mathewhe/aqua_rat huggingface dataset:
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 25
(B) 38
(C) 64
(D) 68
(E) 70
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 276 m
(B) 279 m
(C) 240 m
(D) 207 m
(E) 330 m
Rationale: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 42 = 15
x + 300 = 630
x =330 m.
Answer: E
Answer: (E) 330 m
Question: a man walks at 40kmph and reaches the distance in 10 min less than that of usual . by walking at 60 kmph he reaches 10 minutes earlier. the distance covered by him is.?
(A) 10km
(B) 20km
(C) 30km
(D) 40km
(E) 50km
Rationale: let x be distance in km ,let t be usual time
given 40km/hr=40/60km/min=2/3km/min 10 min less t+10
given 60km/hr=60/60km/min=1km/min 10 min early t-10
since speed=distance/time
2/3=x/t+10.......eq1
1=x/t-10.....eq2
divide eq 1&2
2/3 = t-10/t+10 => t=50min
x=50-10=40km
ANSWER:D
Answer: (D) 40km
Question: A dice has one of the first 5 prime number on each its six sides ,with no two sides having the same number .the dice is rolled 8 times and the results added.the addition is most likely to be closet to
(A) 45
(B) 48
(C) 60
(D) 68
(E) 70
Rationale: if die is rolled then avg score = (2+3+5+7+11 )/5= 28/5
so, most likely sum for 6 times = 28/5 * 8 = 45
ANSWER:A
Answer: (A) 45
Question: What is the greatest positive integer Q such that 3^Q is a factor of 9^10?
(A) Q=5
(B) Q=9
(C) Q=10
(D) Q=20
(E) 30
Rationale: What is the greatest positive integer Q such that 3^Q is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20
Answer: (D) Q=20
Question: The charge for a single room at Hotel P is 50 percent less than the charge for a single room at Hotel R and 20 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G?
(A) 50%
(B) 60%
(C) 75%
(D) 80%
(E) 90%
Rationale: P = 0.5R = 0.8G
R = 0.8G/0.5 = 1.6*G
Thus R is 60% greater than G.
The answer is B.
Answer: (B) 60%
Question: There are three guys who have equal number of bullets. All of them shoot 10 bullets. The remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division. What was the original number of bullets each one had?
(A) 18
(B) 19
(C) 25
(D) 35
(E) 45
Rationale: let initially each was having x bullets
they shot 10 bullets
so 3x-30=x
x=15
so each was having 15 bullets.
total was 45.
ANSWER:E
Answer: (E) 45
Question: A crate measures 6 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=6 for the surface 8*12 face.
Volume = 216pi
Answer C
Answer: (C) 6
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 288
(B) 2609
(C) 245
(D) 298
(E) 221
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer:C
Answer: (C) 245
Question: A boat having a length 9 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
(A) 100 kg
(B) 120 kg
(C) 189 Kg
(D) 180 Kg
(E) 270 Kg
Rationale: Volume of water displaced	= (9 x 3 x 0.01) m3
= 0.27 m3.
Mass of man = Volume of water displaced x Density of water
= (0.27 x 1000) kg
= 270 kg.
Answer: E
Answer: (E) 270 Kg
Question: The ratio of two angles of a triangle is 5:4, and the sum of the angles equals the third angle. Find the smallest angle, in degrees.
(A) 40
(B) 45
(C) 50
(D) 55
(E) 10
Rationale: The three angles are 5x, 4x, and (5x+4x)=9x for some value x, due to the ratio. [note that 4x is the smallest angle]
The three angles of a triangle add up to 180, so
5x+4x+9x = 180
18x = 180
x = 10
the smallest angle is 4x, so 4*10 = 40 degrees
A
Answer: (A) 40
Question: Which of the following lines has x-intercept and y-intercept that are integers E?
(A) y=3x+1
(B) y=√x+1
(C) y=-2/x
(D) y=x^2-1
(E) xy=1
Rationale: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers E and the correct answer is D.
Answer: (D) y=x^2-1
Question: What is the HCF of 2/3, 4/10 and 6/5
(A) 7/45
(B) 1/15
(C) 4/15
(D) 8/45
(E) 9/45
Rationale: Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 10, 5) = 2/30 = 1/15
Answer: Option B
Answer: (B) 1/15
Question: [( 3.242 x 14 ) / 100] = ?
(A) 0.045388
(B) 4.5388
(C) 453.88
(D) 473.88
(E) None of these
Rationale: Answer
Multiplying 3.242 x 14=4.5388
Now divide 4.5388 by 100
So, 4.5388 ÷ 100= 0.045388
∴ Shift the decimal two places to the left as 100
Correct Option: A
Answer: (A) 0.045388
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 520 kmph
(B) 300 kmph
(C) 400 kmph
(D) 720 km/hr
(E) 780 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. 1 2/3 hours =5/3 hours
Required Speed = 1200x3/5 km/hr =720 km/hr
answer :D
Answer: (D) 720 km/hr
Question: If you roll one fair six-sided die, what is the probability that the number is even or less than 3?
(A) 2/3
(B) 1/2
(C) 3/4
(D) 5/6
(E) 1/3
Rationale: The numbers which satisfy the conditions are 1, 2, 4, and 6.
The probability is 4/6=2/3
The answer is A.
Answer: (A) 2/3
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 482
(B) 66
(C) 26
(D) 99
(E) 222
Rationale: 20000(11/10)4 - 20000(6/5)2 = 482.Answer:A
Answer: (A) 482
Question: Two pipes A and B can separately fill a tank in 12 and 20 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 542
(B) 540
(C) 675
(D) 829
(E) 279
Rationale: 1/12 + 1/20 - 1/x = 1/15
x = 15
15 * 45 = 675
Answer: C
Answer: (C) 675
Question: A’s speed is 20/19 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/19
(B) 3/19
(C) 1/10
(D) 1/20
(E) 3/10
Rationale: Let D be the full distance.
Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (20v/19) = xD/v
(19/20)*D/v = x*D/v
x = 19/20
B should have a head start of 1/20 of the full distance.
The answer is D.
Answer: (D) 1/20
Question: The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (d) around the mirror, which of the following could be the value, in inches, of d ?
I. 2
II. 3 1/2
III. 5
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: Area of picture = 16x Area of frame = 33x
Area of picture / (Area of picture + area of frame) = 16x / 49x = 4x/7x.
This results in d value to be a multiple of 1.5 = multiple of 3/2 and since d is not constrained to be only integer all the three choices are possible
For i) the multiple of d is 4/3
For ii) the multiple of d is 7/3
For iii) the multiple of d is 10/3
The key is d can be any real positive number... very tricky problem.. took me > 15 minutes.
Answer is E
Answer: (E) I, II, and III
Question: The sum of the even numbers between 1 and n is 105*106, where n is an odd number, then n=?
(A) 187
(B) 193
(C) 199
(D) 205
(E) 211
Rationale: Let n-1 = 2a.
2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 105*106
Then a = 105 and n = 211.
The answer is E.
Answer: (E) 211
Question: There are 20 poles with a constant distance between each pole. A car takes 21 second to reach the 12th pole. How much will it take to reach the last pole.
(A) 36.4543
(B) 36.2727
(C) 31.45128
(D) 36.41288
(E) 31.41222
Rationale: Assuming the car starts at the first pole.
To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).
11 poles 21 seconds
1 pole (21/11) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
19 pole 19 x (21/11) seconds
= 36.2727 seconds
Answer:B
Answer: (B) 36.2727
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 160. The dividend from the stock is :
(A) 7.5 %
(B) 8 %
(C) 10 %
(D) None of these
(E) Cannot be determined
Rationale: Solution
By investing Rs. 1552,income = Rs. 128.
By investing Rs. 97, income = Rs. (160/1552x97)= Rs.10
âˆ´ Dividend =10%.
Answer C
Answer: (C) 10 %
Question: If x is equal to the sum of the integers from 10 to 20, inclusive, and y is the number of EVEN integers from 10 to 20, inclusive, what is the value of x+y ?
(A) 171
(B) 175
(C) 180
(D) 190
(E) 200
Rationale: sum s= n/2{2a+(n-1)d} = 11/2{2*10+ (11-1)*1} =11*15=165 =X
number of even number =( 20-10)/2 +1 = 6= Y
X+Y = 165+6 =171
A
Answer: (A) 171
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 299
(B) 267
(C) 999
(D) 277
(E) 266
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5
= 999
Answer:C
Answer: (C) 999
Question: Pointing to a man in a photograph. Asha said. "His mother's only daughter is my mother." How is Asha related to that man ?
(A) Sister
(B) Nephew
(C) Wife
(D) Niece
(E) FDD
Rationale: Explanation:
Asha's mother's mother is man's mother i.e.. A.sha's mother is man's sister or Asita is man's niece.
Answer: D) Niece
Answer: (D) Niece
Question: What is the greatest of 3 consecutive integers whose sum is 33?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 33 / 3 = 11
The three numbers are 10, 11, and 12.
The answer is C.
Answer: (C) 12
Question: 2,3,4,5,7,11 which number is wrong in series
(A) 3
(B) 4
(C) 2
(D) 5
(E) 7
Rationale: 4...........
all are prime numbers expect 4
ANSWER:B
Answer: (B) 4
Question: When the integer k is divided by 7, the remainder is 2. Which of the following expressions below when divided by 7, will have a remainder of 5?
I. 4k + 4
II. 6k + 7
III. 8k + 2
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: k = 7j + 2
4k + 4 = 28j + 8 + 4 = 28j + 7 + 5
6k + 7 = 42j + 12 + 7 = 42j + 14 + 5
8k + 2 = 56j + 16 + 2 = 56j + 14 + 4
The answer is D.
Answer: (D) I and II only
Question: Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and three times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) (16/3)b
(B) (17/4)b
(C) (13/3)b
(D) (19/12)b
(E) (7/12)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradley’s total
3b = Andrew’s total
(1/3)b = Charlie’s total
Add each total
b + 3b+ (1/3)b = 4b + (1/3)b = (16/4)b + (1/3)b = (13/3)b
Therefore,choose C.
Answer: (C) (13/3)b
Question: If 15% of 40 is greater than 25% of a number by 2, then the number is?
(A) 12
(B) 8
(C) 15
(D) 20
(E) 16
Rationale: Let the number be x
50% of 40 - 25% of x = 2
25/100 x = (15/100 * 40)-2
x/4 = 4
x = 16
Answer is E
Answer: (E) 16
Question: Five pieces of wood have an average length of 140cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
(A) a) 90
(B) b) 100
(C) c) 110
(D) d) 130
(E) e) 140
Rationale: E. 140
sum of all lengths of all 5 pieces of wood = 140 * 5 = 700
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 700 - 420 = 280
each of these 2 will have length 280/2 = 140
ANswer E
Answer: (E) e) 140
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 1/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?
(A) 30
(B) 45
(C) 270
(D) 90
(E) 135
Rationale: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 30. These are (1/3) of total igneous rocks.
(1/3)*Total igneous rocks = 30
Total igneous rocks = 30 * (3) = 90
Total sedimentary rocks = 2*Total igneous rocks = 2*90 = 180
Total number of rocks = 90 + 180 = 270
Answer (C)
Answer: (C) 270
Question: There are 100 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of manager to 98%?
(A) 1
(B) 2
(C) 50
(D) 49
(E) 97
Rationale: We have 99 managers and 1 director. That 1 director to compose 2% of the total number of people, there must be 50 people in the room, hence 50 managers must leave.
Answer: C.
Answer: (C) 50
Question: In a group of 25 factory workers, 13 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.
(A) 10
(B) 9
(C) 8
(D) 7
(E) 5
Rationale: Total number of worker (M+W): 25
No. of men (M): 11 (Inferred fromHow many of the 11 men)
No. of women (W): 14
Total no. of workers who have brown eyes (B): 13
No. of women who do not have brown eyes: 6
Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8
Remaining 5 are men. (B - 8= 13 - 8= 5)
So 5 out of 11 men have brown eyes.
E
Answer: (E) 5
Question: Exactly 35% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
(A)  20%
(B)  42%
(C)  44%
(D)  50%
(E)  84%
Rationale: You are correct. People who cover local politics are a subset of people who cover politics.
30% of reporters who cover politics do not cover local politics so 70% DO cover local politics.
Reporters covering local politics= 70% of reporters covering politics= 35% ofall reporters
Reporters covering politics/All Reporters = 35/70 = 1/2
Reporters not covering politics/All Reporters = 1/2 = 50%=D
Answer: (D)  50%
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5%
(B) 7%
(C) 8%
(D) 2%
(E) 1%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: (A) 5%
Question: A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 64 km downstream
(A) 1 hour 15 min
(B) 2 hour 40 min
(C) 1 hour 20 min
(D) 1 hour 30 min
(E) 1 hour 50 min
Rationale: Speed of the boat in still water = 42 km/hr
speed of the stream = 10 km/hr
Speed downstream = (42+10) = 52 km/hr
Distance travelled downstream = 64 km
Time taken =distance/speed
=64/52
= 1.23 hours
= 1 hour 15 min.
ANSWER:A
Answer: (A) 1 hour 15 min
Question: A man buys s cycle for $100 and sells it at a loss of 30%. What is the selling price of the cycle?
(A) $50
(B) $60
(C) $70
(D) $80
(E) $90
Rationale: S.P. = 70% of the $100 = 70/100 * 100 = $70
Answer is C
Answer: (C) $70
Question: If a, b are integers and |a-b|=4, which of the following is the smallest possible value of ab?
(A) -4
(B) 0
(C) 16
(D) 7
(E) 40
Rationale: a=2, b=-2. Hence, the answer is A.
Answer: (A) -4
Question: A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 1/5 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?
(A) 2/3
(B) 2/5
(C) 3/5
(D) 3/10
(E) 7/20
Rationale: 1/2 of the small beaker is 1/10 of the large beaker.
1/10 + 1/5 = 3/10
The answer is D.
Answer: (D) 3/10
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 17. What is the last numbers?
(A) 2
(B) 4
(C) 6
(D) 5
(E) 7
Rationale: A + B + C = 48
B + C + D = 45
A + D = 17
A – D = 3
A + D = 17
2D = 14
D = 7
ANSER E
Answer: (E) 7
Question: The ratio of the ages of Raja and David is 2 : 3. The total of their ages is 3.0 decades. The proportion of their ages after 0.5 decades will be
[1 Decade = 10 years]
(A) 17 : 23
(B) 3:4
(C) 4:5
(D) 7:9
(E) 3:6
Rationale: Let, Raja’s age = 2A and David’s age = 3A
Then 2A + 3A = 30
A = 6
Raja’s age = 12 years
and David’s age = 18 years
Proportion of their ages after 5 is = (12 + 5) : (18 + 5)
= 17 : 23
Answer : A
Answer: (A) 17 : 23
Question: A chemist mixes one liter of pure water with x liters of a 30% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 2
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 30%
Concentration of salt in the mixed solution = 20%
The pure solution and the salt solution is mixed in the ratio of --> (30 - 20)/(20 - 0) = 1/2
1/x = 1/2
x = 2
Answer: E
Answer: (E) 2
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $4 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $21.25m
(B) $25.5m
(C) $106.25m
(D) $120m
(E) $153m
Rationale: 2/10*1/6*(total) = 4
1/30*(total) = 4
(total) = 4*30 = 120
Answer: D.
Answer: (D) $120m
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 40 more cows and 15 more buffaloes are brought in, how many days will the fodder last?
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: 2 oxen = 3 buffaloes = 4 cows
Also: 15 buffaloes + 8 oxen + 24 cows
= 10 oxen + 8 oxen + 12 oxen = 30 oxen
There is enough fodder for 1 oxen for 30*48 days.
40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen
The new total is equal to 60 oxen instead of 30 oxen.
30*48 / 60 oxen = 24 days
The answer is B.
Answer: (B) 24
Question: If it is possible to make only one meaningful English word with the second, the fourth, the fifth and seventh letters of the word COURTESY, using each letter only once in the word, which of the following will be the third letter of that word? If no such word can be formed, give 'N' as the answer and if more than one such word can be formed, give 'M' as the answer.
(A) N
(B) B
(C) V
(D) C
(E) M
Rationale: Answer: Option E
Answer: (E) M
Question: Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $10.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost?
(A) a. $3.19
(B) b. $3.75
(C) c. $3.90
(D) d. $4.08
(E) e. $4.23
Rationale: On Monday and Thursday, she spent $10.43total.
On Tuesday and Wednesday, she spent $3.54on each day.
On Friday, she spent $7.89 on lunch.
The average = (10.43 + 2*3.54 + 7.89)/5 = 4.08.
Answer: D.
Answer: (D) d. $4.08
Question: FOG + FOG + FOG + FOG = 1460.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: given,FOG + FOG + FOG + FOG = 1460
4(FOG)=1460
=>FOG=365
Face value of F is:3
Face value of O is:6
Face value of G is:5
so F+O+G=3+6+5=14
ANSWER:D
Answer: (D) 14
Question: Arrange the fractions in ascending order
(A) 5/8 < 7/12 < 3/4< 13/16
(B) 5/8 < 7/12 < 13/16 < 3/4
(C) 5/8 < 3/4< 13/16 < 7/12
(D) 7/12 < 5/8 < 3/4< 13/16
(E) None of these
Rationale: Explanation:
5/8 = .625, 7/12 = .5833, 3/4 = .75, 13/16 = .8125
So order will be
7/12 < 5/8 < 3/4< 13/16
Option D
Answer: (D) 7/12 < 5/8 < 3/4< 13/16
Question: Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 4x + 2 = 0?
(A) 8
(B) 10
(C) 2
(D) 16
(E) 24
Rationale: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -4/1 = -4
ab = 2/1 = 2
Hence a/b + b/a = [(-4)2 - 2(2)]/2 = 4/2= 2.
C)
Answer: (C) 2
Question: What is the minimum number of square tiles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?
(A) 187
(B) 180
(C) 190
(D) 195
(E) 197
Rationale: Length = width
==>square = 5 m 78 cm and 3m 74
5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm
HCF of 578 and 374 = 34
square is 34
=578*374/34*34 == 17*11=187
ANSWER A
Answer: (A) 187
Question: What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6?
(A) 35
(B) 47
(C) 58
(D) 26
(E) 34
Rationale: In 100 consecutive numbers, number of multiples of 5 = 100/5 = 20 (Ignore decimals)
In 100 consecutive numbers, number of multiples of 6 = 100/6 = 16
Number of multiples of 5*6 i.e. 30 = 100/30 = 3
Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58
Answer is C
Answer: (C) 58
Question: In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the female students is single?
(A) 2/7
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/7
Rationale: Let the universal set be X = {all students in the graduate physics course}, such that n(X) = 100
It will contain 2 mutually exclusive sets; M (all male students) & F (all female students), where n(M) = 70, n(F) = 30
Now 2/7 of all male students are married, implying their number = 20.
However the total number of married students = 30, implying 10 married females.
Therefore 20 single females; = 2/3 of total females.
ANSWER:D
Answer: (D) 2/3
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 80% Vermouth by volume. How many ounces of Gin must he add?
(A) n/6
(B) n/3
(C) 3n/5
(D) 5n/6
(E) 8n/5
Rationale: 4 ounces is vermouth
6 ounces of gin...
Total volume 10.
To make vermouth account for 80% of total volume the new volume must be....
x*0.8=4
x=5 ounces....
So now you see that he must add 5 ounces of gin...
Plug in 6 for n in the answer choices and look for answer 5
D
Answer: (D) 5n/6
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, what was the son's age five years back?
(A) 7
(B) 14
(C) 10
(D) 12
(E) 9
Rationale: Let son's present age be x years. Then,
(38−x)=x⇒2x=38⇒x=382=19
Son's age 5 years back =19−5=14
Answer is B.
Answer: (B) 14