)50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 40
and 0.8x = 32
so lowest sale price is 32, which R is 40% of 80
hence, D is the answer
Answer: D
Question: If a certain sample of data has a mean of 29.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
Options:
A)(26.0; 36.5)
B)(24.5; 31.0)
C)(22.0; 35.5)
D)(26.5; 36.0)
E)(25.0; 29.5)
Rationale: The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.
The values between 24 and 34 are within 2.5 standard deviations from the mean.
The answer is C.
Answer: C
Question: If A and b are both odd numbers which of the following is an even number?
Options:
A)a+b
B)a+b+1
C)ab
D)ab+2
E)None
Rationale: Solution
Sum of two odd numbers is always even.
Answer A
Answer: A
Question: A division of a company consists of three men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
Options:
A)1/4
B)2/9
C)3/11
D)5/14
E)6/17
Rationale: Total number of ways to select 2 members = 8C2 = 28
Total number of ways to select 2 females = 5C2 = 10
P(two females) = 10/28 = 5/14
The answer is D.
Answer: D
Question: If integers d and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. db + b^2
II. (d + b)^2
III. d + b
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
I. db + b^2 --> if d=1 and b=2 then db + b^2=6, which is a factor of 30. OK;
II. (d + b)^2 --> (d + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;
III. d + b --> if d=1 and b=2 then d + b=3, which is a factor of 30. OK.
Answer: B.
Answer: B
Question: Flora and Ed will throw five dice each. The score is the sum of points on all five dice. If Flora scores 17 in her attempt, what is the probability that Ed will outscore Flora in his attempt?
Options:
A)3/4
B)2/3
C)1/2
D)1/3
E)1/4
Rationale: The expected value of each die is 3.5 points.
The expected value of 5 dice is 5*3.5=17.5 points.
Since this is the expected value, Ed is equally likely to get a score above 17.5 points as below 17.5 points. Then the probability of scoring 18 or more points is 50%.
P(Ed wins)=1/2
The answer is C.
Answer: C
Question: The milk level in a rectangular box measuring 50 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)
Options:
A)100
B)250
C)750
D)4687.5
E)5635.5
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 50*25*1/2=625 feet^3 of milk must be removed, which equals to 625*7.5=4687.5 gallons.
Answer: D.
Answer: D
Question: TWO WORKERS A AND B ARE ENGAGED TO DO A WORK. A WORKING ALONE TAKES 8 HOURS MORE TO COMPLETE THE JOB THAN IF BOTH WORKED TOGETHER. IF B WORKED ALONE, HE WOULD NEED 4 1/2 HOURS MORE TO COMPLETE THE JOB THAN THEY BOTH WORKING TOGETHER. WHAT TIME WOULD THEY TAKE TO DO THE WORK TOGETHER?
Options:
A)4 HOURS
B)5 HOURS
C)6 HOURS
D)7 HOURS
E)NONE OF THESE
Rationale: LET A AND BE TOGETHER TAKE X HOURS TO COMPLETE THE WORK. THEN, A ALONE TAKES (X+8) HRS AND B ALONE TAKES (X+9/2) HRS TO COMPLETE THE WORK. THEN,
1/(X+8)+1/(X+9/2)=1/X, 1/(X+8)+2/(2X+9)=1/X
X(4X+25)=(X+8)(2X+9)
2X^2=72, X^2=36, X=6
Correct Option : C
Answer: C
Question: A total of 40 men and 25 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
Options:
A) 31
B) 30.2
C) 32
D) 32.5
E) 33
Rationale: Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people
35 * 65 = 40 * 38 + 25 * Aw
=>2275 = 1520 + 25 Aw
=> 25 Aw = 755
=>Aw = 30.2
Answer B
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?
Options:
A)50
B)99
C)88
D)77
E)12
Rationale: 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
Answer: A
Question: Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
Options:
A)24.7 years
B)28.5 years
C)24.6 years
D)23.5 years
E)24.5 years
Rationale: Let Rahul's age be x years.
Then, Sachin's age = (x - 7) years.
(x - 7)/x = 7/9
2x = 63 => x = 31.5
Hence, Sachin's age = (x - 7)
= 24.5 years.
Answer:E
Answer: E
Question: A person has to cover a distance of 100km in 10hour. If he covers one half of the distance in half of the total time; to cover the remaining distance in the remaining time, his speed must be?
Options:
A)20km/hr
B)15km/hr
C)25km/hr
D)10km/hr
E)5km/hr
Rationale: Remaining distance = 50km
Remaining time = 1/2 * 10 = 5 hours
Required speed = 50*5 = 10km/hr
Answer is D
Answer: D
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 5 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: Let the average age of the whole team be x years.
11x - (26 + 31) = 9 (x - 1)
11x - 9x = 48
2x = 48
x = 24.
The average age of the team is 24 years.
The answer is D.
Answer: D
Question: Rajesh is 20 years old and Mary is 30years old. How many years ago was the ratio of their ages 2:5?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: Suppose the ratio was 2:5, x years ago
20-x / 30-x = 2/5
2x = 40
x = 20
Answer is C
Answer: C
Question: If A is the least common multiple of 90,196, and 300, which of the following is NOT a factor of A?
Options:
A)600
B)700
C)900
D)2,100
E)4,900
Rationale: IF A is the least common multiple of 90,196 and 300, which of the following is NOT a factor of A?
A- 600
B- 700
C- 900
D- 2100
E- 4900
90 = 2 * 3 * 3 * 5
196 = 2 * 2 * 7 * 7
300 = 2 * 2 * 3 * 5 * 5
LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7
(TWO 2, TWO 3, TWO 5, TWO 7)
600 = 2 * 2 * 2 * 3 * 5 * 5
700 = 2 * 2 * 5 * 5 * 7
900 = 2 * 2 * 3 * 3 * 5 * 5
2100 = 2 * 2 * 3 * 5 * 5 * 7
4900 = 2 * 2 * 5 * 5 * 7 * 7=A
Answer: A
Question: A car covers a distance of 782 km in 8 hours. Find its speed?
Options:
A)104 kmph
B)89 kmph
C)288 kmph
D)97 kmph
E)87 kmph
Rationale: 782/8
= 97 kmph
Answer: D
Answer: D
Question: From the set of numbers x, y, t, z and w, how many different combinations can we have without the t and z in them? Ex:. (x,y), (x), (w,y,x), etc and (x,y)=(y,x)
Options:
A)6
B)14
C)15
D)16
E)30
Rationale: Another way: Any letter (x, y, w) can be included or not. So, we have 2^3 combinations - 2 empty combination = 6 combinations
A
Answer: A
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 4 boys and 12 girls Will take to construct?
Options:
A)7 days
B)14 days
C)6 days
D)8 days
E)9 days
Rationale: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
4 boys + 12 girls = 4 Ã— 6/4 + 12 = 6+ 12 = 18 girls
8 days to complete the work
Answer: Option D
Answer: D
Question: In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number W of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85?
Options:
A)144
B)189
C)234
D)279
E)309
Rationale: Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.
Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.
If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279.
(10x+18x) < 85.
28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3.
(45x+48x) = 93x.
Max (93x) W= 279.
Answer is D.
Answer: D
Question: What is the Compound Interest on Rs.7000 at 8.5% p.a. compounded half-yearly for 5 years.
Options:
A)3616.5
B)3613.5
C)3313.5
D)3616.5
E)3113.5
Rationale: Compound interest : A = P(1 + r/n)nt
A = 10,613.50
C.I. >> 10,613.50 - 7000 >> Rs. 3613.5
Answer:B
Answer: B
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 40% on the cost price. He then sold the articles by offering a discount of 5% on the labeled price. What is the actual percent profit earned in the deal?
Options:
A)18%
B)20%
C)17%
D)33%
E)None of these
Rationale: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.140.
SP = Rs.140- 5% of 140 = Rs.140-7 = Rs.133.
Gain = Rs.133 â€“ Rs.100 = Rs.33
Therefore, gain/profit percent = 33%.
Answer: Option D
Answer: D
Question: In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the each share of profit?
Options:
A)10800
B)10600
C)10400
D)10200
E)10000
Rationale: Given A=45000 B=30000 C=22500
A:B:C= 450:300:225
As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees
But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital,
So A= 450*4+ 225*9= 1800+2025= 3825
Similarly, B= 300*13=3900
Similarly,C= 225*13= 2925
Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39
B's share=52/142(28400)=10400
ANSWER:C
Answer: C
Question: A group of n people, including Caroline and her best friend Catherine, stand in random order
around a circle, with each order being equally likely. If the probability that Catherine is adjacent
to Caroline is 1/9 , then what is the value of n?
Options:
A)20
B)19
C)18
D)17
E)16
Rationale: Caroline is adjacent to 2 people, and there are n 􀀀 1 people not including Caroline.
Therefore, the probability that Catherine is adjacent to Caroline is 2/n-1 = 1/9 , and solving gives
n = 19 .
correct answer B
Answer: B
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
Options:
A) 3/8
B) 21/25
C) 1/2
D) 3/5
E) 3/4
Rationale: x * 3/100 * 1 + (20000 - x) * 8/100 * 1 = 1440
3x - 8x = 144000 - 160000
=> -5x = -16000
=> x = 32000
So 16800/20000 = 21/25
Answer - B
Answer: B
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)2
B)7
C)6
D)4
E)2
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Answer: D
Question: The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year?
Options:
A)3472
B)8222
C)4370
D)26777
E)8222
Rationale: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x)(8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10%10%.
So 8100+15100⋅x+10100⋅(8100−x)=91008100+15100⋅x+10100⋅(8100−x)=9100
Therefore 8100+320x+110(8100−x)=91008100+320x+110(8100−x)=9100
120x=190120x=190
x=3800x=3800
Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, respectively.
Answer:C
Answer: C
Question: At a certain health club, 30 percent of the members use both the pool and sauna, but 20 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
Options:
A)58 1/3%
B)40%
C)50%
D)62 1/2%
E)75%
Rationale: P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
20% of (70-x) = x => 14 - 0.2x = x => x = 11 2/3% so only P = 70 -x = 58 1/3%
Answer A
Answer: A