mathewhe/aqua_rat huggingface dataset:
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 150
(B) 200
(C) 250
(D) 300
(E) 350
Rationale: The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
ANSWER:B
Answer: (B) 200
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(A) Rs. 4462.50
(B) Rs. 8032.50
(C) Rs. 8900
(D) Rs. 8925
(E) None of these
Rationale: Principal
= (100 x 4016.25) /(9 x 5)
= 401625/45
= Rs. 8925.
Answer: Option D
Answer: (D) Rs. 8925
Question: If log10 2=0.30103,find the value of log10 50
(A) 1.69897
(B) 2.69897
(C) 1.99897
(D) 0.69897
(E) 5.69897
Rationale: log10 50=log10(100/2)=log 100-log 2
=2log10-log 2=2(1)-0.30103=1.69897
ANSWER:A
Answer: (A) 1.69897
Question: What is the units digit of 2222^(333)*3333^(444)?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.
Here's another way to organize the information.
We're given [(2222)^333][(3333)^222]
We can 'combine' some of the pieces and rewrite this product as....
([(2222)(3333)]^222) [(2222)^111]
(2222)(3333) = a big number that ends in a 6
Taking a number that ends in a 6 and raising it to a power creates a nice pattern:
6^1 = 6
6^2 = 36
6^3 = 216
Etc.
Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.
2^111 requires us to figure out thecycleof the units digit...
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).
111 = 27 sets of 4 with a remainder of 3....
This means that 2^111 = a big number that ends in an 8
So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.
(6)(8) = 48, so the final product will be a gigantic number that ends in an 4.
Final Answer:
C
Answer: (C) 4
Question: A man has Rs. 528 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 80
(B) 90
(C) 95
(D) 99
(E) 100
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 528
16x = 528
x = 33.
Hence, total number of notes = 3x = 99.
D
Answer: (D) 99
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 20 percent of the pack would be outfielder cards?
(A) 10
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 20% of toatal Ocards
12-X<.2*12
X>12-2.4
X>9.6
X=10
Ans A
Answer: (A) 10
Question: A train 200m long passes a standing man in 24 seconds. What is the speed of the train?
(A) 30km/hr
(B) 36km/hr
(C) 42km/hr
(D) 50km/hr
(E) 32km/hr
Rationale: Speed of the train = 200/24* 18/5 = 30km/hr
Answer is A
Answer: (A) 30km/hr
Question: A man rows his boat 80 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 1 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
Rationale: Speed downstream = d/t = 80/(2 1/2) = 32 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (32 - 18)/2 = 7 kmph
Answer:E
Answer: (E) 7 kmph
Question: A class consists of 3 boys and 6 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
(A) 9
(B) 18
(C) 36
(D) 60
(E) 240
Rationale: Easiest way is to treat it like an arrangements question in the following manner:
From the boys we need to select 2 to be clown and pet: This can be done in 3*2 ways
Similarly for the girls, we have 6*5 ways.
Thus total = 30+6 = 36 ways. Thus C is the correct answer.
Answer: (C) 36
Question: How much water must be added to 60 litres of milk at 11⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
(A) 10 litres
(B) 12 litres
(C) 15 litres
(D) 18 litres
(E) None of these
Rationale: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 60 litres of milk
= (1⁄4 × 60) litres = 15 litres.
Answer C
Answer: (C) 15 litres
Question: If X represents the product of the first 15 positive integers, then X is not a
multiple of:
(A) a) 99
(B) b) 84
(C) c) 72
(D) d) 57
(E) e) 67
Rationale: a) 99 = 9*11
b) 84 = 4*7*3
c) 72 =9*11
d) 65 = 5*13
e) 57 =19*3
since 19 is not there in first 15 positive numbers it is the only possibility
D)
Answer: (D) d) 57
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 22%. What quantity of whisky is replaced ?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 3/5.
Hence, D is the correct answer.
Answer: (D) 3/5
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?
(A) 33
(B) 38
(C) 40
(D) 21
(E) 25
Rationale: Let there be x pupils in the class.
Total increase in marks = (x * 1/2)
= x/2
x/2 = (83 - 63) => x/2 = 20 => x
= 40.
Answer:C
Answer: (C) 40
Question: In a box of 10 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
(A) 4/9
(B) 5/11
(C) 7/15
(D) 9/22
(E) 12/35
Rationale: # defective pens = 3
# good pens = 7
Probability of the 1st pen being good = 7/10
Probability of the 2nd pen being good = 6/9
Total probability = 7/10 * 6/9 = 7/15
The answer is C.
Answer: (C) 7/15
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
(A) 1/2
(B) 3/4
(C) 3/5
(D) 4/7
(E) 5/3
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: (B) 3/4
Question: How many steel rods, each of length 14 m and diameter 4 cm can be made out of 1.76 cm3 of steel?
(A) 80
(B) 90
(C) 100
(D) 110
(E) 120
Rationale: Volume of 1 rod = (22/7)x(2/100) x (2/100) x 14 ) m3 =11/625 m3
Volume of steel = 1.76 m3
Number of rods =(1.76 x 625/11) =100
answer :C
Answer: (C) 100
Question: The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is?
(A) 21
(B) 23
(C) 31
(D) 33
(E) 35
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
Number to be added = (60 - 37) = 23
B)
Answer: (B) 23
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) 287
(B) 1287
(C) 125
(D) 988
(E) 271
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
Answer: C
Answer: (C) 125
Question: A hall is 6 meters long and 6 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
(A) 96
(B) 100
(C) 104
(D) 108
(E) 112
Rationale: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 108
The answer is D.
Answer: (D) 108
Question: Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary?
(A) Rs.3500
(B) Rs.4000
(C) Rs.4500
(D) Rs.5000
(E) None
Rationale: Explanation:
Let salary be Rs.x. Then,
x-15% of x -30% of 85% of x = 2380
or x- 15x/100−30×85×x/100×100=2380
or 200x-30x-51x=2380×2002380×200
or 119x = 2380×2002380×200 or x 2380×200/119=4000
Correct Option: B
Answer: (B) Rs.4000
Question: Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 28 more cards than Michelle. How many cards did each player have originally?
(A) 45
(B) 27
(C) 54
(D) 36
(E) 38
Rationale: GameMichelleMerry
Initially 54 54 assume
After game 1 36 72
After game 2 60 48
After game 3 40 68
Now Merry has 28 cards more than Michelle. This option gives us exactly what number of cards they had initially.
So the answer is C
Answer: (C) 54
Question: For all positive integers f, f◎ equals the distinct pairs of positive integer factors. For example, 16◎ =3, since there are three positive integer factor pairs in 16: 1 x 16, 2 x 8, and 4 x 4.
What is the greatest possible value for f◎ if f is less than 100?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: I took numbers in reverse order from 99 and got 6 distinct pairs in 96.
I thought it may be because 96=(2^5*3) has (5+1)*(1+1)=12(perhaps maximum) factors.
1*96,2*48*4*24,8*12,16*6,32*3
However, I was not sure while answering this. Please let us know if there is a better way.
Ans: "A"
Answer: (A) 6
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
(A) 2/13
(B) 3/31
(C) 4/41
(D) 5/31
(E) 8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
E
Answer: (E) 8/21
Question: In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (3,-1), (3, 8), (14, 2), (14,-5)?
(A) 76
(B) 88
(C) 100
(D) 112
(E) 124
Rationale: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (9 + 7) × 11 = 88.
The answer is B.
Answer: (B) 88
Question: It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
(A) 10
(B) 30
(C) 20
(D) 15
(E) 40
Rationale: Before:
One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)
The total no. of days required to complete the work = (75 * 20) / 50 = 30
ANSWER:B
Answer: (B) 30
Question: A company consists of 5 senior and 3 junior staff officers. If a committee is created with 3 senior and 1 junior staff officers, in how many ways can the committee be formed?
(A) 12
(B) 30
(C) 45
(D) 80
(E) 200
Rationale: Choose 3 senior from 5 senior and choose 1 junior from 3 junior:
3C5 * 1C3 = 10*3 = 30
Ans: B
Answer: (B) 30
Question: A patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 20 minutes. In how much time will he be able to take all the five tablets?
(A) 1 hour 10 min
(B) 1 hour
(C) 1 hour 20 min
(D) None
(E) Cannot be determined
Rationale: Suppose he takes the first tablet at 8:00 pm. Then the second will be consumed by him at 8:20, third at 8:40, fourth at 9:00 and fifth at 9:20.
Time = 1 hour 20 min
Answer C
Answer: (C) 1 hour 20 min
Question: The cost of cultivating a square field at the rate of Rs.135 per hectare is Rs.1215. The cost of putting a fence around it at the rate of 75 paise per meter would be :
(A) Rs.360
(B) Rs.810
(C) Rs.900
(D) Rs.1800
(E) Rs.1900
Rationale: Area= Total cost/ Rate= (1215/135) hectares= (9*10000) sq.m.
Therefore, side of the square= Ö90000=300m.
Perimeter of the field= (300*4)m= 1200m
Cost of fencing= Rs.(1200*3/4)= Rs.900
ANSWER:C
Answer: (C) Rs.900
Question: You have been given a physical balance and 7 weights of 45, 50, 53, 46, 52, 46 and 80 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 188 kgs.
(A) 183
(B) 185
(C) 182
(D) 184
(E) 181
Rationale: 80 + 52 + 53 = 185
Answer: B
Answer: (B) 185
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A ?
(A) 240
(B) 388
(C) 208
(D) 112
(E) 102
Rationale: The ratio of A & B investments = (3x8 + 2x4):(4x8 + 5x4)
=> 8:13
=> 8/21 x 630 = 240.
Answer: A
Answer: (A) 240
Question: How many three letter words are formed using the letters of the word TIME?
(A) 20
(B) 24
(C) 26
(D) 28
(E) 32
Rationale: Explanation:
The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24.
Answer: Option B
Answer: (B) 24
Question: How many of the following numbers are divisible by 132?
264,396,462,792,968,2178,5184,6336
(A) 4
(B) 5
(C) 6
(D) 7
(E) 89
Rationale: Explanation:
132 = 4 x 3 x 11, So if the number is divisible by all three numbers 4,3 and 11,then the number is divisible by 132 also.
264 => 4,3,11(/)
396 => 4,3,11(/)
462 => 11,3
792 => 4,3,11(/)
968 => 11,4
2178 => 11,3
5184 => 3,4
6336 => 4,3,11(/)
Required number of numbers=4.
Answer: A) 4
Answer: (A) 4
Question: If the cost price of 12 pens is equal to the selling price of 9 pens, the gain percent is:
(A) 80%
(B) 90%
(C) 33%
(D) 40%
(E) 10%
Rationale: Explanation:
Let C.P. of each pen be Re. 1.
Then, C.P. of 9 pens = Rs. 9; S.P. of 9 pens = Rs. 12.
Gain % = 3/9 * 100 = 33%
Answer:C
Answer: (C) 33%
Question: The sum of the heights of two high-rises is x feet. If the first high rise is 36 feet taller than the second, how tall will the second high rise be after they add an antenna with a height of z feet to the top?
(A) (x+z)/2 + 36
(B) 2x−(37+z)
(C) (x−36)/2 + z
(D) x/2 - 37 + z
(E) (2x−37)/z
Rationale: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:
h1 + h2 = x
and h1 = h2 + 36 =>
Q: h2 + z = ?
h2 + h2 + 36 = x => 2h2 = x-376=? h2 = (x-36)/2
=> h2 + z = (x-36)/2 + z, CORRECT ANSWER C
Answer: (C) (x−36)/2 + z
Question: The cost of 2 liters of lube oil is $7. What is the cost of 5 liters of lube oil?
(A) 17.5
(B) 20.5
(C) 24.0
(D) 28.5
(E) 30.0
Rationale: The cost of one liter of oil=7/2=3.5
The cost of five liters of oil = 3.5x5= $ 17.5
Answer: A
Answer: (A) 17.5
Question: What is the greatest prime factor of 2^8 - 1?
(A) 11
(B) 13
(C) 17
(D) 19
(E) 23
Rationale: 2^8-1 = (2^4-1)(2^4+1) = 15*17
The answer is C.
Answer: (C) 17
Question: There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.84 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?
(A) Rs 450
(B) Rs 920
(C) Rs 550
(D) Rs.630
(E) None of these
Rationale: Explanation :
Let the original average expenditure be Rs.x then,
42(x - 1) - 35x = 84 ? 7x = 126 ? x = 18
Therefore original expenditure = Rs.(35 18)=Rs.630.
Answer : D
Answer: (D) Rs.630
Question: The sum of the first 50 positive even integers is 2550. What is the sum T of even integers from 102 to 200 inclusive?
(A) 5100
(B) 7550
(C) 10100
(D) 15500
(E) 20100
Rationale: My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
T=2550+(100*50)=7550.B
Answer: (B) 7550
Question: What is the sum of the odd integers from 35 to 65, inclusive?
(A) 800
(B) 550
(C) 555
(D) 600
(E) 605
Rationale: The mean is 50.
Sum=Mean(# of elements)
There are 16 odd numbers between 35-65 inclusive. 16*50=800
A
Answer: (A) 800
Question: 10% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3213, how much was it in the beginning?
(A) A)3800
(B) B)4200
(C) C)4400
(D) D)4500
(E) E)4600
Rationale: X * (90/100) * (85/100) = 3213
X = 4200
ANSWER:B
Answer: (B) B)4200
Question: Two employees X and Y are paid a total of Rs. 528 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.250
(B) s.280
(C) s.290
(D) s.299
(E) s.240
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 528
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 528
⇒ y[12/10 + 1] = 528
⇒ 22y/10 = 528
⇒ 22y = 5280
⇒ y = 5280/22 = 480/2 = Rs.240
E
Answer: (E) s.240
Question: A flamboyant comic book villain has abducted a bystander! Captain Valiant is alerted to the crime and reaches the start of the villain's trail 30 minutes later. The villain is in a getaway car going 40 kmph, and Captain Valiant can fly at 50 kmph. How long will the bystander have to wait for rescue?
(A) 1 hour
(B) 1 1/2 hours
(C) 2 hours
(D) 2 1/2 hours
(E) 3 hours
Rationale: Distance covered by the villain in 1/2 hour = 20 km
Now, 10 km is compensated in 1 hour
Therefore 20 km will be compensated in 2 hours
Added to the half hour head start, the bystander has been kidnapped for 2 1/2 hours.
Correct Answer: D
Answer: (D) 2 1/2 hours
Question: Find the middle one when The sum of three consecutive even numbers is 36?
(A) 11
(B) 12
(C) 14
(D) 16
(E) 17
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: (B) 12
Question: What is the are of an equilateral triangle of side 18 cm?
(A) 66âˆš3 cm2
(B) 74âˆš3 cm2
(C) 81âˆš3 cm2
(D) 64âˆš5 cm2
(E) 14âˆš3 cm2
Rationale: Area of an equilateral triangle = âˆš3/4 S2
If S = 18, Area of triangle = âˆš3/4 * 18 * 18 = 81âˆš3 cm2;
Answer:C
Answer: (C) 81âˆš3 cm2
Question: A man is 26 years older than his studen. In two years, his age will be twice the age of his student. The present age of his student is:
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Let the student's present age be x years. Then, man's present age = (x + 26) years.
(x + 26) + 2 = 2(x + 2)
x + 28 = 2x + 4
x = 24.
Answer:E
Answer: (E) 24
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 2899
(C) 277
(D) 2870
(E) 2787
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer:A
Answer: (A) 3630
Question: Find the value of X, Y by solving the below equations
X + Y = 15
X - Y = 5
(A) 10, 5
(B) 8, 7
(C) 9, 6
(D) 11, 4
(E) 12, 3
Rationale: X + Y = 15 ---(I)
X - Y = 5 -----(II) by adding (I) and (II)
------------
2X = 20 ==> X = 20/2 = 10
By Replacing the value of X in (I) we get 10 + Y = 15 ==>
Y = 15 -10 = 5.
So, X = 10, Y = 5
Answer A) 10, 5
Answer: (A) 10, 5
Question: A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 64 chose brand C. Which of the following could be the number of customers who preferred brand D?
(A)  1
(B)  8
(C)  14
(D)  20
(E)  27
Rationale: I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.
E
Answer: (E)  27
Question: John had a stock of 1400 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?
(A) 81.57%
(B) 36.5%
(C) 80.67%
(D) 56.5%
(E) 80.57%
Rationale: Let N be the total number of books sold. Hence
N = 62 + 62 + 60 + 48 + 40 = 272
Let M be the books NOT sold
M = 1400 - N = 1400- 272= 1128
Percentage
Books not sold / total number of books = 1128/1200 = 0.81 = 80.57%
correct answer E
Answer: (E) 80.57%
Question: Find the maximum value of the function f(x)=x−5 if x is a number between -5 and 13.
(A) 6
(B) 7
(C) 8
(D) 9
(E) None
Rationale: Solution:
Since f(x) is a linear function whose slope is 1, a positive number, it is strictly increasing for all x. Therefore its maximal value is reached for the largest value of x, x=13 and f(x)=13-5=8.
Answer C
Answer: (C) 8
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 6
(B) 5
(C) 4
(D) 9
(E) 6
Rationale: 9 a.m.
Answer: C
Answer: (C) 4
Question: Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 60 percent. At the same time, it decreased its total working hours by 30 percent. By what percent did this factory increase its output per hour?
(A) 228.5
(B) 228
(C) 229.5
(D) 220
(E) 229
Rationale: Lets assume the initial production was 100 litres of beer for 100 hr.
With the 60% increase the total amount of beer production will be 160 litres and with 30 % decrease in total hours will be reduced to 70 hr.
100hr ----> 100 lts
1hr -----> 1 lts
70hr -----> 160 lts
1hr -----> 2.28 lts
Total Increase in production for 1 hr = 228%
Answer B
Answer: (B) 228
Question: A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 25% impurities to the product. Find the net profit percentage of the dealer?
(A) 44%
(B) 40%
(C) 50%
(D) 56.25%
(E) 36.25%
Rationale: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 25% impurities to the product.
It means that he is selling $5 worth of product for $6.25.
So his profit is $6.25-$4 = $2.25
and his profit percent is
(2.25/4)*100 = 56.25%
Answer:- D
Answer: (D) 56.25%
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/7%
(B) 16 2/6%
(C) 16 2/3%
(D) 16 7/3%
(E) 12 2/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: C
Answer: (C) 16 2/3%
Question: 5n + 2 > 12 and 7n - 5 < 37; n must be between which numbers?
(A) 1 and 8
(B) 2 and 6
(C) 0 and 9
(D) 2 and 7
(E) 2 and 6
Rationale: 5n > 10 --> n > 2
7n < 42 --> n < 6
2 < n < 6
Answer: E
Answer: (E) 2 and 6
Question: At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 4 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?
(A) 7
(B) 14
(C) 25
(D) 27
(E) 30
Rationale: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 27
D
Answer: (D) 27