mathewhe/aqua_rat huggingface dataset:
Question: Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
(A) 29
(B) 33
(C) 55
(D) 30
(E) 32
Rationale: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.
Hence, the required number of straight lines
= ¹¹C₂ - ⁶C₂ - ⁵C₂ + 1 + 1
= 55 - 15 - 10 + 2 = 32
ANSWER:E
Answer: (E) 32
Question: The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
Explanation:
(A) 101
(B) 107
(C) 111
(D) 117
(E) 121
Rationale: Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
Answer: Option C
Answer: (C) 111
Question: John and Lewis leave City A for City B simultaneously at 6 A.M in the morning driving in two cars at speeds of 40 mph and 60 mph respectively. As soon as Lewis reaches City B, he returns back to City A along the same route and meets John on the way back. If the distance between the two cities is 240 miles, how far from City A did John and Lewis meet?
(A) 150 miles
(B) 160 miles
(C) 140 miles
(D) 170 miles
(E) 200 miles
Rationale: Time taken by Lewis to reach City B = 240/60 = 4 hours
In 4 hours, John travels 40*4 = 160 miles
So distance at which they meet should be greater than 160 miles.
Only B satisfies.
Answer is B.
Answer: (B) 160 miles
Question: Rahul's Mathematics test had 85 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 60% problems right. How many more questions he would have to answer more to get
passed
(A) 5
(B) 6
(C) 7
(D) 8
(E) 11
Rationale: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 85 = 51.
He would have to answer 51 - 40 = 11
Answer: Option E
Answer: (E) 11
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 74, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement?
(A) K+37
(B) 2K+37
(C) (74+K)/2
(D) (74-K)/2
(E) 2(74-K)
Rationale: Let y be the years of service at the company.
After y years of service, Sue's age will be K + y.
Sue can retire when (K+y) + y = 74
y = (74 - K)/2
Then Sue's age will be K + y = K + (74 - K)/2 = (74+K) / 2
The answer is C.
Answer: (C) (74+K)/2
Question: Find the number, difference between number and its 3/5 is 50.
(A) 110
(B) 125
(C) 120
(D) 140
(E) 145
Rationale: No = x
then x-3/5x = 50
(2/5)x = 50==> 2x=50*5
x = 125
ANSWER B
Answer: (B) 125
Question: Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Tuesday, how many croissants will Marina eat on the 24th of that month?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: She eat as follow
Mon - 1
Tue - 2
Wed - 3
Thr - 5
Fri - 1(since she had more than 4 previous day)
sat - 6
sunday - 1 (since she had more than 4 previous day)
so 24th day of month she will have 5.
Answer is D
Answer: (D) 5
Question: If x and y are integers and xy = 660, x or y must be divisible by which of the following numbers?
(A) 4
(B) 6
(C) 11
(D) 20
(E) 30
Rationale: xy = 660 = 2 * 2 * 3 * 5 * 11
One of x or y must be divisible by 11.
The answer is C.
Answer: (C) 11
Question: A leak in the bottom of a tank can empty the tank in 6 hrs. An pipe fills water atthe rate of 4 ltrs/min. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs. The capacity of the tank is?
(A) 4670
(B) 4546
(C) 4556
(D) 4675
(E) 5760
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
E
Answer: (E) 5760
Question: How long will it take a sum of money invested at 20% p.a. S.I. to increase double the value?
(A) 12 years.
(B) 8 years.
(C) 15 years.
(D) 13 years.
(E) 10 years.
Rationale: Sol.
Let the sum be x. Then, S.I. = 200% of x = 2x; Rate =20%.
âˆ´ Time = [100 * 2x/5 * 1/x*5] = 10 years.
Answer E
Answer: (E) 10 years.
Question: One tap can fill a water tank four times as fast as another tap. If together the two taps can fill the water tank in 30 minutes then the slower tap alone will be able to fill the water tank in _______ .
(A) 120 min
(B) 150 min
(C) 170 min
(D) 190 min
(E) 250 min
Rationale: Let the slower pipe alone fill the water tank in t minutes.
Then, faster pipe will fill it in t/4 minutes.
Therefore, 1/t + 4/t = 1/30
=>5/t = 1/30
Now solve for t.
=> t=150 min
ANSWER:B
Answer: (B) 150 min
Question: The speed of a train is 102 kmph. What is the distance covered by it in 30 minutes?
(A) 50 kmph
(B) 51 kmph
(C) 41 kmph
(D) 61 kmph
(E) 21 kmph
Rationale: 102 * 30/60
=51 kmph
Answer: B
Answer: (B) 51 kmph
Question: How much simple interest per annum can I negotiate with my Bank so My Family can pay back in 40 years at most double of the money we will borrow.
(A) 4
(B) 5
(C) 2.5
(D) 4.5
(E) 2
Rationale: P = (P*SI*40)/100
100P = P*SI*40
100 = 40SI
Therefore SI = 2.5%
C= 2.5
Answer: (C) 2.5
Question: A certain pilot flew 400 miles to City K at an average speed of 550 miles per hour with the wind and made the trip back at an average speed of 250 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?
(A) 280
(B) 290
(C) 300
(D) 310
(E) 340
Rationale: Avg speed = total distance/ total time
total distance = 800
total time = 400/550 + 400/250 = 128/55
=> avg speed = (800*55)/128 = 340(approx)
ans is E
Answer: (E) 340
Question: It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 1760 cubic metres in 10 minutes. The inner radius of the pipe should be :
(A) √2 m
(B) 2 m
(C) 1⁄2 m
(D) 2√2 m
(E) None of these
Rationale: Let inner radius of the pipe be r.
Then, 1760 = 22⁄7 × r2 × 7 × 10
or r2=1760/22×10=8
or r = 2√2 m
Answer D
Answer: (D) 2√2 m
Question: If x and y are positive integers and 18x=12y what is the least possible value of xy?
(A)  14
(B)  28
(C)  36
(D)  84
(E)  252
Rationale: 18x=12y
=> x/y = 2/3
=> 3x=2y
3(3)=2(3) => x*y=9 But it is not given
3(6)=2(6) => x*y=36
C
Answer: (C)  36
Question: Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 12, and 19, what is the value of r?
(A) 15
(B) 22
(C) 23
(D) 25
(E) 31
Rationale: From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are:
1. q + 12 > 19
2. 12 + 19 > q
3. q + 19 > 12
Equation 3 is true for any positive value of q.
From equation 1, q > 7
From equation 2, 31 > q
Then 31 > q > 7 so q can be any value from 8 to 30 inclusive.
The number of possible values is 23.
The answer is C.
Answer: (C) 23
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
The sum of the first 54 positive even integers is 2550. What is the sum of the even integers from 94 to 200 inclusive?
(A) 5,100
(B) 7,938
(C) 10,100
(D) 15,500
(E) 20,100
Rationale: even numbers from 94 to 200=106/2+1=54
Sum= (200+94)x54/2=7938
So B is the ans.
Answer: (B) 7,938
Question: II - IV + IX = 200
VI + I - V= 100
II - VI + VII = 150
Then,
VII + II + III = ?
(A) 350
(B) 220
(C) 150
(D) 230
(E) 450
Rationale: Correct Answer : E
II - IV + IX = 200 :- VII = 200
VI + I - V= 100 :- II = 100
II - VI + VII = 150 :- III = 150
VII + II + III = 450
Answer: (E) 450
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 4 dollars .How many apples does she buy to share them equally between her twelve kids?
(A) 7.5
(B) 9
(C) 3.5
(D) 7.2
(E) 10
Rationale: cost of each apple = 4 dollars
Apples that Benny can buy with the amount she has=360/4 = 90.
Apples that each kid gets evenly = 90/12 =7.5 Apples.
So the answer is A=7.5
Answer: (A) 7.5
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 6. The numbers are
(A) 12, 24, 30
(B) 12, 24, 38
(C) 12, 24, 362
(D) 6, 12, 18
(E) 12, 24, 321
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 6
\inline \fn_jvn \therefore The numbers are 6, 12, 18
Answer: D) 6, 12, 18
Answer: (D) 6, 12, 18
Question: The C.P of 40 pens is equal to the S.P of 60 pens. Find his gain % or loss%
(A) 25 2/3
(B) 32 1/3
(C) 33 1/3
(D) 25 1/3
(E) 33 2/3
Rationale: 40 CP = 60 SP
60 --- 20CP loss
100 --- ? => 33 1/3%
Answer: C
Answer: (C) 33 1/3
Question: A person buys an article at $380. At what price should he sell the article so as to make a profit of 25%?
(A) 445
(B) 449
(C) 475
(D) 740
(E) 460
Rationale: C
475
Cost price = $380
profit = 25% of 380 = $95
Selling price = Cost price + Profit
= 380+ 95 = 475
Answer: (C) 475
Question: In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities. How many students are involved in either band or sports?
(A) 220
(B) 225
(C) 230
(D) 240
(E) 245
Rationale: 25 + 60 + 140 = 225
There are 225 students involved
in either band or sports.
B)
Answer: (B) 225
Question: A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?
(A) 3/10
(B) 23/60
(C) 7/12
(D) 41/60
(E) 5/6
Rationale: You can use the 'calculating the reverse' method used by Bunuel above or if you would like to calculate the probability of getting a matched set in the usual way, you can think of it in this way:
Bleft (3), Bright(3), Gleft (2), Gright(2)
Bleft, Bright, G
Get a Bleft and Bright in (3/10)*(3/9) ways. Then get any green in 4/8 ways.
Probability of getting B pair and a G = (3/10)*(3/9)*(4/8)*3!
(You multiply by 3! here because you could pick in some other order e.g. Bright, Bleft, G or Bleft, G, Bright etc)
Bleft, Bright, B
Get a Bleft and Bright in (3/10)*(3/9) ways. Then get any blue in 4/8 ways.
Probability of getting B pair and another B = (3/10)*(3/9)*(4/8)*3!/2!
(You multiply by 3! here to account for the order e.g. Bright, Bleft, Bleft or Bleft, Bright, Bright etc but two gloves will be identical so you divide by 2!)
Gleft, Gright, B
Get a Gleft and Gright in (2/10)*(2/9) ways. Then get any Blue in 6/8 ways.
Probability of getting G pair and a B = (2/10)*(2/9)*(6/8)*3!
Gleft, Gright, G
Get a Gleft and Gright in (2/10)*(2/9) ways. Then get any other G in 2/8 ways.
Probability of getting G pair and a G = (2/10)*(2/9)*(2/8)*3!/2!
Adding them all up, you get 41/60.
ANSWER:D
Answer: (D) 41/60
Question: If all the numbers between 11 and 100 are written on a piece of paper. How many times will the number 4 be used?
(A) 87
(B) 267
(C) 68
(D) 26
(E) 21
Rationale: We have to consider the number of 4's in two digit numbers. _ _
If we fix 4 in the 10th place, unit place be filled with 10 ways. If we fix 4 in units place, 10th place be filled with 9 ways (0 is not allowed)
So total 19 ways.
Alternatively:
Answer:A
Answer: (A) 87
Question: A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?
(A) 1.5
(B) 2.5
(C) 3
(D) 4.5
(E) 5
Rationale: we have 15 cups of sauce with 4040 choc and 6060 rasb
cups of choc = 0.4∗15=6
cups of rasb = 0.6∗15=9
now let say we removed x cup of original mix and replaced with x cups of choc.
therefore final number of cups of choc =6−0.4x+x
now this number of cup should be 50% of total = 15/2=7.5
therefore 6−0.4x+x=7.5
on solving x=2.5
ANSWER:B
Answer: (B) 2.5
Question: Find the value for m?
19(m + n) + 17 = 19(-m + n) - 21
(A) 0
(B) -1
(C) 1
(D) 2
(E) 3
Rationale: 19m + 19n + 17 = -19m + 19n - 21
38m= -38 => m = -1
B
Answer: (B) -1
Question: In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining sixteen apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
(A) 32
(B) 16
(C) 64
(D) 80
(E) 16 or 48
Rationale: Let total number be x
No in the interior = (x/8)^2
No outside = 16
So : x - (x/8)^2=16
x^2-64x+16*64=0
(x-32)^2=0
x=32
A
Answer: (A) 32
Question: Ten percent of the women in a college class are science majors, and the non-science majors make up 60% of the class. What percentage of the men are science majors if 40% of the class are men?
(A) 45%
(B) 55%
(C) 65%
(D) 75%
(E) 85%
Rationale: Science majors make up 0.4 of the class.
60% of the class are women and 0.1*0.6 = 0.06 of the class are female science majors.
Then 0.34 of the class are male science majors.
0.4x = 0.34
x = 0.85 = 85%
The answer is E.
Answer: (E) 85%
Question: The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income, what is the ratio of the savings of P, Q and R ?
(A) 15 : 8 : 2
(B) 19 : 7 : 9
(C) 7 : 15 : 10
(D) 12 : 9 : 17
(E) None of these
Rationale: Explanation:
Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively.
Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y)
Now, 6x – 5y = 1/4(6x)
24x – 20y = 6x
18x = 20y
x/y = 20/18 = 10 / 9
Savings of P / Savings of Q = 6x – 5y / 8x – 8y
= [6(x/y) – 5] / [8(x/y) – 8]
= [(6 * 10/9) – 5] / [(8 * 10/9) – 8]
= 15/8
Savings of Q / Savings of R = 8x – 8y / 11x – 12y
= [8(x/y) – 8] / [11(x/y) – 12]
= (8 * 10/9) – 8 / (11* 10/9) – 12
= 8/2
Ratio of savings of P : Q : R = 15 : 8 : 2
ANSWER: A
Answer: (A) 15 : 8 : 2
Question: Evaluate : 1024 x 237 + 976 x 237
(A) 486000
(B) 568000
(C) 378000
(D) 474000
(E) None of them
Rationale: 1024 x 237 + 976 x237 = 237 x (1024 + 976) = 237 x 2000 = 474000.
Answer is D.
Answer: (D) 474000
Question: A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 79%
(B) 58%
(C) 44%
(D) 69%
(E) 43%
Rationale: g% = 30 + 30 + (30*30)/100
= 69%
Answer: D
Answer: (D) 69%
Question: If the cost price of 12 articles is same as the selling price of 25 articles. Find the gain or loss percentage?
(A) 30% Gain
(B) 30% Loss
(C) 40% Gain
(D) 40% Loss
(E) 52% Loss
Rationale: Explanation:
12 cp = 25 sp
Cost price CP = 25
Selling price SP = 12
Formula = (SP-CP)/CP * 100 = (12 - 25)/25 * 100 = 52 % Loss
Answer: Option E
Answer: (E) 52% Loss
Question: In a sample of high school students, 20 percent are sophomores, and 65 percent are not freshmen. What percentage of the high school students are juniors or seniors?
(A) 15
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: 65 percent are not freshman --> This means 65 percent are either sophomores, juniors, or seniors
Already, we know % that are sophomores = 20 %
So, % of juniors and seniors = 65 % - 20 % = 45 % .. => (D)
Answer: (D) 45
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.5
(B) 12.1
(C) 12.9
(D) 12.3
(E) 12.2
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: (B) 12.1
Question: How many days per calendar year is the month a factor of the day
(A) 0
(B) 1
(C) 45
(D) 90
(E) 101
Rationale: Solution: 45
All 31 days in January, because 1 is a factor of all integers
14 of the 28 days in February (because every other day is divisible by 2)
10 of the 31 days in March (the multiples of 3 between 3 and 30)
7 days in April (the multiples of 4 between 4 and 28)
6 days in May (the multiples of 5 between 5 and 30)
5 days in June (the multiples of 6 between 6 and 30)
4 days in July (the multiples of 7 between 7 and 28)
3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)
3 days in September (9th, 18th, 27th)
3 days in October (10th, 20th,30th)
2 days in November (11th, 22nd)
2 days in December (12th, 24th)
And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!
C
Answer: (C) 45
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 14 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
(A) 40
(B) 56
(C) 60
(D) Data inadequate
(E) None of these
Rationale: E+H+G+M/4âˆ’E+S+M+H/4=14
â‡’ G - S = 56
Answer B
Answer: (B) 56
Question: A train 150 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
(A) 20 sec
(B) 32 sec
(C) 36 sec
(D) 38 sec
(E) 40 sec
Rationale: Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(150×2/15) sec=20 sec
ANSWER :A
Answer: (A) 20 sec
Question: If 12 men do a work in 80 days, in how many days will 16 men do it?
(A) 60
(B) 30
(C) 50
(D) 40
(E) 20
Rationale: 12 * 80 = 16 * x
x = 60 days
ANSWER A
Answer: (A) 60
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. Find out the teacher's age in years?
(A) 51 years
(B) 49 years
(C) 53 years
(D) 50 years
(E) 52 years
Rationale: Explanation:
average age of 36 students in a group is 14
Sum of the ages of 36 students = 36 × 14
When teacher's age is included to it, the average increases by one
=> average = 15
Sum of the ages of 36 students and the teacher = 37 × 15
Hence teachers age
= 37 × 15 - 36 × 14
= 37 × 15 - 14(37 - 1)
= 37 × 15 - 37 × 14 + 14
= 37(15 - 14) + 14
= 37 + 14
= 51
Answer: Option A
Answer: (A) 51 years
Question: If x and y are positive integers and y ≠ 1, then xy(y −1) is
(A) Always even
(B) Always odd
(C) Odd only when x is odd
(D) Even only when y is even
(E) Odd only when xy is odd
Rationale: Expression is xy(y-1). We can ignore x and only work with y.
If y = even -> entire expression is even since anything multiplied by even is even
If y = odd, y-1 -> even -> entire expression is even since anything multiplied by even is even
Hence, entire expression will always be even.
Answer (A).
Answer: (A) Always even
Question: n is an integer chosen at random from the set
{1, 5 , 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 15 ?
(A) 0.1
(B) 0.2
(C) 0.15
(D) 0.3
(E) 0.4
Rationale: Set N: there is 4 ways to chose a number
Set P: there is 5 ways to chose a number
so total outcome is 4*5 = 20 which is represent 20 pairs of number
now we have 3 pairs can give us 15 which are (1,14),(5,10) and (9,6) .
3/20 = 0.15
Answer C
Answer: (C) 0.15
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 18 gallons of ethanol, how many gallons of fuel A were added?
(A) 160
(B) 150
(C) 100
(D) 80
(E) 350
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 18 gallons then 0.12A+0.16(200-A)=18 --> A=350.
Answer: E.
Answer: (E) 350
Question: If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?
(A) 33
(B) 38
(C) 60
(D) 88
(E) 22
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirct Proportion)
\inline \fn_jvn \therefore 15:36 ::25:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{15}=60
Hence, 15 men can do it in 60 hours.
Answer: C
Answer: (C) 60
Question: Find the remainder when 3^27 is divided by 5?
(A) 3
(B) 2
(C) 4
(D) 1
(E) 5
Rationale: Solution : 3^27= ((3^4)^6) * (3^3) = (81^6) * 27 then unit digit of (81^6) is 1 so on multiplying with 27,
unit digit in the result will be 7. now, 7 when divided by 5 gives 2 as remainder.
Answer B
Answer: (B) 2
Question: If 9a - b = 10b + 80 = -12b - 2a, what is the value of 2a + 22b?
(A) -4
(B) -2
(C) - 80
(D) 2
(E) 4
Rationale: This implies 9a - b = 10b + 80, 9a -b = -12b -2a, 10b + 80 = -12b -2a
Manipulating the second equation gives us 10b + 80 = -12b - 2a ==> 2a + 22b = - 80
Answer is C
Answer: (C) - 80
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) 456
(B) 234
(C) 285
(D) 342
(E) 213
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C
Answer: (C) 285
Question: A trader sells two brands of petrol; one is Extra Premium and other one is speed. He mixes 12 litres Extra Premium with 3 litres of speed and by selling this mixture at the price of Extra Premium he gets the profit of 9.09. If the price of Extra Premium Rs. 48 per litre, then the price of Speed is:
(A) Rs. 38 per litre
(B) Rs. 42 per litre
(C) Rs. 28 per litre
(D) Rs. 28 per litre
(E) None of These
Rationale: Solution: Selling price mix EP,
= (CP + 9.09% of CP)
48 = 12/11 of CP
CP = 44
No, using Alligation method,
MCQ Aptitude Profit and Loss11
4:1 Thus,
X = 44
Thus, the price of speed brand is Rs. 28/litre.
Answer: Option C
Answer: (C) Rs. 28 per litre
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 3 kmph
(B) 1.5 kmph
(C) 13 kmph
(D) 6.5 kmph
(E) 7.5 kmph
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
ANSWER:B
Answer: (B) 1.5 kmph
Question: a man have 8 t-shirt and some pant.he can dress in 72 ways.then tell me the no. of pant that man have.
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: let he have x pant.
by fundamental principle total no. of ways in which he can dress=8x
8x=72
x=9pants
answer B
Answer: (B) 9
Question: If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 6 € (4 € 5) =
(A) 480
(B) 120
(C) 160
(D) 240
(E) 360
Rationale: working inside out,
(4 € 5) = 2*4*5 = 40
6 € 40 = 2*6*40 = 480
Hence, answer is A
Answer: (A) 480
Question: The line r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2) and is parallel to the line s ≡ mx + 2y − 13 = 0. Calculate the values of m and n.
(A) -6,-1
(B) -3,-2
(C) 3,2
(D) 6,1
(E) 7,2
Rationale: r ≡ 3x + ny − 7 = 0 passes through the point A = (3, 2)
3. 3 +nN . 2 - 7 = 0 n = -1
3/m = - 1/2
m=6
ANSWER : A -6,-1
Answer: (A) -6,-1