mathewhe/aqua_rat huggingface dataset:
Question: Factor | Percent of Respondents |
User-friendly | 56% |
Fast response time | 48% |
Bargain prices | 42% |
The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,300 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
(A) 312
(B) 338
(C) 360
(D) 384
(E) 420
Rationale: The way I looked at is is as follows:
UserFriendly(UF) + FastResponse (FR) = 30%
UF leftover = 56 - 30 = 26%
FR leftover = 48 - 30 = 18%
Sum these = 74% (ie. 74% were either UF+FR, UF, FR)
26% leftover is the maximum number for Bargain Price
26/100 * 1300 = 26 * 13 = 338 (B).
Answer: (B) 338
Question: The average age of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace B, the average would be 21. What are the age of A, B and C?
(A) 22, 18, 20
(B) 20, 20, 18
(C) 18, 22, 20
(D) 21, 20, 19
(E) None of the above
Rationale: Given A + B = 40…(i)
C + B = 38 … (ii)
A + C = 42…(iii)
(i) + (ii) + (iii) ⇒ A + B + C = 60 …(iv)
from (i) and (iv), we get
C = 20 years
∴ B = 18 years and A = 22 years
Answer A
Answer: (A) 22, 18, 20
Question: The area of a square is equal to three times the area of a rectangle of dimensions 15 cm * 5 cm. What is the perimeter of the square?
(A) 30
(B) 80
(C) 50
(D) 60
(E) 70
Rationale: Area of the square = s * s = 3(15 * 5)
=> s = 15 cm
Perimeter of the square = 4 * 15 = 60 cm.
Answer: Option D
Answer: (D) 60
Question: In a 100m race, Sam beats John by 3 seconds. On the contrary, if Sam allowed John to start 24m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?
(A) 4 seconds
(B) 25.33 seconds
(C) 29 seconds
(D) 21 seconds
(E) 6.25 seconds
Rationale: Their difference is 3 second but this difference is 0 if john allows Sam to start the race from 24m ahead . that means Jhon was 24m away from finishing line when they started together . so He will cover 24 m in 3 seconds . so his speed =24/3=8 metre / second . so time taken =100/3=33.33 seconds . so Sam took = 25.33 seconds .
correct answer = B
Answer: (B) 25.33 seconds
Question: If two distinct positive divisors of 128 are randomly selected, what is the probability that their sum will be less than 64?
(A) 2/5
(B) 5/7
(C) 9/14
(D) 15/28
(E) 17/35
Rationale: The positive divisors are 1, 2, 4, 8, 16, 32, 64, 128.
If any of the first six are chosen, the sum will be less than 64.
P(sum is less than 64) = 6/8 * 5/7 = 15/28
The answer is D.
Answer: (D) 15/28
Question: 1500 is increased by 20%. Find the final number.
(A) 1500
(B) 1800.
(C) 1900
(D) 1700
(E) 1660
Rationale: Final number = Initial number + 20%(original number) = 1500 + 20%(1500) = 1500 + 300 = 1800.
Answer B
Answer: (B) 1800.
Question: A fruit drink is made of grapefruit, lemon, and orange juice, where 25 percent of the drink is grapefruit juice and 35 percent is lemon juice. If the drink is made with 20 ounces of orange juice, how many ounces is the drink total?
(A)  60
(B)  80
(C)  50
(D)  100
(E)  40
Rationale: Let the total number of ounces in the drink be x
% of orange = 25%
% of watermelon = 35%
% of grape = 100% - 60% = 40%
But this number is given as 20 ounces
so 40% of x = 20 and x = (20)(100/40) = (20)(5/2)
x = 50
Therefore there a total of 50 ounces in the drink.
Correct answer - C
Answer: (C)  50
Question: The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 and Rs.5.00 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rahul give?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 13
Rationale: Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=> 5a + 5b + 10c + 10d = 10*x.
=> a + b + 2(c+d) = 2 * x . -----------------------------(i)
Since, a + b = 3.5 + 4.5 = 8 .
And,
=> c + d = 2 + 5 = 7 .
Putting these values in (i), we get :-
=> 8 + 2 * 7 = 2 * x.
=> x = 11 .
Answer : D
Answer: (D) 11
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 16 households had a both a car and a bike and 44 had a car, how many had bike only?
(A) 30
(B) 35
(C) 20
(D) 18
(E) 10
Rationale: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-16+11 --> {Bike}=51 --> # those who have bike only is {Bike}-{Both}=51-16=35.
Answer: B.
Answer: (B) 35
Question: A wheel that has 8 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 28 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 15
(B) 16
(C) 17
(D) 14
(E) 20
Rationale: B
16
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 8:: 28: x <-> 14 x x = 8 x 28
x = (8x 28)/14
x = 16
Answer: (B) 16
Question: Thompson had the following scores in an exam (out of 100):
Social Studies: 60
Science: 89
Art: 62
Music: 69
Spanish:84
Biology: 89
What are his average marks ?
(A) 61.5
(B) 72.5
(C) 71.5
(D) 85.5
(E) 75.5
Rationale: Explanation:
Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75.
Answer: E) 75.5
Answer: (E) 75.5
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
(A) 2400
(B) 2888
(C) 277
(D) 271
(E) 128
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer: A
Answer: (A) 2400
Question: The radius of a cylinder is 12 m, height 21 m. the lateral surface area of the cylinder is:
(A) 1584
(B) 1854
(C) 1458
(D) 1485
(E) None of them
Rationale: Lateral surface area = 2πrh
= 2 × 22/7 × 12 × 21
= 44 × 36
= 1584 m(power2)
Answer is A.
Answer: (A) 1584
Question: The sum of two consecutive integers is 21. Find the numbers.
(A) 17, 18
(B) 7, 8
(C) 10, 11
(D) 1, 2
(E) 8, 9
Rationale: n + (n + 1) = 21
2n + 1 = 21
2n = 20
n = 10
Answer: C
Answer: (C) 10, 11
Question: A scientist was researching into animal behavior in his laboratory. He was very interested in studying the behavior of bears. He travelled a mile to the north and reached the north pole. There he saw a bear. He then followed the bear for an 1 hour to the east with a speed of 2km/hr. After that he travelled south and reached his laboratory in 2 hours. What was the colour of the bear?
(A) Black
(B) White
(C) Red
(D) Blue
(E) None
Rationale: This question is based on bear on poles so it should be polo bear and the color of polo bear is white.
ANSWER:B
Answer: (B) White
Question: The sum of the numbers is 660. If the first number be twice the second and third number be one-third of the first, then the second number is:
(A) 48
(B) 54
(C) 72
(D) 84
(E) 180
Rationale: Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 660
11x/3 = 660
x = 180
ANSWER:E
Answer: (E) 180
Question: If a and b are even integers, which of the following is an odd integer?
(A) ab + 2
(B) a(b − 1)
(C) a(a + 5)
(D) 3a + 4b
(E) (a + 3)(b − 1)
Rationale: If a and b are even integers, then:
A. ab + 2: even + even = even
B. a(b − 1): even(odd) = even
C. a(a + 5): even(odd) = even
D. 3a + 4b: even + even = even
E. (a + 3)(b − 1): (odd)(odd) = odd.
Answer is E.
Answer: (E) (a + 3)(b − 1)
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:7
(C) 1:9
(D) 1:5
(E) 1:1
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: (A) 1:2
Question: Two trains 131 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.19
(B) 7.18
(C) 7.16
(D) 7.15
(E) 7.34
Rationale: T = (131 + 165)/ (80 + 65) * 18/5
T = 7.34
Answer: E
Answer: (E) 7.34
Question: Solve the quickfire maths brain teaser √9% = ?
(A) 30%
(B) 40%
(C) 85%
(D) 19%
(E) 29%
Rationale: A
30%
√9%
=> √9/√100
=> 3/10
=> 30/100
=> 30%
Answer: (A) 30%
Question: If Ricky earns a raise of between 4% and 10%, non-inclusive, by what fraction could her salary have increased?
(A) 1/4
(B) 1/5
(C) 1/10
(D) 2/25
(E) 1/20
Rationale: Perhaps it is also easy to just translate the % into fractions:
5%:5/100=1/20
6%: 6/100 = 3/50
7%: 7/100
8%: 8/100 = 4/50 =2/25
9%: 9/100
Only 1/20 exists in the answer choices, so ANS E
Answer: (E) 1/20
Question: The total marks obtained by a student in Mathematics and Physics is 90 and his score in Chemistry is 30 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 30
(C) 25
(D) Data inadequate
(E) None of these.
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 90 and C - P = 30 M + C / 2 = [(M + P) + (C - P)] / 2 = (90 + 30) / 2 = 60.
ANSWER:E
Answer: (E) None of these.
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Six years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) A)24
(B) B)48
(C) C)67
(D) D)56
(E) E)45
Rationale: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,	(5x + 6/4x + 6)=11/9
9(5x + 6) = 11(4x + 6)
45x + 54 = 44x + 66
45x - 44x = 66 - 54
x = 12.
Anand's present age = 4x = 48 years.
Answer:B
Answer: (B) B)48
Question: A train covers a distance of 12 km in 12 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 177
(B) 168
(C) 100
(D) 120
(E) 122
Rationale: Speed = (12/12 * 60) km/hr = (60 * 5/18) m/sec = 16.6 m/sec.
Length of the train = 16.6 * 6 = 100 m.Answer:C
Answer: (C) 100
Question: A taxi company charges $1.40 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?
(A) 4 miles
(B) 4 1/4 miles
(C) 4 3/4 miles
(D) 5 1/2 miles
(E) 6 miles
Rationale: If we start out with $4.90 and have to spend $1.40 for the first quarter-mile, we will have $3.50 left to spend on quarter-mile intervals.
Since $3.50/$0.15 = 23.33, we can buy 23.33 more quarter-miles, and will travel 24.33 quarter miles in all:
24.33 × 1/4 = 6 miles.
The correct answer is choice (E).
Answer: (E) 6 miles
Question: Three rugs have a combined area of 212 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?
(A) 18 square meters
(B) 20 square meters
(C) 24 square meters
(D) 28 square meters
(E) 30 square meters
Rationale: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}
140 = 212 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 24.
Answer: C.
Answer: (C) 24 square meters
Question: Evaluate 28% of 650 + 45% of 280
(A) 232
(B) 308
(C) 252
(D) 262
(E) 282
Rationale: Explanation:
= (28/100) * 650 + (45/100) * 280
= 182 + 126 = 308
Answer: Option B
Answer: (B) 308
Question: A carpenter worked alone for 1 day on a job that would take him 7 more days to finish. He and another carpenter completed the job in 4 more days. How many days would it have taken the second carpenter to do the complete job working alone?
(A) 16
(B) 7
(C) 9
(D) 14
(E) 24
Rationale: A carpenter worked only 1 day on something that takes him 7 MORE days.
Means;
Carpenter finishes his work in 8 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/8 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/8 per day.
Second one worked for 4 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/8+4*1/x=1
5x+32=8x
2x=32
x=16 days.
Ans:A
Answer: (A) 16
Question: How many four letter words are formed using the letters of the word COMPUTER?
(A) 1680
(B) 1789
(C) 1678
(D) 1899
(E) 1788
Rationale: 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 8P4
= 8 * 7 * 6 * 5 = 1680.
Answer: A
Answer: (A) 1680
Question: Sum of two numbers prime to each other is 14 and their L.C.M. is 45. What are the numbers?
(A) 6 and 5
(B) 8 and 5
(C) 9 and 5
(D) 8 and 5
(E) 3 and 5
Rationale: As two numbers are prime,satisfies all
but option C will make the product of numbers i.e 45
ANSWER:C
Answer: (C) 9 and 5
Question: The greatest possible length which can be used to measure exactly the length 7m ,3m 85cm, 12m 95 cm is?
(A) 25cm
(B) 101cm
(C) 56cm
(D) 42cm
(E) 35cm
Rationale: Required length = H.C.F of 700cm, 385cm, 1295cm = 35cm
Answer is E
Answer: (E) 35cm
Question: If a certain manager had received a 5% raise instead of the 8% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise?
(A) 55,000
(B) 58,806
(C) 59,290
(D) 62228.52
(E) 61,620
Rationale: No need of getting involved with decimals ..just work in fractions ..
salary(let X) included 5% increase can be written as
(1+5/100)X=60500
X=60500/1.05------>57619.05
if there is 8% rise in 57619.05
then the salary now is 8% of 57619.05
8*57619.05/100=4609.52
then toal salary after increment=57619.05+4609.52----->62228.52
Ans D
Answer: (D) 62228.52
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 4, and the digit 2 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 300
(E) 320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
3 options for the fourth digit: 0, 4, 8.
Four digit # possible without the restriction (about the digit 2): 4*5*4*3=240
Numbers with two 2-s, 2X2X 1*5*1*3=15.
Thus there are 240-15=225 such numbers.
Answer: C.
Answer: (C) 225
Question: From a pack of 52 cards, 1 card is drawn at random. What is the probability that a king is drawn?
(A) 1/4
(B) 4/13
(C) 1/13
(D) 3/26
(E) 7/52
Rationale: The total number of cards is 52.
The number of kings is 4.
P(king) = 4/52 = 1/13
The answer is C.
Answer: (C) 1/13
Question: The average age of 28 students in a group is 12 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?
(A) 31
(B) 36
(C) 41
(D) 51
(E) None
Rationale: Sol.
Age of the teacher = ( 29 Ã— 13 â€“ 28 Ã— 12 ) years = 41 years.
Answer C
Answer: (C) 41
Question: In how many Q ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?
(A)  736
(B)  768
(C)  792
(D)  840
(E)  876
Rationale: three letters can be arranged in 3! ways.
only one combination EIU is required.
7 letters can be arranged in 7! ways.
thus Q=7!/ 3! * 1 = 840.
D
Answer: (D)  840
Question: The LCM and HCF of two numbers are 100 and 10 respectively. Find the larger of the two numbers if their sum is 110.
(A) 100
(B) 12
(C) 35
(D) 466
(E) 56
Rationale: There are 2 approaches in solving this.
Methode 1.
HCF * LCM = The Actual Number.
100* 10= 1000
So the answer which we are looking for has to be a factor of 1000.
So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000. and then take the highest number as the answer as the question asks abt the highest number.
answer is A
Answer: (A) 100
Question: The manufacturer’s suggested retail price (MSRP) of a certain item is $60. Store A sells the item for 20 percent more than the MSRP. The regular price of the item at Store B is 30 percent more than the MSRP, but the item is currently on sale for 10 percent less than the regular price. If sales tax is 5 percent of the purchase price at both stores, what is the result when the total cost of the item at Store B is subtracted from the total cost of the item at Store A?
(A) $0
(B) $0.63
(C) $1.80
(D) $1.89
(E) $2.10
Rationale: MSRP = 60
Price at Store A =60∗120100=72=60∗120100=72
Price at Store B =60∗130100∗90100=70.2=60∗130100∗90100=70.2
Difference = 72.0 - 70.2 = 1.8
Sales tax applicable = 5% on both
= 1.8 + 0.09 = 1.89
Answer = D
Answer: (D) $1.89
Question: A man on tour travels first 150 km at 50 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 310 km of tour.
(A) 60.11 km/hr
(B) 61.01 km/hr
(C) 62.00 km/hr
(D) 63.11 km/hr
(E) None of these
Rationale: Explanation:
We know Time = Distance/speed
So total time taken =
(150/50+160/80)=5hours
Time taken for 310 Km = 310/5=62.00km/hr
Option C
Answer: (C) 62.00 km/hr
Question: P beats Q by 250 meter in a kilometer race. Find Q's speed if P's speed is 16 meter/sec.
(A) 21 meter/sec
(B) 7 meter/sec
(C) 12 meter/sec
(D) 18 meter/sec
(E) 28 meter/sec
Rationale: P's speed = 16m/s
P's distance = 1000m (as it is a km race)
t = 1000/16 = 62.5 sec
Q's distance = 1000-250= 750m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 750/62.5 = 12 m/s
Hence C is the answer.
Answer: (C) 12 meter/sec
Question: What is the difference between the place values of two sevens in the numeral 54709719 ?
(A) 699300
(B) 99990
(C) 99980
(D) 699930
(E) None of these
Rationale: Explanation:
Required Difference
= 700000 - 700 = 699300
Answer is A
Answer: (A) 699300
Question: The diameter of a garden roller is 1.4 m and it is 4 m long. How much area will it cover in 5 revolutions ? (use Ï€ = 22â„7)
(A) 80 m2
(B) 84 m2
(C) 88 m2
(D) 86 m2
(E) None of these
Rationale: Required area covered in 5 revolutions
= 5 Ã— 2Ï€rh = 5 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 4 = 88 m2
Answer C
Answer: (C) 88 m2
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
(A) 12
(B) 14
(C) 18
(D) 20
(E) 21
Rationale: Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 6 years = (x+ 6) = 20 years..
Ans- D
Answer: (D) 20
Question: A train passes a station platform in 34 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) 110 m
(B) 210 m
(C) 310 m
(D) 360 m
(E) 280 m
Rationale: Speed = 54 x	5/18	m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then,	(x + 300)/34	= 15
x + 300 = 510
x = 210 m.Answer: Option B
Answer: (B) 210 m
Question: For how many integers n is 3^n = n^3?
(A) None
(B) One
(C) Two
(D) Three
(E) More than Three
Rationale: draw a graph with n^3and 2^n, you'll seemore than 3 intercepts between the 2 curves, and the answer is E
Answer: (E) More than Three
Question: A bus takes 8 hours to cover a distance of 600 Km. how much should the speed in Kmph be maintained to cover the same direction in 4/3th of the previous time?
(A) 50 Kmph
(B) 56 Kmph
(C) 63 Kmph
(D) 55 Kmph
(E) 70 Kmph
Rationale: Time = 8
Distance = 600
4/3 of 8 hours = 8 * 4/3 = 10.7 Hours
Required speed = 600/10.7 = 56 Kmph
B
Answer: (B) 56 Kmph
Question: 90% of the population of a village is 8100. The total population of the village is?
(A) 9000
(B) 24000
(C) 26682
(D) 29973
(E) 12312
Rationale: X * (90/100) = 8100
X = 90 * 100
X = 9000
Answer: A
Answer: (A) 9000
Question: The average salary of 15 people in the shipping department at a certain firm is $20,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $15,000 each. What is the average salary of the remaining employees?
(A)  $19,250
(B)  $18,500
(C)  $18,000
(D)  $19,100
(E)  $12,300
Rationale: total salary... 15*20k=300k
5 emp @ 25k =125k
4 emp @ 15k =60k
remaing 6 emp sal = 300k-125k-60k =115k
average=115k/6 = 19100
Ans:D
Answer: (D)  $19,100
Question: If n = 3^4 – 2^4 which of the following is NOT a factor of n?
(A) 13
(B) 65
(C) 1
(D) 13
(E) 5
Rationale: 3^4 - 2^4
= (3^2)^2 - (2^2)^2
=(3^2 + 2^2)(3^2 - 2^2)
=(9+4)(9-4)
=13*5
Therefore, 65 is Not a factor of n.
B
Answer: (B) 65
Question: If A and B are two events such that P (A) = 1/4, P (B) = 1/2 and P (A n B) = 3/8,
find P (not A and not B).
(A) A)6/8
(B) B)5/8
(C) C)4/8
(D) D)3/8
(E) E)2/8
Rationale: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (1/4 + 1/2 - 3/8)
P(not A and not B) = 1 - (3/8)
P(not A and not B) = 5/8.
B
Answer: (B) B)5/8
Question: A reduction of 20% in the price of salt enables a lady to obtain 20 kgs more for Rs.100, find the original price per kg?
(A) 12.6
(B) 1.21
(C) 1.25
(D) 12.4
(E) 12.7
Rationale: 100*(20/100) = 20 --- 20
? --- 1 => Rs.1
100 --- 80
? --- 1=> Rs.1.25
Answer: C
Answer: (C) 1.25
Question: Find the average of all numbers between 2 and 63 which are divisible by 5
(A) 15
(B) 20
(C) 25
(D) 32.5
(E) 35
Rationale: Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60)/12=390/12=32.5
Answer: Option D
Answer: (D) 32.5
Question: In the coordinate plane, a circle centered on point (-3, -4) passes through point (1, 2). What is the area of the circle?
(A) 9π
(B) 18π
(C) 25π
(D) 37π
(E) 52π
Rationale: r^2=(-3-1)^2+(-4-2)^2=16+36=52
Area of circle=πr^2=52π
Answer : E
Answer: (E) 52π
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 4 buckles is how many times that of 5 buckles and 6 buttons?
(A) 7/15
(B) 2/5
(C) 8/15
(D) 3/5
(E) 11/15
Rationale: Let x be the weight of a button and let y be the weight of a buckle.
2x + 2y = (1/3)(3x+11y)
3x = 5y
x = 5y/3
3x + 4y = a(6x+5y)
9y = a(15y)
a = 9/15 =3/5
The answer is D.
Answer: (D) 3/5
Question: There are eight different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
(A) 72
(B) 48
(C) 284
(D) 24
(E) 8
Rationale: Since we have 3 continental pairs (EU, SA, NA), these 4 pairs have 4*3*2*1 =24 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2*2 = 16). So we have 24*16 = 284.
Please correct me if im wrong.
Answer C.
Answer: (C) 284
Question: Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +2?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: p is a positiveeveninteger with apositive units digit--> the units digit of p can be 2, 4, 6, or 8 -->
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.
Intersection of values is 6, thus the units digit of p + 2 is 6 + 2 = 8.
Answer: B.
Answer: (B) 8
Question: Average of 5 numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?
(A) -33
(B) -35
(C) -39
(D) -42
(E) 32
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: (A) -33
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
(A) 180
(B) 183
(C) 190
(D) 210
(E) 212
Rationale: Option 'D'
7p3 = 7 × 6 × 5 = 210
Answer: (D) 210