mathewhe/aqua_rat huggingface dataset:
Question: A ratio between two numbers is 4:5 and their L.C.M. is 200. The first number is
(A) 60
(B) 40
(C) 20
(D) 15
(E) None
Rationale: Sol.
Let the required numbers be 4x and 5x. Then, their L.C.M. is 20x.
∴ 20x = 200⇔ x = 10. Hence, the first number is 40.
Answer B
Answer: (B) 40
Question: If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
(A) 141
(B) 200
(C) 312
(D) 391
(E) 412
Rationale: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 318
3A = 312
A = 102
This IS an EVEN INTEGER! The numbers would be 102, 104 and 106. This IS the answer
Final Answer:
C
Answer: (C) 312
Question: A football field is 8400 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3500 square yards?
(A) 450
(B) 600
(C) 500
(D) 2400
(E) 3200
Rationale: Answer A) 4800 yards need 1200 lbs
1 Yard will need 1200/8400 = 1/7 lbs
3600 Yards will need 1/7* 3500 Yards = 500lbs
C
Answer: (C) 500
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 20 months?
(A) 18:11
(B) 18:15
(C) 20:11
(D) 18:121
(E) 18:112
Rationale: A invests Rs.8000 for 20 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*20 : (8000*4) + (4000*14)
160000 : 88000
A:B = 20:11.Answer:C
Answer: (C) 20:11
Question: If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be odd?
(A)  1/6
(B)  1/3
(C)  1/2
(D)  2/3
(E)  5/6
Rationale: Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 1/3.
Answer: B.
Answer: (B)  1/3
Question: In how many different number of ways 4 boys and 1 girls can sit on a bench?
(A) 120
(B) 140
(C) 160
(D) 180
(E) 200
Rationale: npn = n!
5p5= 5 × 4 × 3 × 2 × 1 = 120
A
Answer: (A) 120
Question: A rectangular lawn of dimensions 90 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) A)4200
(B) B)930
(C) C)9309
(D) D)3900
(E) E)8302
Rationale: Explanation:
Area = (l + b – d) d
(90 + 60 – 10)10 => 1400 m2
1400 * 3 = Rs.4200
Answer: Option A
Answer: (A) A)4200
Question: If 22 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?
(A) 95
(B) 90
(C) 88
(D) 80
(E) 75
Rationale: Let x be the number of students in the school. 0.22x students went to the trip and took more than 100$. They compose (100-75)=25% of all students who went to the trip. Therefore the toal of 0.22x/0.25=0.88x students went to the camping which is 88%.
The answer is C
Answer: (C) 88
Question: Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity Q for the round trip?
(A) 24 miles per hour
(B) 48 miles per hour
(C) 50 miles per hour
(D) 53 1/3 miles per hour
(E) 68 miles per hour
Rationale: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.
Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.
D = (R)(T)
120 = (40)(T)
120/40 = 3 = T
3 hours to drive to SD
On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.
D = (R)(T)
120 = (60)(T)
120/60 = 2 = T
2 hours to drive to SD
Total Distance = 240 miles
Total Time = 3+2 = 5 hours
Average Speed = 240/5 = 48 miles/hour
Final Answer:
B
Answer: (B) 48 miles per hour
Question: If the area of circle is 314 sq cm then its circumference?
(A) 10
(B) 61
(C) 65
(D) 56
(E) 62
Rationale: 22/7 r2 = 314 => r = 10
2 * 22/7 * 10 = 62
Answer: E
Answer: (E) 62
Question: The sector of a circle has radius of 28 cm and central angle 135o. Find its perimeter?
(A) 90cm
(B) 95cm
(C) 100cm
(D) 110cm
(E) 122cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 28) + 2(28)
= 66 + 56 = 122 cm
Answer:E
Answer: (E) 122cm
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 960 grams. Find the profit percent.
(A) 4.166
(B) 3.1
(C) 2.1
(D) 1.256
(E) 3.759
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 960
100 + g / 100 + 0 = 1000 / 960
100+g = 100/96*100
g = 4.166
ANSWER: A
Answer: (A) 4.166
Question: When the positive integer A is divided by 5 and 8, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 8, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
(A) 32
(B) 35
(C) 36
(D) 40
(E) 50
Rationale: A = 5k+3 = 8j+4
B = 5m+3 = 8n+4
A-B = 5(k-m) = 8(j-n)
Thus A-B is a multiple of 5 and 8, so it is multiple of 40.
The answer is D.
Answer: (D) 40
Question: Narendra started a business, investing 30000. Six months later, Chandan joined him with 10000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra?
(A) A)Rs.7000
(B) B)Rs.8000
(C) C)Rs.8500
(D) D)Rs.8571
(E) E)Rs.8700
Rationale: The ratio of their investments = 30000 × 12 : 10000 × 6 = 6: 1.
:. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571.
D)
Answer: (D) D)Rs.8571
Question: In an engineering class that contained 50 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?
(A) 4
(B) 6
(C) 10
(D) 12
(E) 24
Rationale: 1st Question : Three fifths of the students answered the first question correctly - so 3/5∗50=30
2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(50−30)=45∗20=16
total students who answered at least one Q correct =30+16=46
so students who answered BOTH incorrectly = 50−46=4
ANSWER:A
Answer: (A) 4
Question: On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000?
(A) 15
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: 5,000(1 + x)^10 = 20,000
(1+x)^10 = 4 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
5000(1 + x)^n = 40,000
(1+x)^n = 8
(1+x)^n = 2^3
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Answer: (A) 15
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire
rest of the car, then the share of each of the remaining persons increased by ?
(A) 1/9
(B) 1/8
(C) 1/7
(D) 7/8
(E) 8/7
Rationale: When there are eight people, the share of each person is 1/8th the total cost
ANSWER:B
Answer: (B) 1/8
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
(A) 2/2
(B) 1/2
(C) 7/2
(D) 8/2
(E) 6/2
Rationale: Explanation:
The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer:B
Answer: (B) 1/2
Question: Departments A, B, and C have 4 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
(A) 12,610
(B) 40,000
(C) 100,000
(D) 190,000
(E) 400,000
Rationale: 4c1 * 4c1* 4c1*20c2 = 10*10*10*190=12,610. Hence A is the correct answer.
Answer: (A) 12,610
Question: A father is Quadrice as old as his daughter today. After 20 years, he would be only two times as old. At the time of daughter’s birth, how much old the father be?
(A) 30
(B) 10
(C) 40
(D) 20
(E) 60
Rationale: A
30
If the ages of daughter and father today by ‘A’ and ‘4A’ years correspondingly.
4A + 20 = 2 (A+20)
A = 10 years => 4A = 40 years.
At the time of daughter’s birth, father’s Age
40 – 10 = 30 years old
Answer: (A) 30
Question: The unit digit in the product (784 x 618 x 917 x 463) is:
(A) 5
(B) 9
(C) 16
(D) 2
(E) 42
Rationale: Explanation:
Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2
D
Answer: (D) 2
Question: Find the average of all the numbers between 16 and 34 which are divisible by 5?
(A) 10
(B) 20
(C) 28
(D) 30
(E) 15
Rationale: Average = (20+25+30) 3 = 85/3 = 28
Answer is C
Answer: (C) 28
Question: How much time will take for an amount of Rs. 100 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 7
(B) 4
(C) 18
(D) 10
(E) 15
Rationale: Time = (100 * 81) / (100 * 4.5) = 4 years'
Answer:C
Answer: (C) 18
Question: A fill pipe can fill 1/3 of cistern in 20 minutes in how many minutes, it can fill 3/4 of the cistern?
(A) 15 min
(B) 45 min
(C) 25 min
(D) 40 min
(E) 50 min
Rationale: 1/3 of the cistern can fill in 20 min
3/4 of the cistern can fill in = 20*3*3/4 = 45min
Answer is B
Answer: (B) 45 min
Question: There are 4 copies of 5 different textbooks. In how many ways can they be arranged on a shelf?
(A) 20!/4!
(B) 20!/5(4!)
(C) 20!/(4!)^5
(D) 20!
(E) 5!
Rationale: There are 4 copies of 5 different textbooks.20!/((4!)^5)
Answer - C
Answer: (C) 20!/(4!)^5
Question: We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value Q of the ratio A/B?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 1/4
(E) 1/5
Rationale: Q-> A/B=20*21*……*39/21*22*….*39*40=20/40=1/2.
Therefore, the answer is A.
Answer: (A) 1/2
Question: In a bag, there are 10 discs, numbered 1 to 10 (no duplicates). If we randomly choose 4 of the discs, what is the probability that the range of the numbers chosen is 7?
(A) 1 / 14
(B) 1 / 7
(C) 3 / 14
(D) 9 / 28
(E) 4 / 7
Rationale: Probability (A) = No of suitable outcomes where A happens/Total no of outcomes
We use combinations to get "No of suitable outcomes where A happens" and "Total no of outcomes" and then calculate the required probability. So for the time being, just forget that you have to find some probability.
Focus on two things: "No of suitable outcomes where A happens" and "Total no of outcomes"
It is easy to find total number of outcomes. 10C4. e.g. (2, 3, 4, 6), (4, 1, 9, 5) etc etc etc
In how many combinations is range 7? (This is the "No of suitable outcomes where A happens")
(3, 10, a, b), (2, 9, c, d) and (1, 8, e, f)
a and b are numbers between 3 and 10 (so that range doesn't exceed 7)
c and d are numbers between 2 and 9
e and f are numbers between 1 and 8
In how many ways can you choose a and b? 6C2 (Any 2 out of 6 numbers between 3 and 10). So how many 4 number combinations are there which look like this: (3, 10, 4, 6), (3, 10, 7, 5) etc?
I hope you agree it is 6C2.
Similarly, you get 6C2 combinations of the type (2, 9, c, d) and 6C2 of the type (1, 8, e, f).
No of suitable combinations = 6C2 + 6C2 + 6C2
Now, the required probability = No of suitable combinations where A happens/Total no of outcomes
= (3*6C2)/10C4 =3/14
Correct answer is C
Answer: (C) 3 / 14
Question: If 0.25 : x : : 2 : 6, then x is equal to
(A) 0.65
(B) 0.25
(C) 0.75
(D) 0.85
(E) None
Rationale: Sol.
(x×2) = (0.25×6) ⇒ x = 1.5/2 = 0.75.
Answer C
Answer: (C) 0.75
Question: Ravi can do a piece of work in 26 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 15 25/33 days
(B) 16 1/33 days
(C) 17 1/33 days
(D) 17 25/33 days
(E) 18 1/33 days
Rationale: 1/26 + 1/40 = 33/520
520/33
= 15 25/33 days
Answer: A
Answer: (A) 15 25/33 days
Question: Find the invalid no.from the following series 12, 19, 24, 31, 36, 39
(A) 13
(B) 18
(C) 40
(D) 39
(E) 25
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 39 is wrong.
Answer : D
Answer: (D) 39
Question: For every integer n ≥ 3, the function h(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of h(101) + h(100)?
(A) 0
(B) 100
(C) 102
(D) 99
(E) 105
Rationale: h(101) = 1*3*5*7*9*...*99*101
h(100) = 1*3*5*7*9*...*99
h(101) +h(100) = 1*3*5*7*9*...*99 + 1*3*5*7*9*...*97 = 1*3*5*7*9*...*99*(101 + 1) = 1*3*5*7*9*...*99*102
hence:C
Answer: (C) 102
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) 19
(B) 70
(C) 27
(D) 29
(E) 20
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%.Answer: B
Answer: (B) 70
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 65 kilometers, Maxwell's walking speed is 2 km/h, and Brad's running speed is 3 km/h. What is the distance traveled by Maxwell when they meet in the middle?
(A) 25
(B) 23
(C) 22
(D) 24
(E) 26
Rationale: Consider Max starts from Point A and Brad Starts from Point B and move towards each other.
Assume they shall meet at point O after Time 'T'. The question asks us to find OA.
From the question stem we can make out :- Distance OA = 50km - Distance OB
=> 2xT = 65 - 3xT (i.e distance =Speed x Time)
=> 5T = 65
Hence T = 13
OA = 2x 13 = 26 Km
Answer : E
Answer: (E) 26
Question: How many 1/3 pound paperback books together weigh 25 pounds?
(A) 35
(B) 50
(C) 60
(D) 75
(E) 80
Rationale: Explanation:
If each book weighs 1/3 pound, then 1 pound = 3 books. We can set up a proportion to solve: 1 pound / 3 books = 25 pounds / x books. Now cross-multiply:
(1)(x) = (3)(25)
X = 75
Answer :(D)
Answer: (D) 75
Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
(A) 3/13
(B) 3/12
(C) 3/11
(D) 3/12
(E) 3/18
Rationale: Explanation:
Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/52=3/13.
Answer: A
Answer: (A) 3/13
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 11:00 a.m., at what time was it one-eighth full?
(A) 10:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 2:00 a.m.
Rationale: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 11:00 a.m -1 hour = 10:00 a.m.
Answer: A.
Answer: (A) 10:00 a.m.
Question: A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
(A) 1 hour 30 minutes
(B) 1 hour 23 minutes
(C) 1 hour 20 minutes
(D) 1 hour 28 minutes
(E) 1 hour 26 minutes
Rationale: Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3
=> (5d - 4d)/4k = 1/3 => d = 4/3 k
Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes.
Answer:C
Answer: (C) 1 hour 20 minutes
Question: Which of the following are divisible by both 2 and 3?
I. 234,124,422
II. 88,865,544,274
III. 5,555,554,673
(A) I​ only
(B) I and II​
(C) II and III
(D) II Only
(E) I​ and III
Rationale: III. is not divisible by 2 since the last digit is odd so we eliminate option C and E, we are left with option A, B and D
Among option I and II lets check the divisibility of 3
I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3
II. is not divisible by 3 since sum of the digits is not divisible by 3
Thus among the given options only (A) holds true.
Answer: A
Answer: (A) I​ only
Question: Three numbers are in the ratio 3:5:8. The largest number value is 152. Find difference between Smallest & largest number is?
(A) 16
(B) 90
(C) 38
(D) 95
(E) 78
Rationale: Explanation:
== 3:5:8
Total parts = 16
= The largest number value is 152
= The largest number is = 8
= Then 8 parts -----> 152 ( 8 * 19 = 152 )
= smallest number = 3 & Largest number = 8
= Difference between smallest number & largest number is = 8 - 3 = 5
= Then 5 parts -----> 95 (5 * 19 = 95)
Answer: Option D
Answer: (D) 95
Question: Andrew grossed $530 one week by working 49 hours. His manager pays him time-and-a-half for all hours worked in excess of 35 hours. What is Andrew's regular hourly wage?
(A) $10 per hour
(B) $15 per hour
(C) $5 per hour
(D) $12 per hour
(E) $20 per hour
Rationale: Denote by x the regular hourly wage.
Then 1.5x is the hourly overtime wage.
For 35 hours, Andrew received a salary of 35x.
For 49-35=12 hours, he received 12(1.5x)=18x
Total salary: 35x+18x=53x which equals $530.
53x=530 implies x=10 (Andrew receives $10 per hour)
Answer A 10.
Answer: (A) $10 per hour
Question: 4, 12, 48, 240, 1440,10080,80640 (...)
(A) 7620
(B) 10080
(C) 6200
(D) 10020
(E) 725760
Rationale: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6, 7,8,9
Answer : Option E
Answer: (E) 725760
Question: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum E of all possible 2-digit remainders for x/y?
(A) 560
(B) 616
(C) 672
(D) 728
(E) 784
Rationale: ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
E=8(2+3+4....+12)=616.B
Answer: (B) 616
Question: If Albert’s monthly earnings rise by 27%, he would earn $567. If, instead, his earnings rise by only 26%, how much (in $) would he earn this month?
(A) 643
(B) 652
(C) 562
(D) 578
(E) 693
Rationale: =567/1.27∗1.26
=562=562
Answer is C
Answer: (C) 562
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 9 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 38 7/8
(B) 36
(C) 38 4/7
(D) 34 5/7
(E) 34 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 9 tons of cement, then we'll get 9/7*30 = 38 4/7 tons of mixture.
Answer: C.
Answer: (C) 38 4/7
Question: The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds?
(A) 4
(B) 9
(C) 39
(D) 48
(E) 63
Rationale: Given: z=s^2+2s for 0≤s≤7
z(4) = 4^2 + 2*4 = 24
z(7) = 7^2 + 2*7 = 63
Therefore z(7) - z(3) = 63 - 24 = 39 km/hr
Option C
Answer: (C) 39
Question: The ratio of male to female in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one of the males and one of the females in the class?
(A) a)160 degree
(B) b) 168 degree
(C) c)191 degree
(D) d)72 degree
(E) e)204 degree
Rationale: let the common ratio be x.. so M=2x and F=3x and Total=5x
1 of M= 2x and 1 of F= 3x..
Total preferring that carrer =5x
Now 5x= 360, so x=360/5=72..
so x*8/3= 72*8/3=192
D
Answer: (D) d)72 degree
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 160
(B) 175
(C) 180
(D) 195
(E) 205
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 * 8 * 4) = 160.
Therefore, 160 * 2.40 + x * 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER:B
Answer: (B) 175
Question: A certain airline's fleet consisted of 70 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let x be the number of years.
4x > 70 - 3x
7x > 70
x > 10
The answer is E.
Answer: (E) 11
Question: Calculate Rebecca's average score in an exam if she obtained the following marks 70, 57, 69, 89 and 85 out of 100 in different subjects.
(A) 74
(B) 94
(C) 54
(D) 84
(E) 64
Rationale: Explanation:
(70+57+69+89+85)/5=74
Answer: Option A
Answer: (A) 74
Question: In a simultaneous throw of 2 dice, what is the probability of getting a total of 8?
(A) 3/17
(B) 7/36
(C) 1/36
(D) 5/36
(E) 7/17
Rationale: n(S) = 6*6 = 36
E = event of getting a total of 8 = {(2,6),(3,5),(4,4),(5,3),(6,2)}
probability = 5/36
Answer is D
Answer: (D) 5/36
Question: In how many different ways can the letters of the word 'DETAIL' be arranged such that the consonants must occupy only the even positions?
(A) None of these
(B) 64
(C) 120
(D) 36
(E) 360
Rationale: D
3 consonants DTL can be arranged in 3!=6 ways. Similarly 3 vowels can be arranged on odd places in 3!=6 ways.
Total = 6*6 = 36.
Answer: D.
Answer: (D) 36
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 4/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/15
(C) (c) 10/21
(D) (d) 7/31
(E) (e) 1/2
Rationale: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 4 are small and 1 is large. Now let the small ones cost $6. so the large ones would cost $7.
So,
4*6=24 and 1*7=7.
Total revenue was 24+7=31
and Large cup sales as found above is 7
Therefore answer is 7/31
D
Answer: (D) (d) 7/31
Question: What is the greatest of 3 consecutive integers whose sum is 36?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: 36 / 3 = 12
The three numbers are 11, 12, and 13.
The answer is B.
Answer: (B) 13
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
(A) 22.04%
(B) 16.12%
(C) 8%
(D) 18.25%
(E) 10.5%
Rationale: Per quarter, interest = 2.5% So for a year, interest = 10% Due to quarter cumulation, effective yield (YTM) would be slight higher than 10% Answer = 10.5% =ANSWER:E
Answer: (E) 10.5%