mathewhe/aqua_rat huggingface dataset:
Question: In a 1500 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
(A) 100 sec.
(B) 50 sec
(C) 75 sec
(D) Data not sufficient
(E) None of these
Rationale: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1500/5 = 300 sec.
Time taken by Baley to complete the race is D = 1500/4 = 275 sec.
Hence, D-B = 75 sec
ANSWER:C
Answer: (C) 75 sec
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
(A) 7/98
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68
Rationale: 2/7 * 6/7 * 1/3 * 1/8 = 1/98
ANSWER:C
Answer: (C) 1/98
Question: The G.C.D. of 1.08, 0.36 and 0.63 is?
(A) 0.03
(B) 0.09
(C) 0.18
(D) 0.108
(E) none of these
Rationale: Given numbers are 1.08,0.36 and 0.63.
H.C.F of 108, 36 and 63 is 9
H.C.F of given numbers=0.09.
Correct Options:B
Answer: (B) 0.09
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $15,000 and the marginal cost is $200, and the total cost is $25,000, what is the value of n?
(A)  30
(B)  50
(C)  60
(D)  80
(E)  100
Rationale: Total cost for n products = fixed cost for n products + n*marginal cost --> $25,000 = $15,000 + n * $200 --> n = 50.
Answer: B.
Answer: (B)  50
Question: A person travelled from his house to office at 20km/hr and office to house at 80km/hr. Then find the average speed?
(A) 32km/hr
(B) 40km/hr
(C) 48km/hr
(D) 50km/hr
(E) 62km/hr
Rationale: Average speed = (2*20*80)/(20+80)= 32km/hrAnswer is A
Answer: (A) 32km/hr
Question: The total number of plums that grew during each year on a certain plum tree was equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded to the nearest lower integer.) During its 3rd year, this plum tree grew 50 plums. How many plums did it grow during its 6th year?
(A) a) 41
(B) b) 38
(C) c) 35
(D) d) 29
(E) e) 28
Rationale: The answer shud be 38.
(50 - 3 - 4 - 5 =38)
Yes, if you go the 50 - 3 way, then it will be 38. If instead you go the 50 - 4 way (which they have suggested), the answer will be 35. As I said, there is ambiguity here.answer is C
Answer: (C) c) 35
Question: Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 4 hours, how many minutes did it take Cole to drive to work?
(A) 66
(B) 70
(C) 95
(D) 112
(E) 140
Rationale: First round distance travelled (say) = d
Speed = 75 k/h
Time taken, T2 = d/75 hr
Second round distance traveled = d (same distance)
Speed = 105 k/h
Time taken, T2 = d/105 hr
Total time taken = 4 hrs
Therefore , 4 = d/75 + d/105
LCM of 75 and 105 = 525
4= d/75 + d/105
=> 4 = 7d/525 + 5d/525
=> d = 525 / 3 Km
Therefore, T1= d/75
=> T1 = 525 / (3 x 75)
=> T1 = (7 x 60) / 3 -- in minutes
=> T1 = 140 minutes.
E
Answer: (E) 140
Question: Find the average of the series : 312, 162, 132, 142 and 122?
(A) 129
(B) 308
(C) 267
(D) 207
(E) 174
Rationale: Average = (312 + 162 + 132 + 142 + 122)/5
= 870/5
= 174
Answer: E
Answer: (E) 174
Question: How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/6!?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 9
Rationale: 7! = 720
1/1000 < 1/720< 1/100
0.001 < 1/720 < 0.01
So 1/720 has 2 leading zeros
Answer: A
Answer: (A) 2
Question: If a triangle in the xy-coordinate system has vertices at (-2 , -3), (4, -3) and (28, 7), what is the area of the triangle?
(A) 30
(B) 36
(C) 48
(D) 60
(E) 65
Rationale: (-2,-3) is in 3rd quadrant, (4,-3) is in 4th quadrant while (28,7) is in 1st quadrant.
Also, y coordinate of (-2,-3) and (4,-3) is same so they lie on same horizontal line.
So base of triangle = sqrt[(-3+3)^2 + (4+2)^2] = 6
And height of triangle = 7 - (-3)
= 10
So area of triangle = 1/2*6*10
= 30
Hence option (A),
Answer: (A) 30
Question: 8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 14th and the 20th terms?
(A) 324
(B) 335
(C) 346
(D) 357
(E) 368
Rationale: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 14th term is 14 × 11 – 3 = 151.
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 368.
The correct answer is choice (E).
Answer: (E) 368
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1500. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 78%
(B) 35%
(C) 40%
(D) 76%
(E) None of these
Rationale: The total CP = Rs. 16000 + Rs. 1500= Rs. 17500 and SP = Rs. 31150
Profit(%) = (31150 - 17500)/17500* 100 = 78%
ANSWER:A
Answer: (A) 78%
Question: A six-sided die is rolled once. What is the probability that the number rolled is an odd number greater than 4?
(A) 2 / 3
(B) 1 / 6
(C) 3 / 3
(D) 4 / 5
(E) 2 / 4
Rationale: Only 5 so, 1 / 6
correct answer B
Answer: (B) 1 / 6
Question: Midway through his round a golfer hits a magnificent 210 yard drive, which brings his average length per drive for the round up to now from 156 to 162 yards. How far would he have had to hit the drive to bring his average length of drive up from 156 to 165 yards?
(A) 243 yards
(B) 239 yards
(C) 189 yards
(D) 245 yards
(E) 237 yards
Rationale: E
237 yards
Eight holes average 156 = 1, 248 yards,
Nine holes average 162 = 1, 458 yards (+ 210),
Nine holes average 165 = 1, 485 yards (+ 237).
Answer: (E) 237 yards
Question: A car takes 6 hours to cover a distance of 270 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 30 Kmph
(B) 60 Kmph
(C) 65 Kmph
(D) 70 Kmph
(E) None
Rationale: Time = 6
Distence = 270
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 270/9 = 30 Kmph
A)
Answer: (A) 30 Kmph
Question: 108.	Triangle A’s base is 8% greater than the base of triangle B, and A’s height is 8% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
(A)  9 % less
(B)  1 % less
(C)  Equal to each other
(D)  1.6 % more
(E)  9 % more
Rationale: Wish the question specified that we are talking about corresponding height.
Base of A = 9/8 * Base of B
Height of A = 7/8 * Height of B
Area of A = (1/2) * Base of A * Height of A = 9/8 * 7/8 * Area of B = 63/64 * Area of B
Area of A is 1.6% more than the area of B.
Answer (D)
Answer: (D)  1.6 % more
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 2 different boat to go and 8 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 16
(C) 45
(D) 18
(E) 70
Rationale: Ans.(B)
Sol. Number of choices to go by ship = 2 Number of choices to return by airline = 8 From, fundamental principle, total number of ways of performing the journey = 2 x 8 = 16 ways
Answer: (B) 16
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 40.00 a.m.
(B) 10.00 a.m.
(C) 12.00 a.m.
(D) 18.00 a.m.
(E) 19.00 a.m.
Rationale: Explanation:
D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: Option B
Answer: (B) 10.00 a.m.
Question: P and Q invested in a business. The profit earned was divided in the ratio 3 : 4. If P invested Rs 50000, the amount invested by Q is
(A) 30000
(B) 66666
(C) 40000
(D) 20000
(E) 60000
Rationale: Let the amount invested by Q = q
50000:q=3:4
⇒50000×4=3q
⇒q=(50000×4)/3=66666
Answer is B.
Answer: (B) 66666
Question: Joe bought a lawnmower for a 40% off the original price. If the lawnmower cost him $132.48, what is the original selling price of the lawnmower?
(A) $185.47
(B) $331.20
(C) $211.97
(D) $220.80
(E) None of these.
Rationale: Explanation:CP of Joe is 40% of the Original SP.:. Original SP = $132.48x100/60 = $220.80.Answer: Option D.
Answer: (D) $220.80
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 17 kmph
(C) 19 kmph
(D) 17 kmph
(E) 29 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
=10 kmph.
Answer: A
Answer: (A) 10 kmph
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 76 Kmph
(B) 54 Kmph
(C) 72 Kmph
(D) 34 Kmph
(E) 91 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Answer: (C) 72 Kmph
Question: If 4 men working 10 hours a day earn Rs. 1200 per week, then 9 men working 6 hours a day will earn how much per week?
(A) Rs 840
(B) Rs 1320
(C) Rs 1620
(D) Rs 1680
(E) None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 1200 : x
hence 4 * 10 *x = 9 * 6 * 1200
or x = 9*6*1200/ 4*10 = 1620
Answer : C
Answer: (C) Rs 1620
Question: Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter she prepared an envelope with its correct address. If the 4 letters are to be put in 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
(A) 1/24
(B) 1/8
(C) 1/4
(D) 1/3
(E) 3/8
Rationale: Possible sequences are CIII, ICII, and so on...C=correct, I=incorrect
Total possible sequences are 4P1=4 ways.
Lets take the probability of having one particular sequence CIII.
P = 1/4*2/3*1/2*1 = 1/12.
So the probability of having any of the sequence is 4*1/12 =1/3
ANS:D
Answer: (D) 1/3
Question: If x = 1- 4t and y = 2t - 2, then for what value of t does x = y?
(A)  5/2
(B)  1/2
(C)  2/3
(D)  2/5
(E)  0
Rationale: We are given x = 1 – 4t and y = 2t – 2, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 4t for x and 2t – 2 for y in the equation x = y. This gives us:
1 – 4t = 2t – 2
3 = 6t
1/2 = t
The answer is B.
Answer: (B)  1/2
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: (B) 50%
Question: The cost price of 20 articles is equal to the selling price of 25 articles. The loss percent in the transaction is
(A) 5
(B) 20
(C) 25
(D) 30
(E) None of these
Rationale: Let C.P. of 1 article = 1
then C.P. of 25 articles = 25
and S.P. of 25 articles = 20
∴ loss % = 25−20/20×100=25%
Answer C
Answer: (C) 25
Question: 2664 ÷ 12 ÷ 6 = ?
(A) 43
(B) 41
(C) 37
(D) 33
(E) 21
Rationale: Explanation :
2664 ÷ 12 = 222
222 ÷ 6 = 37. Answer : Option C
Answer: (C) 37
Question: Point (g,h) is on the circle represented by g^2+h^2=10, and g, h are integers. How many such points are possible?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: g^2+h^2=10 and g, h are integers means that 10 is the sum of two perfect squares.
10 is the sum of only one pair of perfect squares 1 and 9.
So, there can be 8 such points, 4 in each quadrant:
(1, 3);
(1, -3);
(-1, 3);
(-1, -3);
(3, 1);
(3, -1);
(-3, 1);
(-3, -1).
Answer: E.
Answer: (E) 8
Question: If Janice was 22 years old z years ago and Lisa will be 20 years old in p years, what was the average (arithmetic mean) of their ages 8 years ago?
(A) (z + p)/2
(B) (z - p + 26)/4
(C) (z - p + 16)/4
(D) (z + p + 36)/2
(E) (z - p + 26)/2
Rationale: Today, J = z+22 and L = 20-p
8 years ago, J = z+14 and L = 12-p
The average of their ages was (z-p+26) / 2
The answer is E.
Answer: (E) (z - p + 26)/2
Question: How many integers are divisible by 2 between 10! and 10! + 20 inclusive?
(A) 6
(B) 7
(C) 21
(D) 9
(E) 10
Rationale: C = 21
10! is divisible by 2
There are 20 numbers between 10! and 10!+20 that are divisible by 1.
Hence 21
Answer: (C) 21
Question: Y and F represent two distinct digits. If the number 45Y89F is divisible by 36, what is the value of (Y+F)?
(A) a) 9
(B) b) 3
(C) c) 12
(D) d) 6
(E) e) 10
Rationale: A no. divisible by 36 means it is div by 49 .
to be div by 4 last 2 digits to be multiple of 4 So, F could be either 2 or 6 only
similarly for a number to be div by 9 its sum must be multiple of 9 first. filtering we find Y could be either 1,4,7 only.
To be divisible by 9 only 1 works .(if we choose f=6 then Y have to be 6 but as per condition YF are distinct) So
Y=1
F=2
Ans:- 3.B
Answer: (B) b) 3
Question: If x and y are even integers, which of the following is an odd integer?
(A) x+y
(B) xy
(C) xy+2
(D) x^2+y^2
(E) None of these
Rationale: even+even = even
even * even = even
even+even =even
Answer : E
Answer: (E) None of these
Question: A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
(A) 4500 M3
(B) 27000 M3
(C) 3000 M3
(D) 2700 M3
(E) 3700 M3
Rationale: (3000 * 2 * 5)/60 = 4500 M3
ANSWER:A
Answer: (A) 4500 M3
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the 2nd?
(A) 965
(B) 1245
(C) 1349
(D) 1368
(E) 1578
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 72 percent of the votes cast?
(A) 75%
(B) 58%
(C) 30%
(D) 34%
(E) 25%
Rationale: Total Number of members = 1260
Number of members that cast votes = 525
Since , winning candidate received 72 percent of the votes cast
Number of votes for winning candidate = (72/100)*525 = 378
Percent of total membership that voted for winning candidate = (378/1260)*100 = 30%
Answer C
Answer: (C) 30%
Question: A financier claims to be lending money at simple interest, But he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes
(A) 10.25%
(B) 10%
(C) 9.25%
(D) 9%
(E) None of these
Rationale: Explanation:
Let the sum is 100.
As financier includes interest every six months., then we will calculate SI for 6 months, then again for six months as below:
SI for first Six Months = (100*10*1)/(100*2) = Rs. 5
Important: now sum will become 100+5 = 105
SI for last Six Months = (105*10*1)/(100*2) = Rs. 5.25
So amount at the end of year will be (100+5+5.25)
= 110.25
Effective rate = 110.25 - 100 = 10.25
Option A
Answer: (A) 10.25%
Question: The cash realised on selling a 14% stock is Rs.104.25, brokerage being 1/4% is
(A) 123
(B) 106
(C) 100
(D) 156
(E) 104
Rationale: Explanation:
Cash realised= Rs. (104.25 - 0.25)
= Rs. 104.
Answer: E
Answer: (E) 104
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 22 kmph
(B) 77 kmph
(C) 14 kmph
(D) 17 kmph
(E) 18 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer:C
Answer: (C) 14 kmph
Question: A and B started a business investing Rs. 36,000 and Rs. 12,000 respectively. In what ratio the profit earned after 3 years be divided between A and B respectively?
(A) 1:3
(B) 1:2
(C) 2:1
(D) 3:1
(E) None of these
Rationale: A:B = 36000 : 12000 = 3:1.
ANSWER:D
Answer: (D) 3:1
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Tuesday
(B) Monday
(C) Sunday
(D) Wednesday
(E) SWW
Rationale: Sunday
The year 2004 is a leap year and therefore, two days will be preceded from Tuesday
Answer:C
Answer: (C) Sunday
Question: when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 14
(A) 1
(B) 3
(C) 4
(D) 5
(E) 2
Rationale: case1
N=5,8,11,14,17,20
case 2
M=5,9,13,17,21
Therefore n=17
Remainder of 17/14 will be 3
B
Answer: (B) 3
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x + 2y) is positive integer II. xy^2 is positive integer III. (y^2 - x) is positive integer
(A) I,II only
(B) I only
(C) II only
(D) III only
(E) none of these
Rationale: I. It is true if 3x < 2y
II. It is not true because given x is a negative integer - * + = -
III. It is true
Answer : D
Answer: (D) III only
Question: Simplify: 5005-5000+10
(A) 4505
(B) 4509
(C) 4501
(D) 4508
(E) None of them
Rationale: 5005-5000+10
=5005-(5000/10)
=5005-500
=4505.
Answer is A
Answer: (A) 4505
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
(A) 1
(B) 3
(C) 6
(D) 8
(E) 9
Rationale: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
C
Answer: (C) 6
Question: If $11,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years?
(A)  compounding annually
(B)  compounding daily
(C)  compounding monthly
(D)  compounding quarterly
(E)  All four of these would produce the same total
Rationale: This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.
This process will be repeated every day till the amount matures
Answer = B
Answer: (B)  compounding daily
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 11/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 11/21
(B) 14/31
(C) 7/15
(D) 17/35
(E) 1/2
Rationale: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 11/5 units. Total time for Basic would be 10*1=10 and total time for Deluxe would be 5*11/5=11 --> total time for both of them would be 10+11=21 --> deluxe/total=11/21.
Answer: A.
Answer: (A) 11/21
Question: A batsman makes a score of 84 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
(A) 19
(B) 29
(C) 36
(D) 49
(E) 59
Rationale: let the average after 17th inning =x
Then average after 16th inning=(x-3)
Therefore 16(x-3)+84=17x
Therefore x=36
ANSWER:C
Answer: (C) 36
Question: If Finn was 19 months old one year ago, how old was he, in months, x months ago?
(A) x − 30
(B) x − 12
(C) 18 − x
(D) 24 − x
(E) 31 − x
Rationale: Age Today = 19 months + 12 months (1year) = 31 months
X months ago- Today's Age - X = 31 - X
Ans- E
Answer: (E) 31 − x
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $5 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 34.4%
(D) 12%
(E) 15%
Rationale: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So
3(15) = 45 - Fox
2(18) = 36 - Pony
The total discount discount is $5 and you are asked to find the percent discount of pony jeans,
so 45(18 - X)/100 + 36(X)/100 = 5 or 45*18 -45*x + 36*x =5*100 or 9x = -5*100 +45*18
x= 310/9 =34.4
C
Answer: (C) 34.4%
Question: A cycle is bought for Rs.1000 and sold for Rs.2000, find the gain percent?
(A) 11
(B) 20
(C) 100
(D) 77
(E) 12
Rationale: 1000 ---- 1000
100 ---- ? => 100%
Answer: C
Answer: (C) 100
Question: If abc = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1
(A) None
(B) I only
(C) II only
(D) I and III
(E) II and III
Rationale: abc = b^3 implies abc - b^3 = 0
or b*(ac-b^2)=0
which implies either b=0 or ac=b^2
so, either of them or both of them can be true, but none of them must be true.
Answer A
Answer: (A) None
Question: The age of man is three times the sum of the ages of his two sons. Seven years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :
(A) 40 years
(B) 45 years
(C) 50 years
(D) 55 years
(E) 63 years
Rationale: Solution
Let the sum of present ages of the two sons be x years.
Then,father's present age = 3x years.
âˆ´ (3x + 7)=2 (x +14) â‡” 3x + 7 = 2x + 28â‡” x =21.
Hence,father's present age = 63 years. Answer E
Answer: (E) 63 years
Question: Jane and Ashley take 13 1/3 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
(A) 10 Days
(B) 15 Days
(C) 16 Days
(D) 17 Days
(E) 20 Days
Rationale: Let us assume that the work is laying 40 bricks.
Jane =3 bricks per day
Ashley = 1 brick per day
Together = 4 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 12
Remaining bricks = 40 - 20 = 20
So together, they would take 20/4 =5
Total no. of days = 8 + 4 + 5 = 17
Answer is D
Answer: (D) 17 Days
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:11. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 19
(B) 17
(C) 13
(D) 11
(E) 12
Rationale: 7*5: 5*x = 7:11
x = 11
Answer: D
Answer: (D) 11
Question: What is the smallest positive integer x, such that 5000x is a perfect cube?
(A) 4
(B) 6
(C) 8
(D) 25
(E) 18
Rationale: Take out the factors of 5000 that will come 10^3*5. for perfect cube you need every no. raise to the power 3. for 5000x to be a perfect cube, you need two 5 that means 25.
D is the answer.
Answer: (D) 25
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/8
(B) 5/9
(C) 5/7
(D) 5/2
(E) 5/3
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done 4C2 . 4C1 ways.
The required probability = (5 * 4)/9C2 = 20/36 = 5/9
Answer: B
Answer: (B) 5/9
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/15
(B) 18 2/11
(C) 18 2/14
(D) 18 2/16
(E) 18 2/12
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%.Answer: B
Answer: (B) 18 2/11
Question: Which of the following is closer to (5!+4!)-(5!-4!)?
(A) 48
(B) 84
(C) 240
(D) 420
(E) 52
Rationale: 5!+4!)-(5!-4!)=120+24-120+24
= 48
Answer: A
Answer: (A) 48
Question: The total number of digits used in numbering the pages of a book having 346 pages is
(A) 732
(B) 990
(C) 1098
(D) 930
(E) 1405
Rationale: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 247) = (9 + 180 + 741) = 930.
ANSWER:D
Answer: (D) 930