mathewhe/aqua_rat huggingface dataset:
Question: If 3^p - 3^(p-1) = 162 then p(p-1) =
(A) 12
(B) 16
(C) 20
(D) 30
(E) 81
Rationale: It seems like you were really close but you solved for p - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of p(p -1), e.g. (3)(4) = 12. Even then, had you figured p has to be a little bigger (plugging in 4 for p gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (p - 1) exponent place.
Again, a quick plugging in should get you (C) 20 as, the only other answer with consecutive integers as factors is far too big.
Answer: (C) 20
Question: total dinning bill of 7 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
(A) 21.84
(B) 22.84
(C) 23.84
(D) 24.84
(E) 25.84
Rationale: dinner bill of 7 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/7 = $ 21.84
ANSWER:A
Answer: (A) 21.84
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 10
(B) 17
(C) 15
(D) 11
(E) 16
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: A
Answer: (A) 10
Question: If the areas of the three adjacent faces of a cuboidal box are 120 cm², 72 cm² and 60 cm² respectively, then find the volume of the box.
(A) 120 m³
(B) 400 m³
(C) 660 m³
(D) 720 cm m³
(E) None
Rationale: Sol.
Let the length, breadth and height of the box be, l, b, and h respectively, Then,
Volume = lbh = √(lbh)² = √lb * bh * lh = √120 * 72 * 60 = 720 cm³
Answer D
Answer: (D) 720 cm m³
Question: Two stations P and Q are 65 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 9 am
(B) 12 am
(C) 10.30 am
(D) 12.30 am
(E) 11 am
Rationale: Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 65
=> 20x + 25(x-1) = 65
=> 45x = 90
=> x= 2
Means, they meet after 2 hours after 7 am, ie, they meet at 9 am
Answer is A.
Answer: (A) 9 am
Question: A bag contains 9 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
(A) 1/7
(B) 2/9
(C) 3/11
(D) 3/55
(E) 2/3
Rationale: Total number of balls = 9+2 = 11
n(S) = 11C3 = 11*10*9 / 3*2 = 165
n(E) = 2C2* 9C1 = 9
Probability = 9/165 = 3/55
Answer is D
Answer: (D) 3/55
Question: Find the missing number:
3 6 18 ? 7 8
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: 3*2=6
6*2+6=18
18*2=36
36*2+6=78
we add 6 to product alternately. so blank is replaced by 36
ANSWER:B
Answer: (B) 36
Question: Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 70th number in this set?
(A)  557
(B)  608
(C)  613
(D)  616
(E)  621
Rationale: The set S = {5, 13, 21, 29, ..................... }
1st Number = 8 * 0 + 5 = 5
2nd Number = 8 * 1 + 5 = 13
3rd Number = 8 * 2 + 5 = 21
70th Number = 8 * (70-1) + 5 = 557
Answer = A
Answer: (A)  557
Question: What is the least value of x, So that 2x5476 is divisible by 9
(A) 7
(B) 8
(C) 9
(D) 3
(E) 2
Rationale: Explanation:
The sum of the digits of the number is divisible by 9.
Then the number is divisible by 9.
2 + x + 5 + 4 + 7 + 6 = 24 + x
Least value of x may be '3',
So that the total 24 + 3 = 27
is divisible by 9.
Answer: Option D
Answer: (D) 3
Question: A rectangle having length 120 cm and width 50 cm. If the length of the rectangle is increased by ten percent then how much percent the breadth should be decreased so as to maintain the same area.
(A) 25%
(B) 33.33%
(C) 40%
(D) 7.69%
(E) None of these
Rationale: Explanation :
Solution: (10/(120+10) * 100)% = 7.69%
Answer : D
Answer: (D) 7.69%
Question: A trader bought a car at 20% discount on its original price. He sold it at a 65% increase on the price he bought it. What percent of profit did he make on the original price?
(A) A)2%
(B) B)12%
(C) C)14%
(D) D)20%
(E) E)32%
Rationale: Original price = 100
CP = 80
S = 80*(165/100) = 132
100 - 132= 32%
E)
Answer: (E) E)32%
Question: A 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230m
(B) 240m
(C) 250m
(D) 260m
(E) 270m
Rationale: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s
time= 9sec
let the lenght of second train is x
total distance covered= 260 + x
therefore, D= speed*time
thus 260 + x = 500/9 * 9
x= 500-260=240 m
ANSWER:B
Answer: (B) 240m
Question: A man travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the distance amount?
(A) 2
(B) 4
(C) 5
(D) 1
(E) 3
Rationale: dist 3x km ==> x/3+x/4+x/5 = 47/60
47x/60 = 47/60
x=1 then tot dist = 3*1 = 3 km
ANSWER E
Answer: (E) 3
Question: The perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 38 cm2
(B) 85 cm2
(C) 50 cm2
(D) 45 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 40/2 = 50 cm2
Answer:C
Answer: (C) 50 cm2
Question: If the HCF of two numbers is 2 and their LCM is 70, then the numbers are:
(A) 2, 235
(B) 6, 70
(C) 4, 70
(D) 14, 10
(E) 15, 20
Rationale: Explanation:
HCF of the two numbers is 2
Let us take two numbers are x and y
Their LCM= 70
LCM is the product of two numbers.
LCM/HCF = 70/2 = XY/2
xy=70×2 = 140
xy = 140
x = 14, y = 10 or x = 70, y = 2.
But according to the options, the numbers are x = 14 and y = 10.
Answer: D
Answer: (D) 14, 10
Question: What will be the compound interest on a sum of Rs. 29,000 after 3 years at the rate of 12% p.a.?
(A) s.11123.77
(B) s.11742.91
(C) s.11123.20
(D) s.10123.28
(E) s.10123.21
Rationale: Amount = [29000 * (1 + 12/100)3]
= 29000 * 28/25 * 28/25 * 28/25
= Rs. 40742.91
C.I. = (40742.91 - 29000)
= Rs. 11742.91
Answer:B
Answer: (B) s.11742.91
Question: Special codes are designated by either a 7-letter or an 8-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
(A) 2 (26)^8
(B) 26(26)^7
(C) 27(26)^7
(D) 26(26)^8
(E) 27(26)^8
Rationale: 26^7+26^8 = 26^7(1+26)=27*26^7
The answer is C.
Answer: (C) 27(26)^7
Question: The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
(A) 281
(B) 771
(C) 440
(D) 767
(E) 1981
Rationale: r = 7 h = 3
2πr(h + r) = 2 * 22/7 * 7(10) = 440
Answer:C
Answer: (C) 440
Question: The sum of the even numbers between 1 and n is 89*90, where n is an odd number, then n=?
(A) 167
(B) 173
(C) 179
(D) 185
(E) 193
Rationale: Let n-1 = 2a.
2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 89*90
Then a = 89 and n = 179.
The answer is C.
Answer: (C) 179
Question: A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 88
(B) 27
(C) 32
(D) 80
(E) 12
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 200 + 120 = 320 m.
Time taken = 320/10 = 32 sec.
Answer: C
Answer: (C) 32
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 100 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 100xy
(B) 100y - x
(C) 100x/y
(D) 100y/x
(E) 100x - 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)
100 = D/(x*pi)
D = 100 * x * pi ---------- (3)
From equation (2)
Revolutions = D/(y*pi) = (100 * x * pi) / (y*pi) = 100x/y
Answer (C)
Answer: (C) 100x/y
Question: How long does a train 110 meters long running at the speed of 72 km/hour take to cross a bridge 132 meters in length ?
(A) 12.1 sec
(B) 10 sec
(C) 11 sec
(D) 13 sec
(E) 13.2 sec
Rationale: Speed = 72 km/hour = 72*(5/18) m/sec
= 20 m/sec
Total distance = 110+132 = 142 m
Time = D/S
= 242/20 = 12.1 seconds
ANSWER A
Answer: (A) 12.1 sec
Question: What is the maximum number of pieces of birthday cake of size 4” by 4” that can be cut from a cake 20” by 20”?
(A) 5
(B) 10
(C) 16
(D) 20
(E) 25
Rationale: Each length =20" each piece =4"
Cake could be divided to maximum of 25 pieces
Answer: E
Answer: (E) 25
Question: How many ways are there to split a group of 4 girls into two groups of 2 girls each? (The order of the groups does not matter)
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: the combination is 4C2 /2
= 4!/2!*2! *2 = 3
E
Answer: (E) 3
Question: Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2
(A) 26
(B) 22
(C) 25
(D) 27
(E) 29
Rationale: (4)^11x (7)^5 x (11)^2
= (2 x 2)^11 x (7)^5 x (11)^2
= 2^11 x 2^11 x7^5x 11^2
= 2^22 x 7^5 x11^2
Total number of prime factors = (22 + 5 + 2) = 29.
Answer is E.
Answer: (E) 29
Question: A certain restaurant offers 8 different curry, 5 different main courses, 6 different ice creams. If customers choose one salad, one main course and two different ice creams for their meal, how many different meals are possible?
(A) 120
(B) 240
(C) 480
(D) 500
(E) 600
Rationale: MAGOOSHOFFICIAL SOLUTION:
To count the number of curry, we have to count the possibilities for the three components, and then, according to the Fundamental Counting Principle, we multiply. For more on the FCP, see this blog.
For salads, there are 8 possibilities. Done.
For main courses, there are 5 different possibilities. Done.
For ice creams, there are 6 choices, but we pick two different choices. This would be 6C2. To calculate this, we can use the shortcut, nC2 = (n*(n-1))/2.
6C2 = (6*5)/2 = 15
So, there are 15 combinations of two different desserts.
For the number of meals, we multiply 8*5*15. We know 8*5 = 40. Then, we need 40*15. Well, 4*15 = 60, so 40*15 must be 600.
Answer = (E)
Answer: (E) 600
Question: In a certain corporation, there are 300 male employees and 150 female employees. It is known that 40% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
(A) 1/2
(B) 2/3
(C) 3/5
(D) 7/10
(E) 11/15
Rationale: P(female) = 150/450 = 1/3
P(male with advanced degree) = 0.4*300/450 = 120/450 = 4/15
The sum of the probabilities is 9/15 = 3/5
The answer is C.
Answer: (C) 3/5
Question: A train 125 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 40
(B) 55
(C) 60
(D) 79
(E) 80
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 10) km/hr.
x - 10 = 45 => x = 55 km/hr.
Answer: Option B
Answer: (B) 55
Question: A began business with 12000 and is joined afterwards by B with 72000. When did B join, if the profits at the end of the year are divided equally?
(A) 8 months
(B) 9 months
(C) 10 months
(D) 7 months
(E) None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12000 : (12 – x) × 72000
or 12 : 6(12 – x)
Since profit is equally divided so
12 =6(12 – x) or x = 10. Thus B joined after 10 months.
Answer C
Answer: (C) 10 months
Question: A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?
(A) 1200
(B) 1260
(C) 1301
(D) 1340
(E) 1400
Rationale: sol. let the new sp be Rsx.then
(100-loss%) : (1st sp)=(100+gain%) (2nd sp)
{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.
Option B
Answer: (B) 1260
Question: The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?
(A) 100 %
(B) 200%
(C) 300%
(D) 600%
(E) None of these
Rationale: Explanation:
Let the salaries of A, B, C be x, 2x and 3x respectively.
Then,2x + 3x = 6000 => x = 1200.
A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600.
Excess of C's salary over A's=[ (2400 /1200) x 100] = 200%.
Answer: B
Answer: (B) 200%
Question: A certain number of persons can finish a piece of work in 100 days. If there were 10 persons less, it would take 10 more days finish the work. How many persons were there originally?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: Explanation:
Assume that x persons can finish a piece of work in 100 days
Also it is given that (x−10) persons can finish a piece of work in 110 days (∵ 100 + 10 = 110)
More persons, less days(indirect proportion)
Hence we can write as(persons) x : (x−10) :: 110 : 100
⇒100x=110(x−10)
⇒100x=110x−1100
⇒10x=1100
⇒x=1100/10=110
Answer: Option C
Answer: (C) 110
Question: In how many ways can a team 16 be chosen out of a batch of 20 players?
(A) 4845
(B) 6852
(C) 3125
(D) 5846
(E) 7846
Rationale: Required number of ways= 20C16= 20C(20-16) = 20C4
= (20*19*18*17)/(4*3*2*1)
= 4845.
ANSWER:A
Answer: (A) 4845
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in meterr?
(A) 40 m
(B) 60 m
(C) 65 m
(D) 70 m
(E) 80 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: Two trains run in opposite directions on a circular track. Train Q travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?
(A) 3
(B) 6
(C) 9
(D) 18
(E) 22
Rationale: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train Q be X, thus that covered by the train B will be 12*3.14-X
dQ = X dB = 12*3.14 - X
Times taken by A and B are
tQ= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of Q and B: totalSpeed = 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tQ =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5.
Answer: (B) 6
Question: Complete the numerical series by replacing the question mark with the correct numbers.
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
9+5+5 = ??????
(A) 454584
(B) 454585
(C) 454586
(D) 454587
(E) None
Rationale: Solution:
454585
Explanation:
Number is formed as (numA*numB)(numB*numC)(numC*numA)
Following the formular, 1st row will be like
5+3+2 => 5*3 3*2 2*5 => 151022
Simillarly
(9*5)(9*5)(9*5+9*5-5) => 454585
Answer B
Answer: (B) 454585
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
(A) 5/1
(B) 5/9
(C) 5/8
(D) 5/6
(E) 5/2
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 =5/9.
Answer:B
Answer: (B) 5/9
Question: If 12 machine can finish a job in 40 days, then how many more machines would be needed to finish the job in one -fourth less time?
(A) a. 4
(B) b. 8
(C) c. 10
(D) d. 12
(E) e. 16
Rationale: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 12 machines (identical ones, I assume) work simultaneously for 40 days, they will do a total of 12*40 machine-days of work. So the job requires 12*40 days of machine work in total. We instead want the job done in 1/4 less time, so in 30 days. So we'll need 12*40/30 = 16 machines, or 4 additional machines.
A
Answer: (A) a. 4
Question: In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?
(A) $2.4 million
(B) $2.9 million
(C) $3.0 million
(D) $3.1 million
(E) $3.6 million
Rationale: Let the number of pairs of shoes sold in 1985 = N
let price per pair of shoe sold in 1985 = P
In 1986,number of pairs of shoes sold decreased by 20 % = .8N
Price per pair increased by 20% = 1.2P
Company's revenue from sale of shoes in 1986 = 3 million$
=> .8N * 1.2 P = 3
=>.96 NP = 3
=> NP = 3/.96 = 3.125 million $
Answer D
Answer: (D) $3.1 million
Question: If E is an integer greater than 6, which of the following must be divisible by 3?
(A) E(E+1)(E-4)
(B) N(N+2)(N-1)
(C) N(N+3)(N-5)
(D) N(N+4)(N-2)
(E) N(N+5)(N-6)
Rationale: Now take E = 3k , E = 3k+1 E = 3k+2..put in all the choices. If by putting all the values of E we get it is divisible by 3, then it is correct answer choice.
A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: (A) E(E+1)(E-4)
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 76 m
(B) 178 m
(C) 235 m
(D) 187 m
(E) 176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2
=> 2(140 + x)= 750 => x = 235 m.
Answer: C
Answer: (C) 235 m
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 45 true?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Answer B
(a+b)(a-b)=45
3cases For (a+b), (a-b)
45, 1
15, 3
9, 5
Answer B
Answer: (B) 3
Question: Miguel is 50 years old. He is 5 years older than thrice his son’s age. Find the age of his son.
(A) 11years
(B) 12years
(C) 13years
(D) 14years
(E) 15years
Rationale: sons age=x
50-3x=5
x=15years
ANSWER:E
Answer: (E) 15years
Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth.The percentage of decrease in area is :
(A) 13%
(B) 14%
(C) 18%
(D) 20%
(E) 28%
Rationale: Let original length =x and original breadth =y.
Decrease in area =xy-(80/100*x*90/100*y)=(xy-18/25*xy)=7/25*xy.
Decrease% = (7/25*xy*1/xy*100)%=28%.
Answer is E
Answer: (E) 28%
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) 3000
(B) 1230
(C) 2000
(D) 5600
(E) 3400
Rationale: C
C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
Answer: (C) 2000
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 1/25
(B) 2/21
(C) 5/26
(D) 3/41
(E) 1/115
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?
(A) 777
(B) 500
(C) 789
(D) 776
(E) 881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
Answer B
Answer: (B) 500
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
(A) 8/3
(B) 2
(C) 8/5
(D) 5/8
(E) 5/3
Rationale: Distance traveled by Eddy = 450 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 450/3 = 150 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 150/75 = 2
Answer B
Answer: (B) 2
Question: What is x if x + 2y = 10 and y = 3?
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: Substitute y by 3 in x + 2y = 10
x + 2(3) = 10
x + 6 = 10
If we substitute x by 4 in x + 6 = 10, we have 4 + 6 = 10.
x = 4
correct answer is D) 4
Answer: (D) 4
Question: A factory has a fixed cost of $35,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 14,000
(C) 18,000
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =35000
no of items required = 35000/2.5 = 14000
Ans B
Answer: (B) 14,000
Question: A deer is standing 60 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 15 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?
(A) 125
(B) 135
(C) 145
(D) 155
(E) 165
Rationale: Let x be the length of the tunnel.
When the deer runs 60 meters west, the train goes 600 meters to a point 15 meters from the west entrance of the tunnel.
When the deer runs east, the deer runs x-60 meters while the train goes x + 600 + 15 meters.
x + 600 + 15 = 10(x-60)
9x = 1215
x = 135 meters
The answer is B.
Answer: (B) 135
Question: The triplicate ratio of 1:4 is?
(A) 1:64
(B) 1:62
(C) 1:34
(D) 3:64
(E) 5:64
Rationale: 1^3: 4^3 = 1:64
ANSWER:A
Answer: (A) 1:64
Question: Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?
(A) 188
(B) 100
(C) 177
(D) 268
(E) 266
Rationale: Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 100 min.
AnswerB
Answer: (B) 100
Question: There are 3 questions in a question paper. If the questions have 4,3 and 2 solutions respectively, find the total number of solutions
(A) 24
(B) 25
(C) 30
(D) 40
(E) 54
Rationale: Here question 1 has 4 solutions, question 2 has 3 solutions and question 3 has 2 solutions.
=> By the multiplication (counting) rule,
Total number of solutions=4Ã—3Ã—2==4Ã—3Ã—2= 24
ANSWER A
Answer: (A) 24