mathewhe/aqua_rat huggingface dataset:
Question: If the number of students in each of three groups are in the ratio 8:9:10, and also the number of students in each group is a multiple of 5. then the following statements are true.
I. The product of number of students of each group is divisible by both 2 and 3.
II. The product of number of students of each group is divisible by 125
III. The product of number of students of each group is divisible by 125, 2 and 3
(A) I
(B) II
(C) III
(D) All of the above
(E) None of the above
Rationale: The product of consecutive positive integers are divisible by both 2 and 3.
Since the number of students in each group is divisible by 5, the product will be divisible by 125
Hence statement III is correct.
Answer:D
Answer: (D) All of the above
Question: Kavi spends 50% of his monthly salary on food and saves 80% of the remaining amount. If his monthly salary is Rs.19,000, how much money does he save every month ?
(A) Rs.2000
(B) Rs.600
(C) Rs.8000
(D) Rs. 3800
(E) Rs.1200
Rationale: Explanation:
Kavi's monthly income = Rs.19,000
He spends 50% on food.
The total money spent on food = 50/100 * 19000 = Rs. 9500
Now, his monthly remaining income = Rs.19000 – Rs.9500 = Rs. 9500
Out of Rs. 9500, he saves 40%.
Amount saved = 40/100 * 9500 = Rs. 3800
ANSWER:D
Answer: (D) Rs. 3800
Question: I. a3 - 405 = 324,
II. b2 - 72 = 9 to solve both the equations to find the values of a and b?
(A) a > b
(B) a ≥ b
(C) a < b
(D) a ≤ b
(E) a = b or the relationship between a and b cannot be established.
Rationale: a3 = 729 => a = 9
b2 = 81 => b = ± 9
a ≥ b
ANSWER:B
Answer: (B) a ≥ b
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 30° is?
(A) 35m2
(B) 36m2
(C) 37m2
(D) 38m2
(E) 40m2
Rationale: 30/360 * 22/7 * 12 * 12
= 37 m2
Answer:C
Answer: (C) 37m2
Question: Mohan purchased 15 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
(A) A)Rs.598
(B) B)Rs.594
(C) C)Rs.596
(D) D)Rs.550
(E) None of these
Rationale: Explanation:
Price of 15 kgs of rice at Rs.26/kg = 15x26 = Rs.390
Price of 10 kgs of pulses at Rs.26/kg = 10x26 = Rs.260
Therefore, Total amount = Rs.390+Rs.260 = Rs.550
Answer: Option D
Answer: (D) D)Rs.550
Question: Mary charges $8.50 per hour to clean a house. If she works 22 hours, how much
does she earn in one week?
(A) $687.00
(B) $112.50
(C) $187.00
(D) $487.50
(E) $387.50
Rationale: Multiply 22 hours x $8.50 =
Answer: $187.00
correct answer C
Answer: (C) $187.00
Question: In a class of students, 1/2 of the number of girls is equal to 1/5 of the total number of students. What is the ratio of boys to girls in the class?
(A) 1/2
(B) 3/2
(C) 1/3
(D) 2/3
(E) 4/3
Rationale: (1/2)G=(1/5)(B+G)
5G=2B+2G
3G=2B
B/G=3/2.
The answer is B.
Answer: (B) 3/2
Question: There were totally 100 men.84 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 100-(100-84)-(100-75)-(100-85)-(100-70)
= 100-16-25-15-30
=100-86
=14
ANSWER:D
Answer: (D) 14
Question: What will be in unit's place digit of 3 to the power 34.
(A) 1
(B) 6
(C) 3
(D) 0
(E) 9
Rationale: as the unit place digit of 3 to the power of 1 is 3, to the power of 2 is 9.to the power of 3 is 7 ,to the power of 4 is 1 and it'll be repeated again in the same order.... so the unit place digit of 3 to the power of 34 is 9..
ANSWER:E
Answer: (E) 9
Question: Jalal weighs twice as much as Meena. Meena's weight is 60% of Bahar's weight. Dolly weighs 50% of Laila's weight. Laila weighs 19% of Jalal's weight. Who among these 5 persons weighs the least?
(A) Bahar
(B) Dolly
(C) Jalal
(D) Laila
(E) Meena
Rationale: Let Jalal weigh 100 kg.
Then Meena = 50 kg, Bahar = 83.33 kg, Laila = 19 kg, Dolly = 9.5 kg
Therefore clearly Dolly is the lightest.
ANSWER:B
Answer: (B) Dolly
Question: Solve x2 – 7x = 0
(A) 0,7
(B) 1,7
(C) 2,7
(D) 3,7
(E) 4,7
Rationale: This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved
x2 – 7x = 0
x(x – 7) = 0
x = 0 or x – 7 = 0
x = 0 or x = 7
The solution is x = 0, 7
ANSWER A 0,7
Answer: (A) 0,7
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGAR', if repetition of letters is not allowed?
(A) 690
(B) 60
(C) 740
(D) 760
(E) 780
Rationale: The word 'LOGAR' has 5 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 5P3
=
5
×
4
×
3
=
60
Option B
Answer: (B) 60
Question: A train running at the speed of 56 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 140 m
(B) 786 m
(C) 566 m
(D) 546 m
(E) 445 m
Rationale: Speed = 56 * 5/18 = 140/9 m/sec
Length of the train = speed * time = 140/9 * 9
= 140 m
Answer: A
Answer: (A) 140 m
Question: If w and t are positive integers, wt + w + t cannot be
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let wt + t + w = x
Add 1 on both sides:
wt + t + w + 1 = x + 1
t(w + 1) + w + 1 = x + 1
(w + 1)(t + 1) = x + 1
Minimum value of (w + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime --> wt + t + s cannot be 6
Answer: B
Answer: (B) 6
Question: A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 30 percent.
(A) 145
(B) 90
(C) 175
(D) 160
(E) 130
Rationale: 1 hr =20 percent.Thus 15 min=5 percent .Now to charge 30 percent 90 min.Answer:B
Answer: (B) 90
Question: If the average (arithmetic mean) of 18 consecutive odd integers is 414, then the least of these integers is
(A) a) 497
(B) b) 518
(C) c) 519
(D) d) 521
(E) e) 525
Rationale: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 18 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 9th and 10th numbers in the set). This means that numbers 9 and 10 in this set are 413 and 415. Because we know that number 9 is 413, we know that the smallest number is 8 odd numbers below this, which means that it is 8*2 = 16 below this (every odd number is every other number). Therefore 413-16 = 397, answer choice A
Answer: (A) a) 497
Question: A car started running at a speed of 38 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
(A) 47 km
(B) 76 km
(C) 25 km
(D) 15 km
(E) 30 km
Rationale: A
47 km
The total distance covered by the car in the first 10 hours = 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 + 56= sum of 10 terms in AP whose first term is 30 and last term is 56 = 10/2 [38 + 56] = 470 km.
Answer: (A) 47 km
Question: H.C.F. of 513, 1134 and 1215 is
(A) 27
(B) 21
(C) 76
(D) 42
(E) 33
Rationale: H.C.F. of 513, 1134 and 1215 = 3 × 3 × 3 = 27
Answer: Option A
Answer: (A) 27
Question: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.3, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.008
(B) 0.147
(C) 0.488
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probablity of rain = 0.3
Therefore, probability of no rain = 0.7
0.7*0.7*0.3 = 0.147
Hence B
Answer: (B) 0.147
Question: If 10 men can make 200 tables working for 15 days at the rate of 8 hr per day, how many tables can 5 men make working for 10 days at the rate of 6 hr a day?A
(A) 150
(B) 50
(C) 250
(D) 100
(E) 120
Rationale: formula
men* days * workinghour / work
so m1*d1*t1/ w1 = m2*d2*t2 / w2
= 50
ANSWER:B
Answer: (B) 50
Question: A and B together can do a work in6 days. If A alone can do it in 42 days. In how many days can B alone do it?
(A) 11
(B) 7
(C) 8
(D) 20
(E) 25
Rationale: B
7
1/6 â€“ 1/42 = 1/7 => 7
Answer: (B) 7
Question: A cistern can be filled by a tap in 7 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?
(A) 4.5 hrs
(B) 5 hrs
(C) 6.5 hrs
(D) 17.2 hrs
(E) 31.5 hrs
Rationale: Net part filled in 1 hour= 1/7 -1/9= 2/63
Therefore the cistern will be filled in 63/2 hours or 31.5 hours.
ANSWER:E
Answer: (E) 31.5 hrs
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 80 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 5%
(B) 75%
(C) 25%
(D) 40%
(E) 50%
Rationale: The complete round trip consists of driving to the service center and then back home again.
So, once the technician drives to the service center he/she has already competed 50% of the entire trip.
Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%
Only one answer choice works.
Answer:
B
Answer: (B) 75%
Question: A shop sells chocolates at re.1 each. U can exchange 3 wrappers for 1 chocolate. If u have Rs.100, how many chocolates can you totally get?
(A) 147
(B) 148
(C) 149
(D) 145
(E) 141
Rationale: for 100 rupees we will get 100 chocolates
then for 3 wrappers we will get 1 chocolate so 100/3==33 chocolates and we left with one more wraper the 33+1=34 ...34/3=11...one more wrapper so 12/3=4 ..4/3=1 and one more wrapper so finally...100+33+11+4+1=149
ANSWER:C
Answer: (C) 149
Question: A trader bought a car at 20% discount on its original price. He sold it at a 50% increase on the price he bought it. What percent of profit did he make on the original price?
(A) A)10%
(B) B)12%
(C) C)14%
(D) D)20%
(E) E)22%
Rationale: Original price = 100
CP = 80
S = 80*(150/100) = 120
100 - 120 = 20%
D)
Answer: (D) D)20%
Question: In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?
(A) 1:9
(B) 1:6
(C) 1:3
(D) 1:1
(E) 1:3
Rationale: Number of men in the colony = 4/7 (70) = 40
Number of women in the colony = 3/7 (70) = 30
Number of educated women in the colony = 1/5 (30) = 6
Number of uneducated women in the colony = 4/5 (30) = 24
Number of educated persons in the colony = 8/35 (70) = 16
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30
Number of educated men and uneducated men are in the ratio 10:30 => 1:3
Answer: E
Answer: (E) 1:3
Question: If rupee one produces rupees nine over a period of 25 years, find the rate of simple interest?
(A) 22 1/7 %
(B) 36 %
(C) 22 1/8 %
(D) 22 1/2 %
(E) 22 1/2 %
Rationale: 9 = (1*25*R)/100
R = 36 %
Answer:B
Answer: (B) 36 %
Question: Sripad has scored average of 64 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?
(A) 79
(B) 28
(C) 76
(D) 27
(E) 21
Rationale: Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 64.
i.e (58+58+x)/3 = 64
116 + x = 192
x = 76 marks.
Therefore, the maximum marks he can score in maths is 76.
Answer: C
Answer: (C) 76
Question: Roses can be purchased individually for $7.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?
(A)  156
(B)  162
(C)  316
(D)  324
(E)  325
Rationale: Buy as many $50 deals as possible. We can by 650/50=13 two dozen roses, thus total of 13*24 = 312 roses.
We are left with 680 - 650 = $30. We can buy 30/7.3 = ~4 roses for that amount.
Total = 312 + 4 = 316.
Answer: C.
Answer: (C)  316
Question: The average age of a class of 42 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 45 Years
(B) 46 Years
(C) 59 Years
(D) 52 Years
(E) 54 Years
Rationale: Total age of students is 42X16 = 672 Years Total age inclusive of teacher = 43X (16+1) = 731 So, Teacher's age is 731-672= 59 Yrs There is a shortcut for these type of problems Teacher's age is 16+(43X1) = 59 Years Answer : C
Answer: (C) 59 Years
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is
(A) Rs.9471
(B) Rs.12,628
(C) Rs.18,040
(D) Rs.12,228
(E) None
Rationale: Solution
Ratio of their shares	=(35000Ã—8):(42000Ã—10)
= 2 : 3.
Suganya's share	= Rs.(31570 Ã—2/5)
= Rs.12228.
Answer D
Answer: (D) Rs.12,228
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be.
(A) 60 km/h
(B) 55 km/h
(C) 40 km/h
(D) 70 km/h
(E) 80 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=40/60hr=2/3hr
New speed = 40* 3/2 kmph= 60kmph
Answer : A.
Answer: (A) 60 km/h
Question: A train 650 m long is running at a speed of 117 km/hr. In what time will it pass a bridge 325 m long?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Speed = 117 * 5/18 = 65/2 m/sec
Total distance covered = 650 + 325 = 975 m
Required time = 975 * 2/65 = 30 sec
Answer: A
Answer: (A) 30
Question: Find the value of ( 0.75 * 0.75 * 0.75 - 0.001 ) / ( 0.75 * 0.75 - 0.075 + 0.01)
(A) 0.845
(B) 1.908
(C) 2.312
(D) 0.001
(E) 0.002
Rationale: (0.75*0.75*0.75-0.001)=0.75^3 -0.1^3
0.75*0.75-0.075+0.01=0.75^2-0.1^2
a^3-b^3=(a+b)(a^2-ab+b^2)
so after cancellation remainning term is (a+b) i.e 0.75+0.1=0.85
nearly to 0.845
ANSWER:A
Answer: (A) 0.845
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
(A) 9 years
(B) 29 years
(C) 18 years
(D) 19 years
(E) 17 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 34 * 3 = 196 - 75 - 102 = 19 years.
ANSWER:D
Answer: (D) 19 years
Question: A train speeds past a pole in 25 seconds and a platform 150 m long in 30 seconds. Its length is?
(A) 23
(B) 22
(C) 21
(D) 30
(E) 19
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 25 => y = x/25
(x + 150) / 30 = x / 25
x = 30 m.
Answer:D
Answer: (D) 30
Question: Two trains are moving in opposite directions with speed of 150 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
(A) 56
(B) 48
(C) 47
(D) 30
(E) 25
Rationale: Explanation:
Relative speed = 150+90 = 240 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/240 hr = 1/120 hr = 3600/120 seconds = 30 seconds
Answer: Option D
Answer: (D) 30
Question: LCM of 2/7,3/14 and 5/3is
(A) 45
(B) 35
(C) 30
(D) 25
(E) None
Rationale: Explanation:
LCM of numerators /HCF of denominators= LCM of 2, 3, 5/HCFof7,14,3 = 30/1=30
Correct Option: C
Answer: (C) 30
Question: A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone?
(A) 5
(B) 5 1/2
(C) 7 1/2
(D) 6
(E) 20
Rationale: Son's 1day work = 1/4 - 1/5 = 1/20
Son alone can do the work in 20days = 20 days
Answer is E
Answer: (E) 20
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.13000 after a year?
(A) 3630
(B) 3900
(C) 8828
(D) 2387
(E) 2813
Rationale: 6300:4200:10500
3:2:5
3/10 * 13000 = 3900
Answer: B
Answer: (B) 3900
Question: An error 1% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 2.01
(B) 30.1
(C) 3.01
(D) 25.01
(E) 4.05
Rationale: Explanation:
100 cm is read as 101 cm.
A1 =(100 × 100)cm2 = 10000
and A2= (101 × 101)cm2= 10609
(A2 - A1) = 10201-10000 = 201
=> 201/10000*100 =2.01
Answer : A
Answer: (A) 2.01
Question: If the cost price is 81% of selling price then what is the profit percentage.
(A) 22.45
(B) 23.45
(C) 32.45
(D) 23.54
(E) 23.55
Rationale: selling price=Rs100 : then cost price=Rs 81:profit =Rs 19.
Profit={(19/81)*100}%=23.45%
Answer is B.
Answer: (B) 23.45
Question: Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 6 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
(A) 1/7
(B) 1/6
(C) 1/5
(D) 1/2
(E) 1/3
Rationale: Suppose the portion of her salary that she saved is X
and the remaining portion is Y
X+Y= total take home salary
given, 12X = 6Y
or 2X = Y
Total take-home salary= X+ 2X= 3X
hence, she saved 1/3-rd portion of her take home salary
E
Answer: (E) 1/3
Question: On a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
(A) $5
(B) $15
(C) $23
(D) $100
(E) $105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
500(1.10)^2 = 500(1.21) = 605
and Lana would have
800(1.05)^2 = 800(1.1025) = 882
Thus, Tim earned 105 dollars, while Lana earned 82 dollars
The difference is $23 and the answer is C.
Answer: (C) $23
Question: John completes a piece of work in 320 days, Rose completes the same work in 480 days. If both of them work together, then the number of days required to complete the work is?
(A) 190
(B) 192
(C) 194
(D) 196
(E) 198
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 320 × 480/800 = 192 days
Answer is B
Answer: (B) 192
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(A) 20
(B) 18
(C) 12
(D) 14
(E) 15
Rationale: A's 2 day's work = 1/20 x 2 = 1/10
(A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 1/10
Work done in 3 days = A's 2 day's work + (A + B + C)'s 1 day's work
Work done in 3 days = 1/10 + 1/10
Now, work is done in 3 days = 2/10 = 1/5
So, 1/5 cork is done in 3 days.
So, work will be done in (3 x 5) = 15 days.
So, correct answer is E
Answer: (E) 15
Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 23?
(A) 101
(B) 187
(C) 191
(D) 201
(E) 264
Rationale: ok, not sure if this is the best explanation, but here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 23 = t 3 + 3 + 4 + 5 + 6....+ 22
the 3 + 4 + 5 + ... + 22 sequence is equal the sequence 1 + 2 + ... + 22, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 22 sequence is equal to n*(n+1)/2 with n being 22, so equal to 22 * 23 / 2 = 253
so :
t 23 = t 3 + 253 - 3
t 23 = 14 + 253- 3 = 253 + 11 = 264, hence answer E
Answer: (E) 264
Question: Out of seven models, all of different heights, five models will be chosen to pose for a photograph. If the five models are to stand in a line from shortest to tallest, and the fourth-tallest and sixth-tallest models cannot be adjacent, how many different arrangements of five models are possible?
(A) 6
(B) 11
(C) 17
(D) 72
(E) 210
Rationale: Total no. of ways "5 models can be selected from 7" = 7C5 = 21.
Fourth tallest and Sixth tallest can never stand adjacent to each other. Also, all selected models will be lined up from shortest to tallest.
Hence, we have to pull out the no. of ways 4 & 6 stand adjacent to each other from the above total, i.e = 21.
The following will be the way in which 4 & 6 stand close to each other.
1 2 3 4 6
1 2 4 6 7
1 3 4 6 7
2 3 4 6 7
So, the answer will be 21-4 = 17 ways.
ANS:C
Answer: (C) 17
Question: Two pipes A and B can separately fill a tank in 10 and 15 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) 450
(B) 540
(C) 542
(D) 829
(E) 279
Rationale: 1/10 + 1/15 - 1/x = 1/15
x = 10
10 * 45 = 450
Answer: A
Answer: (A) 450
Question: A rectangular table seats 3 people on each of two sides, with every person directly facing another person across the table. If 6 people choose their seats at random, what is probability that person P directly faces person Q?
(A) 1/5
(B) 1/8
(C) 2/7
(D) 5/6
(E) 3/5
Rationale: Person P will be seated somewhere at the table.
Each of the other 5 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/5.
The answer is A.
Answer: (A) 1/5
Question: In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?
(A) 1:4
(B) 1:3
(C) 2:3
(D) 3:4
(E) None of these
Rationale: Explanation:
33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B
Answer: (B) 1:3
Question: Of 30 applicants for a job, 11 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 14
(B) 13
(C) 8
(D) 7
(E) 5
Rationale: C. 8
30 - 3 = 27
27 - 11 - 18 = -8
Then 8 are in the intersection between 4 years experience and degree.
Answer C
Answer: (C) 8
Question: How many multiples of 2 are there between 10 and 100(both are inclusive)?
(A) 2
(B) 7
(C) 6
(D) 46
(E) 3
Rationale: the answer is (100-10)/2+1=46
Answer is D
Answer: (D) 46
Question: If the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is
(A) a) 407
(B) b) 518
(C) c) 519
(D) d) 521
(E) e) 525
Rationale: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 8 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 4th and 5th numbers in the set). This means that numbers 4 and 5 in this set are 413 and 415. Because we know that number 4 is 413, we know that the smallest number is 3 odd numbers below this, which means that it is 3*2 = 6 below this (every odd number is every other number). Therefore 413-6 = 407, answer choice A
Answer: (A) a) 407
Question: If N = 2^0.15 and N^b = 32, b must equal
(A) 3/80
(B) 3/5
(C) 4
(D) 100/3
(E) 80/3
Rationale: 15/100 = 3/20
N = 2 ^ 3/20
N^b = 2^5
(2^3/20)^b = 2^5
b = 100/3
Answer: D
Answer: (D) 100/3
Question: The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone?
(A) 87
(B) 26
(C) 48
(D) 37
(E) 20
Rationale: π * 12 * 4
= 48
Answer:C
Answer: (C) 48