mathewhe/aqua_rat huggingface dataset:
Question: Let A be the positive integer satisfying the following equation.
9/10
+
99/102th +
999/103rd + · · · +
9999999999/1010th =
A/1010th
How many 8’s appear in the decimal representation of A ?
(A) 0
(B) 1
(C) 5
(D) 8
(E) 9
Rationale: The sum equals (1- 0.1) + (1- .01) +...+ (1 - .0000000001) = 10 .1111111111 =
9:8888888889. Thus A = 98888888889
correct answer E
Answer: (E) 9
Question: A man was asked to state his age in years. His reply was , "Take my age 6 years hence, multiply it by 6 and subtract 6 times my age 6 years ago and you will know how old I am." What was the age of the person ?
(A) 18
(B) 92
(C) 72
(D) 26
(E) 19
Rationale: Explanation:
Let the present age of person be x years.
Then, 6(x + 6) - 6(x - 6 ) = x <=> (6x + 36) - (6x - 36) = x <=> x = 72..
Answer: C
Answer: (C) 72
Question: In what time will a railway train 120 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 12 sec
(B) 7 sec
(C) 8 sec
(D) 9 sec
(E) 10 sec
Rationale: T = 120/36 * 18/5
= 12 sec
Answer:A
Answer: (A) 12 sec
Question: Given that there are 8 cricket players per team, how many ways can you select 10 cricket players from 2 teams if no more than 3 players can be selected from each team?
(A) 2456
(B) 3136
(C) 1452
(D) 3565
(E) 2134
Rationale: Now from each group we have to select 5 persons only: 8C3 * 8C3 = 56 * 56 = 3136
Total ways=3136 ways.
Answer B
Answer: (B) 3136
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 76 Kmph
(B) 68 Kmph
(C) 79 Kmph
(D) 25 Kmph
(E) 28 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: (B) 68 Kmph
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 40%
(C) 70%
(D) 80%
(E) 90%
Rationale: C
70%
Let C.P. = $ 100. Then, profit = $ 320, S.P. = $ 420
New C.P. = 125% of $ 100 = $ 125.
New S.P. = $ 420
Profit = 420 - 125 = $ 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer: (C) 70%
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(A) 827 cm2
(B) 216 cm2
(C) 285 cm2
(D) 178 cm2
(E) 176 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer:C
Answer: (C) 285 cm2
Question: P has $35 more than what Q and R together would have had if both B and C had 1/7 of what P has. How much does P have?
(A) $45
(B) $47
(C) $49
(D) $51
(E) $53
Rationale: P = (2/7)*P+35
(5/7)*P=35
P=49
The answer is C.
Answer: (C) $49
Question: The total expense of a boarding house is partly fixed and partly variable with the number of boarders. When the number of boarders is 25, then the charge is Rs 70 per head and the same is Rs 60 when the number of boarders is 50. What would be the charge per head if there are 100 boarders?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 55
Rationale: consider x as partly fixed and y as partly variable.
as number of boarders has been changing consider it as y.
sum(total expense including fixed n change)=x+25y=1750(25*70)
x+60y=3000(60*50)
by solving those equations v get x as 500 and y as 50
now do for 100 boarders 100y=100*50=5500
per head consists of 5500/100=55.
ANSWER:E
Answer: (E) 55
Question: If YWVSQ is 25 - 23 - 21 - 19 - 17, Then MKIGF
(A) 13 - 11 - 9 - 7 - 9
(B) 13 - 11 - 9 - 7 - 6
(C) 13 - 11 - 9 - 7 - 7
(D) 13 - 11 - 9 - 7 - 3
(E) 13 - 11 - 9 - 7 - 1
Rationale: MKIGF = 13 - 11 - 9 - 7 - 6
Note: this is a dummy question. Dont answer these questions
Answer:B
Answer: (B) 13 - 11 - 9 - 7 - 6
Question: The salary of a person was reduced by 25%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
(A) 10%
(B) 33.33%
(C) 20%
(D) 25%
(E) 50%
Rationale: Let the original salary be $100
new salary = $75
increase on 75 = 25
increase on 100 = [(25/75)100]% = 33.33%
Answer is B
Answer: (B) 33.33%
Question: Find the numbers which are in the ratio 5:2:4 such that the sum of the first and the second added to the difference of the third and the second is 18?
(A) 4,3,22
(B) 4,4,22
(C) 10,4,8
(D) 9,6,12
(E) 9,2,23
Rationale: Let the numbers be a, b and c.
a:b:c = 5:2:4
Given, (a + b) + (c - b) = 21
=> a + c = 21
=> 5x + 4x = 18 => x = 2
a, b, c are 5x, 2x, 4x
a, b, c are 10, 4, 8.
Answer:C
Answer: (C) 10,4,8
Question: If m and n are even integers, which of the following is an odd integer?
(A) mn + 2
(B) m(n − 1)
(C) m(m + 5)
(D) 3m + 4n
(E) (m + 3)(n − 1)
Rationale: If m and n are even integers, then:
A. mn + 2: even + even = even
B. m(n − 1): even(odd) = even
C. m(m + 5): even(odd) = even
D. 3m + 4n: even + even = even
E. (m + 3)(n − 1): (odd)(odd) = odd.
Answer is E.
Answer: (E) (m + 3)(n − 1)
Question: By how much does the larger root of the equation 2a^2+5a = 12 exceed the smaller root?
(A)  5/2
(B)  10/3
(C)  7/2
(D)  14/3
(E)  11/2
Rationale: For 2a^2+5a = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).
Answer: (E)  11/2
Question: The cross-section of a water channel is a trapezium in shape. If the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 880 square meters, what is the depth of the channel (in meters)?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 1/2 * d * (14 + 8) = 880
d = 80
The answer is D.
Answer: (D) 80
Question: At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?
(A) 24
(B) 55
(C) 66
(D) 88
(E) 21
Rationale: In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5
Answer: A) 24min
Answer: (A) 24
Question: Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 3 dollars .How many apples does she buy to share them equally between her six kids?
(A) 20
(B) 9
(C) 15
(D) 7
(E) 10
Rationale: cost of each apple = 3 dollars
Apples that Benny can buy with the amount she has=360/3 = 120.
Apples that each kid gets evenly = 120/6 =20 Apples.
So the answer is A=20
Answer: (A) 20
Question: A and B complete a work in 4 days. A alone can do it in 6 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.7 days
(C) 3.6 days
(D) 2.4 days
(E) 5.75 days
Rationale: 1/4+ 1/6 = 5/12
12/5 = 2.4 days
Answer:D
Answer: (D) 2.4 days
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 6 years ago ? (RBI Assistant 2015)
(A) 24
(B) 18
(C) 12
(D) 15
(E) 13
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 6 years ago = 21 - 6 = 15 years
answer :D
Answer: (D) 15
Question: How many prime numbers are between 25/3 and 84/6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 25/3 = 8.xxx
84/6 = 14.xxx
So we need to find Prime numbers between 8 (Exclusive) - 13 (Inclusive)
There are 2 Prime numbers 1113
Hence answer will be (B) 2
B
Answer: (B) 2
Question: Two tables are purchased for the total cost of Rs. 5000. First table is sold at 40% profit and second at 40% loss. If selling price is same for both the tables, what is the cost price of the table that was sold at profit?
(A) Rs. 1500.
(B) Rs. 2500.
(C) Rs. 3500.
(D) Rs. 4500.
(E) Rs. 5500.
Rationale: Ans: 140% of cost price of first table = 60% of cost price of second table.
Therefore, Cost price of first table : Cost price of second table
= 60 : 140 = 3 : 7
Therefore, Cost price of first table = 3/10× 5000 = Rs. 1500.
Answer A
Answer: (A) Rs. 1500.
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 21. What is the last numbers?
(A) 2
(B) 4
(C) 9
(D) 5
(E) 7
Rationale: A + B + C = 48
B + C + D = 45
A + D = 21
A – D = 3
A + D = 21
2D = 18
D = 9
ANSWER C
Answer: (C) 9
Question: Broke’s only source of income comes from his job as a question writer. In this capacity, Broke earns a flat salary of $200 per week plus a fee of $9 for every question that he writes. Every year, Broke takes exactly two weeks of unpaid vacation to visit his uncle, a monk in Tibet, and get inspired for the next year. If a regular year consists of 52 weeks and the number of questions that Broke wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Broke’s median annual income over the past 5 years?
(A) $22,474
(B) $25,673
(C) $27,318
(D) $28,477
(E) $31,227
Rationale: Okay u just need less than one min to answer this question. any odd number greater than 20 means that that last digit must be 1,3,5,7, or 9. 9$ per week for every question. So (odd)(odd) will give odd digit. A and C out. (50 weeks) (200) = 10,000. subtract this amount from option B, D and E and u will find that only option D is divisible by 9 (once 10,000 is subtracted from 28477) so its the right choice..D.
Answer: (D) $28,477
Question: From a pack of 52 cards, 1 card is drawn at random. What is the probability that a jack, queen, or king is drawn?
(A) 1/4
(B) 1/12
(C) 2/13
(D) 3/13
(E) 3/26
Rationale: The total number of cards is 52.
The number of jacks, queens, or kings is 12.
P(jack, queen, king) = 12/52 = 3/13
The answer is D.
Answer: (D) 3/13
Question: At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: If it were a line/column combination/permutation problem, the solution would be : 5! = 120.
However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24.
ANS:C
Answer: (C) 24
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 15 pumps work to empty the tank in 1 day?
(A) 3.5
(B) 4.8
(C) 5.1
(D) 5.2
(E) 6.3
Rationale: 3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 15 pumps then
48/15=3.5 hrs.
answer :A
Answer: (A) 3.5
Question: Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels?
(A) 480
(B) 540
(C) 600
(D) 720
(E) 900
Rationale: 4C2 x 3C3 x 5! = 720
The answer is D.
Answer: (D) 720
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 3889
(C) 8908
(D) 3780
(E) 2709
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer: A
Answer: (A) 1000
Question: The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students?
(A) 52.6
(B) 52.4
(C) 52.1
(D) 69.5
(E) 52.9
Rationale: Sum of the marks for the class of 40 students = 40 * 44 = 1760
Sum of the marks for the class of 45 students = 45 * 70 = 3150
Sum of the marks for the class of 85 students =
2760 + 3150 = 5910
Average marks of all the students = 5910/85 = 69.5.Answer: D
Answer: (D) 69.5
Question: Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960?
(A) 50%
(B) 51.22%
(C) 5.26%
(D) 7.20%
(E) 27.38%
Rationale: Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25
Number of families owning computer in 1960 = 25 * 115/100 = 28.75
Number of families in 1960 = 105
The percentage = 28.75/105 * 100 = 27.38%.
Option: E
Answer: (E) 27.38%
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 8 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
(A) 22
(B) 21
(C) 88
(D) 37
(E) 24
Rationale: Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 8) + 6000 (v - 8) <=> 2000v = 48000 <=> v = 24
Answer: E) 24
Answer: (E) 24
Question: The average age of 28 students in a group is 16 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?
(A) 45
(B) 36
(C) 41
(D) 51
(E) 48
Rationale: Sol.
Age of the teacher = ( 29 Ã— 17 â€“ 28 Ã— 16 ) years = 45 years.
Answer A
Answer: (A) 45
Question: Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.
(A) 72
(B) 21
(C) 84
(D) 53
(E) 18
Rationale: Sol. Let a = 13, b = 14 and c = 15. Then, S = (1/2)(a + b + c) = 21.
(s- a) = 8, (s - b) = 7 and (s - c) = 6.
Area = (s(s- a) (s - b)(s - c)^(1/2) = (21 *8 * 7*6)^(1/2) = 84 cm^2.
Ans: C
Answer: (C) 84
Question: In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
(A) 1/68
(B) 62/89
(C) 12/68
(D) 11/84
(E) 5/6
Rationale: Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer:E
Answer: (E) 5/6
Question: The average age of the district level hockey team of eleven is 22 years.The average age gets no change when the coach age is also included.what is the age of the coach ?
(A) 22 yrs.
(B) 23 yrs.
(C) 25 yrs.
(D) 24 yrs.
(E) 21 yrs.
Rationale: Explanation:
Total age of players in team = 22 x 11 = 242
When coach is included, total members = 12, Avg age is 22
Total age when coach is included = 22x12 = 264
Age of coach = 264-242 = 22 yrs.
Answer: A
Answer: (A) 22 yrs.
Question: Sneh's age is 1/6 th of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated two years before, then what is Sneh's present age?
(A) 10 years
(B) 25 years
(C) 35 years
(D) None of these
(E) Cannot be determined
Rationale: Solution
Vimal's age after 10 years	= (8+2+10)years
= 20 years.
Sneh's father age after 10 years	= 40 years
Sneh's father Present age	= 30 years
Therefore Sneh's age	= (1/6 x 30)years
= 5 years.
Answer D
Answer: (D) None of these
Question: The wages earned by Robin is 44% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
(A) 23%
(B) 18.75%
(C) 30%
(D) 30.55%
(E) 100%
Rationale: Explanatory Answer
Let the wages earned by Erica be $100
Then, wages earned by Robin and Charles will be $144 and $160 respectively.
Charles earns $44 more than Robin who earns $144.
Therefore, Charles' wage is 44/144*100 = 30.55%.
The correct choice is (D)
Answer: (D) 30.55%
Question: Tom was asked how old he was. He replied "In 2 years I will be twice as old as I was five years ago.' How old is he ?
(A) 11
(B) 13
(C) 12
(D) 15
(E) 17
Rationale: C
12
If Tom's age is X years
X+2=2(X-5)
X+2=2X-10
X=12
Answer: (C) 12
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively.The Sum is :
(A) Rs. 1800
(B) Rs. 1450
(C) Rs. 1360
(D) Rs. 6800
(E) None
Rationale: Solution
Sum = S.I xT.D/ ( S.I) - ( T.D)= 85 x80/85 - 80=Rs.1360.
Answer C
Answer: (C) Rs. 1360
Question: Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Rationale: 30% of the members have passed the test, thus 70% have not passed the test.
We also know that 30+12=42 members have not passed the test, thus 0.7*Total=42 --> Total=60.
Answer: A.
Answer: (A) 60
Question: Consider two statements
Statement 1 => If T is an integer and T=2p+1 where p is not an integer.
Statement 2 => If Y is an integer and Y=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of T and Y respectively
(A) 1) Odd,Even
(B) 2) Odd,Odd
(C) 3) Even,Odd
(D) 4) Even,Even
(E) 5) Cannot be determined
Rationale: answer will be E
T = integer
T = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even T would odd
if n odd T would be even
ANSWER IS E
Answer: (E) 5) Cannot be determined
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 36. Find their present ages.
(A) 20, 28
(B) 21, 27
(C) 35, 45
(D) 35, 55
(E) of these
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 36
20x = 60 => x = 3
Their present ages are 12, 21 and 27 years respectively.
ANSWER:B
Answer: (B) 21, 27
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
(A) 31
(B) 42
(C) 62
(D) 72
(E) 71
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer:B
Answer: (B) 42
Question: A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be:
(A) 40-42
(B) 39-41
(C) 38-40
(D) 37-38
(E) 36-37
Rationale: 5%(35.5) = 1.775
8%(35.5) = 2.84
total amount could have been 35.5+1.775 and 35.5+2.84
=> could have been between 37.275 and 38.34
=> approximately between 37 and 38
Answer is B.D
Answer: (D) 37-38
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 12 more blue balls than white balls, and six times as many red balls as blue balls, how many white balls does The box has ?
(A) 8
(B) 10
(C) 2
(D) 14
(E) 16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 12 more blue balls than white balls...
Equation #2: y = 12 + z
...thrice as many red balls as blue balls...
Equation #3: x = 6y
Solve equation #2 for z: z = y - 12
Now, we can replace both x and z with y in Equation #1
6y + y + (y - 12) = 100
8y - 12 = 100
5y = 112
y = 14
There are 14 blue balls. This is 12 more than the number of white balls, so z = 2. That's the answer. Just as a check, x = 84, and 84 + 14 + 2 = 100.
Answer = 2,(C)
Answer: (C) 2
Question: The dimensions of a field are 16.5 m by 10 m. A pit 10 m long, 5.5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
(A) 2 m
(B) 3 m
(C) 1 m
(D) 2.5 m
(E) 3.5 m
Rationale: The volume of the earth removed is 10*5.5*4 = 220 m^3.
The remaining area of the field is 16.5*10 - 10*5.5 = 110 m^2.
220 m^3 of the earth evenly spread over the area of 110 m^2 will rise the height by (height) = (volume)/(area) = 220/110 = 2 m.
Answer: A
Answer: (A) 2 m
Question: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 500 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
(A) 1.66%
(B) 1.96%
(C) 10%
(D) 15%
(E) 19%
Rationale: I think there is a typo in question.
It should have been "By weight Liquid 'X ' makes up..... "
Weight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B
When 500gms of A and 700gms of B is mixed :
Weight of Liquid X = (0.8 * 500)/100 + (1.8* 700)/100 = 16.6gms
% of Liquid X in resultant mixture = (16.6/1000) *100 = 1.66%
A
Answer: (A) 1.66%
Question: What is the remainder when 17^200 is divided by 18 ?
(A) 3
(B) 1
(C) 2
(D) 4
(E) 7
Rationale: (17^200 - 1^200) is completely divisible by (17 + 1) as 200 is even.
=> (17^200 - 1) is completely divisible by 18.
Hence, when 17^200 is divided by 18, we will get 1 as remainder.
Answer is B
Answer: (B) 1
Question: Josh spends a total of $5.5 buying W items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then W may be which of the following?
(A) 99
(B) 100
(C) 101
(D) 112
(E) 113
Rationale: W items in the convenience store$5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
Answer: (C) 101
Question: 18800 / 470 / 20
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Explanation:
18800 / 470 / 20 = (18800 / 470) / 20 = 40 / 20 = 2
Answer: B
Answer: (B) 2
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and x. How many integer values can x take?
(A) 23
(B) 22
(C) 15
(D) 8
(E) 7
Rationale: In acute angle triangles all angles in the triangle should be less than 90.
The maximum length of x can be when it is the hypotenuse of the triangle.
So, x= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of x can be when side of length 12 is the hypotenuse of the triangle.
So, x = sqrt (19^2 - 12^2) = 14.7 (approx)
So, x>14.7 and x<22.5.
Hence, possible values for x can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Answer: (D) 8
Question: A firm has 3 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
(A) 64
(B) 68
(C) 72
(D) 76
(E) 80
Rationale: The number of ways to form a group of 3 is 9C3 = 84
The number of groups with no senior partner is 6C3 = 20
The number of groups with at least one senior partner is 84-20 = 64
The answer is A.
Answer: (A) 64
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?
(A) 34
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 7
7[2x + 10] = 5[3x + 10]
14x + 70 = 15x + 50
15x - 14x = 70 - 50
x = 20
Then the first number is = 2
2x = 40
Short cut method:
a:b = 2:3
c:d = 5:7
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 7 ~ 3 * 5 = 14 ~ 15 = 1
2. If 10 is added both the number means 10 * 5 = 50 and 10 * 7 = 70,
Then 50 ~ 70 = 20
===> 1 -----> 20
===> 2 -----> 40 (Answer is = 40)
C
Answer: (C) 40
Question: Which number is the odd one out?
321
265
143
234
567
890
(A) 321
(B) 142
(C) 653
(D) 845
(E) 658
Rationale: A
321
In the rest there is the same difference between each digit, eg: 3 (Ã¢â‚¬â€œ1) 2 (Ã¢â‚¬â€œ1)1.
Answer: (A) 321
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 350, what is the least possible value of n?
(A) 5
(B) 7
(C) 12
(D) 13
(E) 14
Rationale: 350 = 2 * 5 * 5 * 7
so the least value forNcan be 7.
B
Answer: (B) 7
Question: A Man can row upstream at 52kmph and downward stream at 12 kmph. Find Man's rate of the current
(A) 2.8km/hr
(B) 52km/hr
(C) 20km/hr
(D) 50km/hr
(E) 6.8km/hr
Rationale: Rate of the current=1/2(52-12)km/hr
=20km/hr
correct option is :C
Answer: (C) 20km/hr