mathewhe/aqua_rat huggingface dataset:
Question: A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed
against the current will be
(A) 11 kmph
(B) 10 kmph
(C) 14 kmph
(D) 17 kmph
(E) None of these
Rationale: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 5 = 15
Now speed against the current will be
speed of the man - speed of the current
= 15 - 5 = 10 kmph
Answer: B
Answer: (B) 10 kmph
Question: Three pipes A, B and C can fill a tank from empty to full in 20 minutes, 20 minutes and 30 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution Q in the liquid in the tank after 3 minutes?
(A) 5/8
(B) 6/8
(C) 4/8
(D) 2/8
(E) 3/8
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/20 + 1/20 + 1/30) = 6/15
Part filled by B in 3 minutes = 3/20
Required ratio = 3/20 * 15/6 =3/8
Answer:E
Answer: (E) 3/8
Question: Two trains 180 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9
(B) 10.7
(C) 10.3
(D) 10.8
(E) 12.24
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 180 + 160 = 340 m.
Required time = 340 * 9/250 = 306/25 = 12.24sec.
'Answer: E
Answer: (E) 12.24
Question: Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is:
(A) 24
(B) 54
(C) 34
(D) 45
(E) 25
Rationale: D = 10x + y
S = 10x^2 + y^2
S-D --> (10x^2 + y^2) - (10x + y) = 27 --> 10x (x-1) + y (y+1) = 27
ANSWER:B
Answer: (B) 54
Question: If 17m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
(A) 2m −1
(B) 4m
(C) 6m
(D) m/5
(E) 6m/5
Rationale: 17m - n = p
Add n to both sides:
17m = n + p
Add m to both sides:
18m = n + p + m
Now, divide both sides by 3
6m = (n + p + m)/3 = the average of n, p, and m
C
Answer: (C) 6m
Question: When positive integer n is divided by 4, the remainder is 1. When n is divided by 7, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 35?
(A) 1
(B) 2
(C) 5
(D) 19
(E) 20
Rationale: When positive integer n is divided by 4, the remainder is 1 i.e., n=4x+1
values of n can be one of {1, 5, 9, 13, 17, ...........29, 33, 37..................}
Similarly,
When n is divided by 7, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 12, 19, 26, 33, 40,........}
combining both the sets we get
n={5,33, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 35 or 35x
in case of n=33 p=2
so for min value of p, we take min value of n.
B is the answer.
Answer: (B) 2
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
(A) 277 m
(B) 704 m
(C) 278 m
(D) 288 m
(E) 378V
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm
= 704 m
Answer: B
Answer: (B) 704 m
Question: The average age of husband, wife and their child 3 years ago was 24 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
(A) 31 years
(B) 40 years
(C) 50 years
(D) 55 years
(E) None
Rationale: Solution
Sum of the present ages of husband, wife and child	= (24x3+3x3) years
= 81 years.
Sum of the present ages of wife and child	= (20x2+5x2) years
= 50 years.
âˆ´ Husband's present age	= (81 - 50) years
= 31 years.
Answer A
Answer: (A) 31 years
Question: In a store there is a number of people, out of which 1/30 are children, 1/6 are women and the remaining 120 are men. How many children are in the store?
(A) 50
(B) 120
(C) 150
(D) 5
(E) 25
Rationale: Let x be the number of people in the store.
x/30+x/6=6x/30=x/5 is the number of children and women
The number of men is x-x/5=4x/5, that is 4x/5=120. Thus, x=150.
The number of children is 1/30*150=5.
Answer D 5.
Answer: (D) 5
Question: An article is bought for Rs.1450 and sold for Rs.1420, find the loss percent?
(A) 2%
(B) 4%
(C) 6%
(D) 8%
(E) 12%
Rationale: 1450 ---- 30
100 ---- ? => 2%
Answer:A
Answer: (A) 2%
Question: If the LCM of 9, 7, 2, and q is 504, which of the following could be q?
(A) 7
(B) 8
(C) 6
(D) 9
(E) 5
Rationale: Using elimination method, eliminate the option to arrive at 8
if x is replaced by 8 and the LCM is calculated you arrive at 504
B
Answer: (B) 8
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.27000. A's share is?
(A) s.7500
(B) s.7200
(C) s.6000
(D) s.5750
(E) s.9000
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 27000 = 9000
ANSWER:E
Answer: (E) s.9000
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. x+ y > z
III. yz > xz
IV. xy > y + z
(A) I only
(B) II only
(C) II and III only
(D) II and IV only
(E) III and IV only
Rationale: lets see the choices..
I. x > z...
we do not know the values or the relative values ... need not be true..
II. x+ y > z
we take the worst case that z is the largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y.. need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ANSWER:B
Answer: (B) II only
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y − 2)
II. z<(x − 1)/(y − 2)
III. z>(x + 1)/(y + 2)
(A) I only
(B) I and II
(C) II and III
(D) II only
(E) I and III
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y − 2) --> 2/3 > 1/1 --> False
II. z<(x − 1)/(y − 2) --> 2/3 < 1/1 --> True
III. z>(x + 1)/(y + 2) --> 2/3 > 3/5 --> True
Answer: C
Answer: (C) II and III
Question: 24 oz of juice P and 25 oz of juice T are mixed to make smothies X and Y . The ratio of p to T in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to T ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice T will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice T = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Answer: (D) 20
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 120 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 6 o'clock?
(A) 60 miles
(B) 80 miles
(C) 110 miles
(D) 120 miles
(E) 400 miles
Rationale: Answer = C. 110 miles
Relational speed = 120 - 100 = 20 miles per hour
In 4 hours, difference = 20 * 4 = 120 miles
Fast train trailing 10 miles, so effective difference = 120 - 10 = 110 miles
Answer: (C) 110 miles
Question: Jack took a 3-hour bike ride. In the second hour he travlled 18 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
(A) 54.0
(B) 54.9
(C) 55.5
(D) 57.0
(E) 63.0
Rationale: Let the distance travelled in the first hour be x. Thus, 1.2x = 18 , x = 15. Now, the distance travelled in the 3rd hour = 18+1/4∗18 = The only option ending with a 0.5 in the decimal's place is C.
Correct answer is C
Answer: (C) 55.5
Question: The bankers discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
(A) Rs. 360
(B) Rs. 432
(C) Rs. 540
(D) Rs. 1080
(E) Rs. 1280
Rationale: Sum = (B.D*T.D)/(B.D-T.D)
(72*60)/72-60;
360
ANSWER:A
Answer: (A) Rs. 360
Question: The train leaves from New York City every 40 minutes from Boardman station. A man told John Watson that the train had left 15 minutes ago and the next train to New York City will leave at 9:40 p.m. At what time, man convey this information to John Watson?
(A) 6:15 PM
(B) 7:15 PM
(C) 8:15 PM
(D) 9:15 PM
(E) None
Rationale: Solution
Time of John Watson last missed the train = 8:40 PM - 40 min = 8:00 PM As this information has been given to John Watson 15 minutes after the train has already left, the man gave the information at 8:00 p.m. + 15 min = 8:15 PM
Answer C
Answer: (C) 8:15 PM
Question: In order to obtain an income of Rs. 15000 from 80% stock at Rs. 200, one must make an investment of
(A) Rs.30000
(B) Rs.37000
(C) Rs.37500
(D) Rs.40000
(E) Rs.40500
Rationale: Explanation :
Market Value = Rs. 200.
Required Income = Rs. 15000.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.80 (ie,80% of the face value 100), investment = Rs.200
To obtain Rs.15000, investment = 200/80Ã—15000=Rs.37500
Answer : Option C
Answer: (C) Rs.37500
Question: emblem is coded as 216;
crude is coded as 125
hi will be ?
(A) 243
(B) 64
(C) 8
(D) 32
(E) 16
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
hi = 2^3 =8
ANSWER:C
Answer: (C) 8
Question: A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain?
(A) 12.5%
(B) 16.7%
(C) 22.5%
(D) 27.5%
(E) 33.3%
Rationale: Let x be the original number of each color so there are a total of 5x candies.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.2x
red + yellow = 0.45x
red = 0.225x, since red = yellow.
The answer is C.
Answer: (C) 22.5%
Question: Three pieces of timber 48 m, 56 m and 72 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
(A) 8 m
(B) 4 m
(C) 2 m
(D) 6 m
(E) None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 48, 56, 72 = 8 m
Correct Option: A
Answer: (A) 8 m
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
(A) 2/113
(B) 3/115
(C) 1/108
(D) 2/213
(E) 3/215
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: (C) 1/108
Question: The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 21. What is the last numbers?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: A + B + C = 18
B + C + D = 15
A + D = 21
A – D = 3
A + D = 21
2D = 18
D = 9
ANSWER:E
Answer: (E) 9
Question: A professional stock trader just signed her new yearly contract with her employer. She will receive a 6% raise over last year's pay for her base pay, plus the chance to earn a performance bonus of up to $3,000. Last year, she earned no performance bonus. This year, assuming that she earns the full performance bonus, her new pay will be effectively an 8% raise. What will her new pay be assuming that she earns the full performance bonus.
(A) 162,000
(B) 173,000
(C) 180,000
(D) 213,000
(E) 284,000
Rationale: let x = last year's pay
this year's pay + 3,000 = this year's effective pay
(1+.06)*x + 3,000 = (1+.08)*x
1.06x + 3,000 = 1.08x
3,000 = .02x
150,000 = x
thus the new pay effectively is (1+.08)*150,000 = 162,000
A
Answer: (A) 162,000
Question: Set B consists of 19 elements. The average of set B is L. If a new element is added to the set and the average grows by K, what is the value of the new element?
(A) a) L(1 + K / 5)
(B) b) L * (K/100) - 20L
(C) c) 20L(1+K/100)
(D) d) 20(1+K/100)-19L
(E) e) L*(K/5)-19
Rationale: Let's assume the value of new element to bea. So converting the word problem into equation,
(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K
But according to the answer options, problem writer wanted to conveyk% percent rise in average value.
If we consider this case than resulting equation will be,
(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]
==> a= 20L + KL/5 -19L
==> a= L + KL/5 , which is equivalent to option [A]
Answer: (A) a) L(1 + K / 5)
Question: Which is a better investment 12% stock at 200 or 7 2/3 stock at 150?
(A) 12% stock at 200
(B) Cannot be compared, as the total amount of investment is not given
(C) 7 2/3 stock at 150
(D) Both are equally good
(E) None
Rationale: Let investment in each case be Rs. (200 x 150).
Income in 1st case = Rs.12 x 200 x 150/200	= Rs. 1800.
Income in 2nd case = Rs.23 x 200 x 150/(3*150)= Rs. 1533.3
Clearly, 12% stock at 200 is better.
ANSWER:A
Answer: (A) 12% stock at 200
Question: What is the probability of flipping a fair coin three times and the coin landing on heads on exactly one flip?
(A) 3/8
(B) 5/8
(C) 7/8
(D) 1/8
(E) 1/4
Rationale: Probability = (Favorable combination)/(Total combination)
Favorable combination = (HTT, TTH, THT) ==> 3
Total combination = 8 (2^3)
Probability = (3)/(8)
(A)
Answer: (A) 3/8
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
(A) 3
(B) 9
(C) 0
(D) 4
(E) 1
Rationale: S = (1 + 2 + 3)/2
= 3
Answer:A
Answer: (A) 3
Question: If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100 (both inclusive) varies by how much?
(A) 330
(B) 360
(C) 380
(D) 400
(E) 420
Rationale: unit place increased by 3. So 6,16,26,....96. Total 10*3 = 30 increased.
ten's place increased by 30. So 60,61,...69. Total 10*30 = 300 increased.
So total varies = 300 + 30= 330.
ANSWER:A
Answer: (A) 330
Question: The average (arithmetic mean) of eight numbers is 43.1. If the sum of half of these numbers is 158.4, what is the average of the other half?
(A) 12.8
(B) 24.2
(C) 46.6
(D) 72.1
(E) 96.8
Rationale: arithmetic mean = sum / total numbers
sum = 43.1 * 8 = 344.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 344.8-158.4 = 186.4
Arithmetic mean of the 4 nos = 186.4/4 = 46.6
Hence, C is the answer.
Answer: (C) 46.6
Question: The average of the two-digit numbers, which remain the same when the dibits inter-change their positions, is
(A) 23
(B) 39
(C) 55
(D) 28
(E) 01
Rationale: Explanation:
Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99) / 9
=( (11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55) / 9
= (4 * 110 + 55)/9 = 495 / 9 = 55.
Answer: C
Answer: (C) 55
Question: A train 100 meters long completely crosses a 300 meters long bridge in 36 seconds. What is the speed of the train is?
(A) 32 kmph
(B) 76 kmph
(C) 34 kmph
(D) 43 kmph
(E) 40 kmph
Rationale: S = (100 + 300)/36
= 400/36 * 18/5
= 40
Answer:E
Answer: (E) 40 kmph
Question: Two unbiased coin are tossed .what is the probability of getting atmost one head?
(A) 4/5
(B) 3/4
(C) 4/7
(D) 9/7
(E) 3/4
Rationale: Here S={HH,HT,TH,TT}
Let Ee=event of getting one head
E={TT,HT,TH}
P(E)=n(E)/n(S)=3/4
Ans: E
Answer: (E) 3/4
Question: Running 3/4th of his usual rate, a man is 15min late. Find his usual time in hours ?
(A) 6/4 hrs
(B) 3/4 hrs
(C) 9/4 hrs
(D) 3/4 hrs
(E) 1/4 hrs
Rationale: Explanation:
Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time
so 1/3rd of the usual time = 15min
or usual time = 3 x 15 = 45min = 45/60 hrs = 3/4 hrs.
Answer: B
Answer: (B) 3/4 hrs
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 17 hours
(B) 28 hours
(C) 19 hours
(D) 14 hours
(E) 14 hours
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer: B
Answer: (B) 28 hours
Question: In a hostel, the number of students decreased by 10% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
(A) 19%
(B) 15%
(C) 25%
(D) 40%
(E) 7.4%
Rationale: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)
Originally,
C = FNP
When number of students decrease by 8%, and the price of food increases by 20%,
C = F(new) * (0.9N) * (1.2P)
=> F(new) = F/(0.9*1.2)
=> F(new) = 0.9259F
Therefore the new cost of food must be 92.59% of the old cost, or the cost of food must decrease by 7.4% (option E)
Answer: (E) 7.4%
Question: If a = -2, what is the value of –(a^2 + a^3 + a^4 + a^5)?
(A) 20
(B) -4
(C) 0
(D) 4
(E) 14
Rationale: if a = -2, then putting values in equation
= -[ (-2)^2 + (-2)^3 + (-2^4) + (-2^5) ]
= -[ 4 - 8 + 16 - 32 ]
= 20
Answer = A = 20
Answer: (A) 20
Question: When members of a certain club elected a chairman, each member voted for one of the three candidates. If candidate 1 received three times as many votes as the other two candidates together and candidate 2 received nine more votes than candidate 3, which of the following can be the number of members in the club?
(A) 24
(B) 30
(C) 32
(D) 36
(E) 40
Rationale: Let x denote the number of votes for candidate 1, y the number of votes for candidate 2, and z the number of votes for candidate 3. The stem gives that x=3(y+z) and y=z+9. The number of club members =x+y+z=4(y+z)=4(2z+9)=8z+36. Because z must be a non-negative integer, the club can contain 36, 44, 52, ... members. Among the listed choices only choice D fits.
Answer: D
Answer: (D) 36
Question: If x and y are positive integers, and (4x)/(3y) is an integer, which of the following must be true?
I) x is a multiple of 4.
II) y is a multiple of 3.
III) x·y is a multiple of 3.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: For (4x)/(3y) to be an integer, x must be a multiple of 3. So, x * y is a multiple of 3.
Hence, C. ( rest two statements may or may not be valid)
ANSWER:C
Answer: (C) III only
Question: Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 30 litres of tomato juice?
(A) 3.75 liters.
(B) 2.5 liters.
(C) 8.5 liters.
(D) 2.6 liters.
(E) 2.1 liters.
Rationale: Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
â‡’â‡’ 10%(30) = 80%(x)
â‡’â‡’ x = 3.75 liters.
Answer:A
Answer: (A) 3.75 liters.
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and g. How many integer values can g 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 g can be when it is the hypotenuse of the triangle.
So, g= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of g can be when side of length 12 is the hypotenuse of the triangle.
So, g = sqrt (19^2 - 12^2) = 14.7 (approx)
So, g>14.7 and g<22.5.
Hence, possible values for g can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Answer: (D) 8
Question: What will be the cost of building a fence around a square plot with area equal to 25 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 1160
(B) 1251
(C) 1102
(D) 1352
(E) 1450
Rationale: Let the side of the square plot be a ft.
a2 = 25 => a = 5
Length of the fence = Perimeter of the plot = 4a = 20 ft.
Cost of building the fence = 20 * 58 = Rs. 1160.
Answer: A
Answer: (A) 1160
Question: 9 men and 6 women will finish a work in 5 days, similarly 3 men and 15 women can finish the same work in 10 days then in how many days 9 men and 10 women will finish the same work.
(A) 185/41 days
(B) 175/41 days
(C) 195/41 days
(D) 195/51 days
(E) 195/49 days
Rationale: 9 men and 6 women will finish a work in 5 days, similarly 3 men and 15 women can finish the same work in 10 days .
so 45 men + 30 women = 30 men +150 women
15 men = 120 women
1 man = 8 women
9 men = 72 women
9 men + 6 women = 78 women
9 men +10 women = 82 women.
78 women complete work in 5 days
82 women will complete work in 5*78/82 = 5*39/41 = 195/41 days
ANSWER:C
Answer: (C) 195/41 days
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 280 votes. The total number of votes polled was?
(A) 600 votes
(B) 700 votes
(C) 770 votes
(D) 800 votes
(E) 860 votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 280
40% = 40×7 = 280
100% =100×7 =700 votes
B)
Answer: (B) 700 votes
Question: Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-1) = 0, then b + c =
(A) 18
(B) 15
(C) -15
(D) -11
(E) -24
Rationale: f(x) = x^2 + bx + c. If f(6) = 0 and f(-1) = 0, then b + c =
f(6) = 0= 36+6b+c--- Taking 36 to the other side
-> 6b+c= -36
f(-1) = 0= 1-b+c --- taking -b+c to the other side
-> b-c=1
When we add these 2 equations, we get 7b= -35---> b= -5
And while substituting b= -5 we get c= -6.
b+c= -11--- Answer D
Answer: (D) -11
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
(A) 288
(B) 2889
(C) 1000
(D) 2770
(E) 27912
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
Answer: C
Answer: (C) 1000
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
(A) 3:3
(B) 8:7
(C) 4:8
(D) 2:9
(E) 2:7
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
nswer: B
Answer: (B) 8:7
Question: Ajay spends 25 per cent of his salary on house rent, 10 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is Ajayâ€™s income?
(A) Rs.67500
(B) Rs.80500
(C) Rs.60700
(D) Rs.70500
(E) None of these
Rationale: Explanation:
Savings = Income â€“ expenditure
100 â€“ (25+10+15+10) = 40%
40% of income = Rs.27000
:. Income = 27000 x 100/40 = Rs. 67500.
Answer: Option A
Answer: (A) Rs.67500