mathewhe/aqua_rat huggingface dataset:
Question: Among 400 students, 51% study sociology, 46% study mathematics and 40% study biology. If 34% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
(A) 30
(B) 90
(C) 148
(D) 172
(E) 188
Rationale: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 136
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 184 + 204 - 136 = 252
So, in the image we know that the number of students in the zone with the black boundary = 252
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 400, we can write:
252 +b+w= 400
Or,b+w= 400 - 252 = 148
That is,b= 148 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 148
C
Answer: (C) 148
Question: If xy+2z = x(y+z), which of the following must be true?
(A) 1. x=2 and z=0
(B) 2. x=1 and y=1
(C) 3. y=1 and z=0
(D) 4. x=1 or y=0
(E) 5. x=1 or z=0
Rationale: xy+2z=x(y+z)
xy+2z=xy+xz
2z=xz
it means x=2 or z=0
Answer A
Answer: (A) 1. x=2 and z=0
Question: In a certain accounting class of 90 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 65%, and the students on the make-up date had an average score of 85%, what was the average score for the entire class?
(A) 68%
(B) 71%
(C) 73%
(D) 75%
(E) 79%
Rationale: 70% of the students took the final exam on the assigned day --> 0.7*90 = 63 students took the final exam on the assigned day, with an average score of 65.
The rest of the students took the exam on a make-up date --> 90 - 63 = 27 students took the exam on a make-up date, with an average score of 85.
(Average Score) = (Sum of the scores)/(Total students) = (63*65 + 27*85)/90 = 71.
Answer: B.
Answer: (B) 71%
Question: A man has Rs. in the denominations of 100-rupee notes, 500-rupee notes and 1000-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 70
(B) 80
(C) 60
(D) 40
(E) 20
Rationale: Let number of notes of each denomination be x.
Then 100x + 500x + 1000x = 32000
1600x = 32000
x = 20.
Hence, total number of notes = 3x =60.
Answer is C
Answer: (C) 60
Question: If the President and Vice President must sit next to each other in a row with 7 other members of the Board, how many different seating arrangements are possible?
(A) 120
(B) 240
(C) 300
(D) 360
(E) 80640
Rationale: We need to take President and VP as one unit. Therefore we have 8 people to arrange=8! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=8!*2!=80640 ways
Answer E
Answer: (E) 80640
Question: A train moves with a speed of 108 kmph. Its speed in metres per second is :
(A) 10.8
(B) 18
(C) 30
(D) 38.8
(E) None of these
Rationale: Explanation:
108 kmph = (108 X 5/18)m/sec= 30 m / s. Answer: C
Answer: (C) 30
Question: The annual interest rate earned by an investment increased by 11 percent from last year to this year. If the annual interest rate earned by the investment this year was 22 percent, what was the annual interest rate last year?
(A) 17%
(B) 19%
(C) 18%
(D) 20%
(E) 22%
Rationale: let i = interest rate
i(this year) = i(last year) + 0.11i(last year) = 1.11i(last year)
22 = 1.11 x i(last year)
i(last year) = 22/1.1 = 220/11 = 20%
Answer : D
Answer: (D) 20%
Question: If the average (arithmetic mean) of x + 2, x + 3, and x + 4 is 0, then x =
(A) –4
(B) –3
(C) –2
(D) –1
(E) 0
Rationale: (x+2 + x+3 + x+4)/3 = 0
=>3x + 9 = 0
=>x = -3
Answer B
Answer: (B) –3
Question: The marks obtained by Vijay and Amith are in the ratio 6:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 1:5
(B) 4:5
(C) 9:5
(D) 9:8
(E) 9:7
Rationale: 6:5
3:2
-------
18:15:10
18:10
9:5
ANSWER:C
Answer: (C) 9:5
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
(A) 0.20833
(B) 0.14544
(C) 0.25632
(D) 0.35466
(E) 0.63435
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
A
Answer: (A) 0.20833
Question: Prizes totaling $30,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
(A) (a) $5,000
(B) (b) $12,000
(C) (c) $35,000
(D) (d) $25,000
(E) (e) $65,000
Rationale: The highest prize cannot possibly be less than 1/3rd of 30,000 (because in this case the sum of 3 prizes would be less than 30,000) and cannot be more than 30,000.
Answer: B.
Answer: (B) (b) $12,000
Question: On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 48 centimeters assuming that 1-inch is 2.54 centimeters?
(A) 174.2
(B) 212
(C) 288.1
(D) 296
(E) 302
Rationale: 1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 48 cm.:
48/(2.54*1.5) = x / 24 ---> x = 24*47/(3.81) = 302
Answer will be E.
Answer: (E) 302
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $60. What is the percent decrease?
(A) 20%
(B) 30%
(C) 40%
(D) 70%
(E) 80%
Rationale: The is always the difference between our starting and ending points. In this case, it’s 100 – 60 = 40. The “original” is our starting point; in this case, it’s 100. (40/100)*100 = (0.4)*100 = 40%.
C
Answer: (C) 40%
Question: In how many E ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
(A) E=288
(B) E=144
(C) 12
(D) 48
(E) 96
Rationale: 4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.
W_W_W_W
Number of ways = 4!*3! = 24 * 6 = 144
Answer B
Answer: (B) E=144
Question: A train 120 m in length crosses a telegraph post in 12 seconds. The speed of the train is?
(A) 16 kmph
(B) 88 kmph
(C) 36 kmph
(D) 18 kmph
(E) 19 kmph
Rationale: S = 120/12 * 18/5
= 36 kmph
Answer: C
Answer: (C) 36 kmph
Question: How many ways could four cars can be parked at a parking lot with seven parking empty parking spots in which three of the seven spots will remain empty?
(A) 840
(B) 28
(C) 7
(D) 920
(E) 838
Rationale: ways in which 4 spots out 7 can be selected = 7C4
ways in which 4 cars can be arranged in 4 seats = 4!
Total ways of arrangement =7C4*4!
=(7*6*5/3*2)*24
=35*24
=840
Ans = A
Answer: (A) 840
Question: which number replaces the question mark and completes the puzzle ?
2 + 2 = 4,
3 + 3 = 18,
4 + 4 = 48,
6 + 6= ?
(A) 180
(B) 190
(C) 180
(D) 170
(E) 160
Rationale: Solution:
180
2 + 2 = 4 {2 * 2 * 1}
3 + 3 = 18 {3 * 3 * 2}
4 + 4 = 48 {4 * 4 * 3}
6 + 6 = 180 {6 * 6 * 5}
Answer A
Answer: (A) 180
Question: A mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 4 ltr - Water
36 ltr - milk
Let X water be added then the new mixture must have 20% water
Then
4 + X = 20/100 (40+X)
X=5
ANSWER:C
Answer: (C) 5
Question: what is the sum of the first 20 odd natural numbers
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 20 odd natural numbers=(20)^2=400
ans 400
ANSWER:B
Answer: (B) 400
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
(A) 65.5
(B) 63.5
(C) 60.5
(D) 61.5
(E) 62.5
Rationale: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
New capacity of bucket = 2/5 x
Therefore, Required number of buckets = (25x)/(2x/5)
= (25x) x 5/2x
= 125/2
= 62.5
Answer is E.
Answer: (E) 62.5
Question: Two 6 faced dice are thrown together. The probability that both show the same number on them is ?
(A) 1/6
(B) 1/12
(C) 1/18
(D) 1/2
(E) 1/4
Rationale: It all 3 numbers have to be same basically we want doublets. 11, 22, 33, 44, 55 and 66. Those are six in number. Further the three dice can fall in 6 * 6 = 36 ways.
Hence the probability is 6/36 = 1/6
Answer:A
Answer: (A) 1/6
Question: If 4a = 16b and 9b = 14c, Find a:b:c?
(A) 52:13:7
(B) 13:7:52
(C) 7:13:52
(D) 64:14:9
(E) None of these
Rationale: Explanation:
(4a = 16b ==> a/b = 16/4)
and (9b = 14c ==> b/c = 14/9)
==> a:b = 16:4 and b:c = 14:9
a:b:c = 64:14:9
Answer: Option D
Answer: (D) 64:14:9
Question: If Y > X and XM < YM, what must be true?
(A) M >0.
(B) M < Y.
(C) X < 0.
(D) M < 0.
(E) Y < 0.
Rationale: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when -ve is multiplied on both sides. That means M is -ve
A is the answer
Answer: (A) M >0.
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 26
(B) 30
(C) 37
(D) 43
(E) 45
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
C)
Answer: (C) 37
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) (216 + 1)
(B) (216 - 1)
(C) (7 x 223)
(D) (296 + 1)
(E) (296 + 3)
Rationale: Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
Answer:D
Answer: (D) (296 + 1)
Question: A military camp has a food reserve for 250 personnel for 40 days. If after 15 days 50 more personnel are added to the camp, find the number of days the reserve will last for?
(A) 25
(B) 67
(C) 26
(D) 29
(E) 18
Rationale: Explanation:
As the camp has a reserve for 250 personnel that can last for 40 days, after 10 days the reserve left for 250 personnel is for 30 days. Now 50 more personnel are added
in the camp.
Hence, the food reserve for 300 personnel will last for:
250:300::x:30 ……..(it is an indirect proportion as less men means more days)
x = (250*30)/300
x = 25 days
ANSWER: A
Answer: (A) 25
Question: The sum of all two digit numbers divisible by 4 is
(A) 1242
(B) 1542
(C) 1742
(D) 1610
(E) 1842
Rationale: Required numbers are 12,16,20 . . . . . 96
This is an A.P. in which a=12,d=4 and l=96.
Let the number of terms in it be n.Then t=96
So a+(n-1)d=96.
12+(n-1)*6=96,
12+4n-4=96
4+4n=96
4n=96-4
n = 92/4
then n=23.
Required sum
=n/2(a+l)
=23/2(12+96)
=1242
Answer is A
Answer: (A) 1242
Question: Of the 90 electronics components that a factory must manufacture, 50 percent would be most e¢ ciently manufactured by Machine A and the remaining 50 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 90 components. If 50 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
(A)  80
(B)  32
(C)  90
(D)  33
(E)  36
Rationale: A can manufacture 50 % of 90 efficiently, which is 45.
B can manufacure 50 % of 90 efficiently, which is 45.
Now 50 % of 90 are produced by A. This means 45 parts. Since A can produce 45 efficiently, all 45 are produced efficiently. Rest (45) is produced by B, which can produce max. 45 parts efficiently.
Hence parts that were produced efficiently = 45+45 = 90. (C).
Answer: (C)  90
Question: The largest natural number which exactly divides the product of any four consecutive natural numbers is
(A) 6
(B) 12
(C) 24
(D) 120
(E) none
Rationale: Sol.
Required number = 1 × 2 × 3 × 4 = 24.
Answer C
Answer: (C) 24
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 10 o'clock in the morning?
(A) 80°
(B) 60°
(C) 30°
(D) 10°
(E) 120°
Rationale: The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour.
In 2 hours, the angle traced by the hour hand is 2×30° = 60°
The answer is B.
Answer: (B) 60°
Question: Susan can type 10 pages in 5 minutes. Mary can type 5 pages in 10 minutes. Working together, how many pages can
they type in 30 minutes?
(A) 15
(B) 20
(C) 25
(D) 65
(E) 75
Rationale: susan can type 2 pages in 1 min
mary can type 0.5pages in 1 min
so, both of them work together they type 2.5 pages in 1 min
so,in 30 min they type (30*2.5)= 75 pages
ANSWER:E
Answer: (E) 75
Question: Mary works in a restaurant a maximum of 50 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
(A) 300
(B) 420
(C) 460
(D) 320
(E) 400
Rationale: Mary receives $8(20)=$160 for the first 20 hours.
For the 30 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(30)=$300.
The total amount is $160+$300 = $460
Answer C 460.
Answer: (C) 460
Question: A certain sum of money at simple interest amounted Rs.698 in 7 years at 5% per annum, find the sum?
(A) 338
(B) 277
(C) 517
(D) 678
(E) 261
Rationale: 698 = P [1 + (7*5)/100]
P = 517
Answer:C
Answer: (C) 517
Question: The area of a triangle is with base 3m and height 10m?
(A) 88 m2
(B) 10 m2
(C) 66 m2
(D) 15 m2
(E) 31 m2
Rationale: 1/2 * 3 * 5 = 15 m2
Answer: C
Answer: (C) 66 m2
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $5,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
(A)  7,500
(B)  24,500
(C)  25,500
(D)  26,500
(E)  27,500
Rationale: OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 5,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 5,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 400 = 0.10x
Combine terms and subtract 0.08x from both sides:
150 = 0.02x
Divide both sides by 0.02:
7,500 = x
Your answer is A.
Answer: (A)  7,500
Question: 101 Ã— 101 + 99 Ã— 99 = ?
(A) 10002
(B) 20004
(C) 20002
(D) 20102
(E) 20202
Rationale: Explanation :
(a + b)2 + (a âˆ’ b)2 = 2(a2 + b2)
(Reference : Basic Algebraic Formulas)
1012 + 992 = (100 + 1)2 + (100 âˆ’ 1)2 = 2(1002 + 12) = 2(10000 + 1) = 20002. Answer : Option C
Answer: (C) 20002
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations T could be chosen from this menu?
(A) 10
(B) 20
(C) 40
(D) 80
(E) 100
Rationale: T=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Answer: (C) 40
Question: The two lines y = x and x = -6 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
(A) 16
(B) 3√2
(C) 8
(D) 2√2
(E) (√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-6, -6) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(6 × 6) = 18; so z = 18.
The next step requires us to find the length of a side of a cube that has a face area equal to 18. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 18. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 18. Clearly s = √18 =3√2 , oranswer choice (B).
Answer: (B) 3√2
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 73 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
(A) 8715
(B) 0152
(C) 3581
(D) 5329
(E) 9126
Rationale: D
5329
n^1
73 * 73= 5329 (sum of first 73 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Answer: (D) 5329
Question: An article is bought for Rs.1300 and sold for Rs.1250, find the loss percent?
(A) 3 11/13%
(B) 3 2/9%
(C) 3 5/3%
(D) 3 2/3%
(E) 3 7/3%
Rationale: 1300 ---- 50
50 ---- ? => 3 11/13%
Answer: A
Answer: (A) 3 11/13%
Question: Solve : 0.6*0.6+0.6*0.6
(A) 0.46
(B) 0.56
(C) 0.64
(D) 0.65
(E) None of them
Rationale: = 0.6*0.6+(0.6*6) = 0.36+0.1 = 0.46
Answer is A.
Answer: (A) 0.46
Question: During a trip on an expressway, Lon drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5%
(B) 50%
(C) x/12%
(D) 60/x%
(E) 500/x%
Rationale: so Lon drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E
Answer: (E) 500/x%
Question: If T persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
(A) z
(B) x
(C) x/y
(D) z/x
(E) y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
T person can do z jobs in y days..
so T person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: (E) y/z
Question: A day-trader plans to invest a total of $23,300 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment?
(A) $2,800
(B) $3,000
(C) $3,700
(D) $3,800
(E) $3,900
Rationale: We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice).
Total of 14 minimized investments = (14)(1400) = $???600
The 15th investment + $???600 = $23,300
So, the HUNDREDS DIGITS of the 15th investment must be 7
Answer: C
Answer: (C) $3,700
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/3% profit
(B) 50/6% profit
(C) 16 2/3% loss
(D) 100/3% loss
(E) None of these
Rationale: Explanation:
10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer IS C
Answer: (C) 16 2/3% loss
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
(A) 728 ways
(B) 735 ways
(C) 767 ways
(D) 723 ways
(E) 720 ways
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer:E
Answer: (E) 720 ways
Question: The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability Q that the next couple the maitre 'd seats will not order dessert?
(A)  20%
(B)  25%
(C)  40%
(D)  60%
(E)  75%
Rationale: could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
Q=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25%
Answer: (B)  25%
Question: The profit earned after selling a T-shirt for Rs.575/- is the same as loss incurred after selling the same T-shirt for Rs.295/-. What is the cost price of the T-shirt?
(A) Rs.425/-
(B) Rs.435/-
(C) Rs.415/-
(D) Rs.245/-
(E) None of these
Rationale: Explanation:
Let ‘x’ be the CP. Then 575-x = x-295
x = Rs.435
Answer: Option B
Answer: (B) Rs.435/-
Question: Excluding stoppages, the speed of a bus is 50 km/hr and including stoppages, it is 36 km/hr. For how many minutes does the bus stop per hour?
(A) 118 min
(B) 10 min
(C) 18 min
(D) 16 min
(E) 15 min
Rationale: Due to stoppages, it covers 14 km less.
Time taken to cover 14 km = 14/50 * 60
= 16 min.
Answer:D
Answer: (D) 16 min
Question: Ajay bought a motor cycle for Rs. 50,000. 2 years later he sold it to Vijay at 10% less of the cost price. Vijay spend 5% of the purchasing price on its maintenance. Later Vijay displayed the sale price of his motorcycle Rs. 50,000. Chetan wanted to purchase it at 15% discount but Vijay gave him two successive discounts of 10% and 5% instead of 15% in one time. What is the actual discount availed by Chetan?
(A) 15%
(B) 15.5%
(C) 14.5	%
(D) 16.5%
(E) Cannot determined
Rationale: Solution: 100 ----10%↓(1st discount)---> 90----5%↓---> 85.5
Net discount = 100-85.5 = 14.5%.
Answer: Option C
Answer: (C) 14.5	%
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates Q apply to what fraction of a week?
(A)  1/2
(B)  5/8
(C)  9/14
(D)  16/21
(E)  9/10
Rationale: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates Q /Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Answer: (C)  9/14
Question: If x and y are integers such that x^2= y and xy = 27, then x – y = ?
(A) -30
(B) -20
(C) -6
(D) 5
(E) 20
Rationale: here x and y are integers .
x^2=y xy =27.
substitute x^2=y in xy => x^3=27.
here X3 is positive ,
x is also positive.
x=3 then y=9.
x-y=-6
so option C is correct
Answer: (C) -6
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) 85 Kmph
(B) 68 Kmph
(C) 103 Kmph
(D) 60 Kmph
(E) 90 Kmph
Rationale: Answer: Option B
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) 68 Kmph