mathewhe/aqua_rat huggingface dataset:
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 11
(B) 77
(C) 12
(D) 99
(E) 02
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer: C
Answer: (C) 12
Question: Company KW is being sold, and both Company A and Company B were considering the purchase. The price of Company KW is 50% more than Company A has in assets, and this same price is also 100% more than Company B has in assets. If Companies A and B were to merge and combine their assets, the price of Company KW would be approximately what percent of these combined assets?
(A) 66%
(B) 75%
(C) 86%
(D) 116%
(E) 150%
Rationale: Let the price of Company A's assets be 100
Price of assets of KW is 50% more than company A's assets which is 150
Price of assets of KW is 100% more than company B's assets which means price of Company B's assets is half the price of KW = 75
A+B = 175
KW = 150
KW/(A+B)*100 = 150/175*100 = 85.7% or 86%
ANSWER:C
Answer: (C) 86%
Question: A certain boxer has agreed to pay his opponent a fee of 4% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $26,250 after weighing in seven pounds over the specified limit, what was the boxer's purse?
(A) $65,625
(B) $105,000
(C) $150,000
(D) $93,750
(E) $1,050,000
Rationale: .04*7 = .28
26250/.28 = $93,750
Answer: D
Answer: (D) $93,750
Question: In a class of 38 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 14
Rationale: 26 + 20 - 17 = 29
38 - 29 = 9 play neither
Answer is C
Answer: (C) 9
Question: The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 686, Krishan has ?
(A) s. 2890
(B) s. 4046
(C) s. 1190
(D) s. 1620
(E) s. 2680
Rationale: Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 686 : N
&there N = 289 x 686 / 49
= Rs. 4046
Answer :B
Answer: (B) s. 4046
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 2%
(B) 4%
(C) 6%
(D) 9%
(E) 2%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer:B
Answer: (B) 4%
Question: A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $32,000 commission, how many machines did she sell?
(A)  90
(B)  110
(C)  105
(D)  115
(E)  120
Rationale: First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 34000 - 30000 = 4000
So 10 more machines..
Total = 110 machines
IMO B..
Answer: (B)  110
Question: An alloy weighing 60 ounces is 20 percent copper. How many ounces of copper must be added to create an alloy that is 60 percent copper?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: An alloy of 60oz which is 20% copper means there is 12 oz of gold. To get to an alloy that is 60% copper, let's use this expression: (12 + x)/(60 + x) = 0.60 with x representing the amount of pure copper that must be added to get to 60%. The expression we are using represents the new total weight of pure copper over the new total weight of the alloy and this fraction should represent 60% or 0.6. you will see that 60 is the correct answer, as 72/120=0.6
Choose C
Answer: (C) 60
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 45% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A) 5%
(B) 10%
(C) 15%
(D) 35%
(E) 30%
Rationale: The formula is
n(AUBUC) = n(A)+n(B)+n(C)-B+A-N
where B is both (it will sum of (AB), (BC), (CA)).
and A is All
and N is neither
so plugging in we get
100 = 60+50+45+10-B-0
B = 65.
exactly two = 65 - 3(10) = 35
subtracting 10% three times as this value is including in all the (AB), (BC), (CA).
Answer D
Answer: (D) 35%
Question: A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
(A) 1
(B) 2
(C) 8
(D) 11
(E) 10
Rationale: Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
Answer :A
Answer: (A) 1
Question: Two cars start from the opposite places of a main road, 105 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
(A) 65
(B) 38
(C) 20
(D) 28
(E) 21
Rationale: Answer: C) 20 km
Answer: (C) 20
Question: If N = 2^0.25 and N^b = 8, b must equal
(A) 3/80
(B) 3/5
(C) 12
(D) 5/3
(E) 80/3
Rationale: 25/100 = 1/4
N = 2 ^ 1/4
N^b = 2^3
(2^1/4)^b = 2^3
b =12
Answer: C
Answer: (C) 12
Question: If $400 is deposited into a savings account at an annual interest rate of 3% that compounds monthly, what is the value of the investment after 8 years?
(A) 574.65
(B) 514.23
(C) 508.35
(D) 536.87
(E) 235.87
Rationale: Using CI Formula:
A=P(1+r/n)^n*t
A=400(1+3/2)^2*8
A=508.35.
Option: C
Answer: (C) 508.35
Question: The wheel of a motorcycle, 70 cm in diameter makes 40 revolutions in every 10 seconds. What is the speed of the motorcycle in km/hr
(A) 30.68 km/hr
(B) 31.68 km/hr
(C) 32.68 km/hr
(D) 33.68 km/hr
(E) None of these
Rationale: Explanation:
In this type of question, we will first calculate the distance covered in given time.
Distance covered will be, Number of revolutions * Circumference
So we will be having distance and time, from which we can calculate the speed. So let solve.
Radius of wheel = 70/2 = 35 cm
Distance covered in 40 revolutions will be
40 * Circumference =40 * 2*\pi*r =40∗2∗22/7∗35=8800cm
=8800/100m=88m
Distance covered in 1 sec =88/10=8.8m
Speed=8.8m/s=8.8∗18/5=31.68km/hr
Option B
Answer: (B) 31.68 km/hr
Question: What is the absolute value of twice the difference of the roots of the equation J= 5y^2 − 20y + 15 = 0 ?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: J=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.
Answer: E.
Answer: (E)  4
Question: Yesterday's closing prices of 2,420 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
(A) 484
(B) 726
(C) 1,100
(D) 1,320
(E) 1,694
Rationale: Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 2420 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1) & (2) to get H = 1320.
D is answer.
Answer: (D) 1,320
Question: 10 is 6% of a, and 6 is 10% of b. c equals b/a. What is the value of c?
(A) 3/10
(B) 6/17
(C) 9/25
(D) 10/33
(E) 12/35
Rationale: 6a/100 = 10
a = 500/3
b/10 = 6
b = 60
c = b/a = 60*3/ 500 = 9/25
The answer is C.
Answer: (C) 9/25
Question: At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but,not together?
(A) (5 + 5/11 )min past 5
(B) (5 + 5/11 )min past 7
(C) (5 + 5/11 )min past -0
(D) (5 + 7/11 )min past 7
(E) (5 + 5/71 )min past 7
Rationale: Explanation:
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min spaces are gained in min = min
so, Required time = min past 7
Answer: B)
Answer: (B) (5 + 5/11 )min past 7
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Tuesday. They were very happy. What day of the week would come on 14 Feb. 2010?
(A) monday
(B) tuesday
(C) sunday
(D) wednesday
(E) thursday
Rationale: feb 14 2005 - tuesday
feb 14 2006 - wednesday
feb 14 2007 - thursday
feb 14 2008 - friday
feb 14 2009 - sunday[since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - monday
ANSWER:A
Answer: (A) monday
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. 84 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 9.2 years and the standard deviation is 3.5 years, what percent of the distribution has more than 12.7 years as a shelf’s average life?
(A) 18%
(B) 19%
(C) 20%
(D) 21%
(E) 22%
Rationale: Average = 9.2
SD = 3.5
9.2 - 3.5 < 84% of distribution < 9.2 + 3.5
5.7 < 84% of distribution < 12.7
42% is outside this range.
Given: Distribution is symmetric. So 21% of distribution is less than 5.7 and the other 21% of distribution is greater than 5.7.
Answer: D
Answer: (D) 21%
Question: If 20 men can build a wall 66 meters long in 6 days, what length of a similar can be built by 86 men in 8 days?
(A) 49
(B) 39
(C) 29
(D) 19
(E) None of them
Rationale: Let the required length be x meters
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)= x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Answer is A.
Answer: (A) 49
Question: In a tournament, there are n teams T1 , T2 ....., Tn with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & T1. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?
(A) n(k-1)
(B) k(n-1)
(C) n(k-2)
(D) k(n-2)
(E) (n-1)(k-1)
Rationale: Explanation :
Let T1 - T6 be the number of teams, and let 1,2,3,4,5,6….be the players in the teams.
Total players if there are no repetition is 6*4 here. Generally, it is n * k. (n = number of teams, k = player/team). However, we see that, in each team, 1 player is repeated. i.e.
T1 & T2 have 4 in common (So 1 can be subtracted)
T2 & T3 have 7 in common (So 1 can be subtracted)
T3 & T4 have 10 in common (So 1 can be subtracted)
T4 & T5 have 13 in common (So 1 can be subtracted)
T5 & T6 have 16 in common (So 1 can be subtracted)
T6 & T1 have 1 in common (So 1 can be subtracted)
So, totally from each column 1 can be subtracted.
There are “n” columns totally, so n can be subtracted ( Here 6 needs to be subtracted)
So, here we have 6 * 4 – 6 players. Generally we have n * k – n i.e n(k-1) players.
Answer : A
Answer: (A) n(k-1)
Question: From the sale of sleeping bags, a retailer made a gross profit of 13% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?
(A) 3.0
(B) 3.36
(C) 24.78
(D) 25.0
(E) 31.36
Rationale: Cost price * 1.13 = Selling price --> Cost price * 1.13 = $28 --> Cost price = $24.78.
Answer: C.
Answer: (C) 24.78
Question: A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 70% more recliners. What is the percentage increase of the gross?
(A) 10%
(B) 15%
(C) 20%
(D) 36%
(E) 50%
Rationale: Say a recliner is actually worth $100
If she sells 100 recliners then she earns $10000
After the discount of 20%, she will earn $80 per recliner and she sells 70% more ie.,170 recliners
Hence her sales tields 170*80=$13600
Increase in sales=13600-10000=$3600
So% increase = 3600*100/10000 =36%
D is the answer
Answer: (D) 36%
Question: A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?
(A) 3456
(B) 4056
(C) 4156
(D) 4567
(E) 6532
Rationale: Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
Answer: (B) 4056
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 16 hours respectively. The ratio of their speeds is
(A) 4:1
(B) 4:2
(C) 4:5
(D) 4:3
(E) 4:6
Rationale: Ratio of their speeds = Speed of first train : Speed of second train
= √16−−√4
= 4:2
Answer is B.
Answer: (B) 4:2
Question: Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 40 minutes earlier than usual. How much time did the man spend walking?
(A) 45 minutes
(B) 50 minutes
(C) 40 minutes
(D) 55 minutes
(E) 35 minutes
Rationale: As they arrived 40 minutes earlier than usual, they saved 40 minutes on round trip from home to station (home-station-home) --> 20 minutes in each direction (home-station) --> wife meets husband 20 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-20 minutes=40minutes.
Answer: C
Answer: (C) 40 minutes
Question: Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold five as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold five times as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
(A) Andy
(B) Bob
(C) Cary
(D) Dora
(E) Ellen
Rationale: a= 5e
b =3 +e
c = 5b = 15+ 5e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C
Answer: (C) Cary
Question: A man can row his boat with the stream at 18 km/h and against the stream in 8 km/h. The man's rate is?
(A) 5 kmph
(B) 2 kmph
(C) 7 kmph
(D) 8 kmph
(E) 3 kmph
Rationale: DS = 18
US = 8
S = ?
S = (18 - 8)/2 = 5 kmph
Answer:A
Answer: (A) 5 kmph
Question: In how many ways can be 4 boys and 4 girls sit around circular table so that no two boys sit next to each other?
(A) (5!)^2
(B) (6!)^2
(C) 3!4!
(D) 11!
(E) (5!)^2*6!
Rationale: first fix one boy and place other 3 in alt seats so total ways is 3!
now place each girl between a pair of boys... total ways of seating arrangement of girls 4!
total is 4!*3!
ANS C
Answer: (C) 3!4!
Question: In a bag, there are three 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?
(A) 60
(B) 61
(C) 64
(D) 84
(E) 960
Rationale: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:
1) The minimum number on any given die is 1
2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.
With 4 dice, we could end up with any SUM between:
4 (if we rolled 1s on all 4 dice)
to
64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).
Thus, there are only 61 possible sums.
B
Answer: (B) 61
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 40 minutes?
(A) 80
(B) 100
(C) 160
(D) 240
(E) 300
Rationale: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 40 minutes the population increases by 40 x 4 = 160 people.
Answer. C.
Answer: (C) 160
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 5 years
(B) 6 years
(C) 7 years
(D) 9 years
(E) 15 years
Rationale: (4000*T*5)/100 = (5000*5*4)/100
T = 5 years
ANSWER:A
Answer: (A) 5 years
Question: Replace X with the appropriate number in
1 , 2 , 3 , 4 , 7 , 10 , 11 , X
(A) 12
(B) 13
(C) 15
(D) 16
(E) 18
Rationale: A
list of consecutive numbers that does not contain a 'i' in the spelling
Answer: (A) 12
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 182 votes. Find the total number of valid votes?
(A) 455
(B) 570
(C) 480
(D) 520
(E) 550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 182 => 4x/10 = 182
=> 4x = 1820 => x = 455.
ANSWER:A
Answer: (A) 455
Question: Rahim bought 50 books for Rs.1000 from one shop and 40 books for Rs.800 from another. What is the average price he paid per book ?
(A) 28
(B) 20
(C) 27
(D) 29
(E) 21
Rationale: Average price per book
= (1000+ 800) / (50 + 40)
= 1800 / 90
= Rs.20
Answer:B
Answer: (B) 20
Question: By selling a house for Rs.55000, it was found that 1/10 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 38020
(B) 38000
(C) 38028
(D) 38019
(E) 47500
Rationale: CP + CP/10 = 55000
CP = 50000
SP = 50000*(95/100)
=47500
Answer: E
Answer: (E) 47500
Question: Ratio of the ages of Mahesh and Nilesh is 5 : x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
(A) 13.9
(B) 16.5
(C) 14.7
(D) 12.5
(E) 14.5
Rationale: Let the present ages of Mahesh, Nilesh and Ramesh be m, n and r respectively.
m/n = 5/x ------ (1)
m = r - 18 ------ (2)
r + 9 = 47 ------ (3)
m - n = r ----- (4)
(3) => r = 47 - 9 = 38 years
(2) => m = 38 -18 = 20 years
(1) => 20/n = 5/x => n = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5
Answer:E
Answer: (E) 14.5
Question: If [x] is the greatest integer less than or equal to x, what is the value of [-11.6]+[13.4]+[12.7]?
(A)  3
(B)  10
(C)  13
(D)  16
(E)  17
Rationale: You are asked what the closest lesser integer value to [x] is.
[-11.6] = -12.0
[13.4] = 13.0
[12.7] = 12.0
Therefore , answer is: -12.0 + 13.0 + 12.0 = 13.0
Option A.
Answer: (C)  13
Question: A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
(A) 28
(B) 21
(C) 29
(D) 27
(E) 13
Rationale: 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer:B
Answer: (B) 21
Question: A question paper has 2 parts, A & B, each containing 5 questions. If a student has to choose 3 from part A & 4 from part B, in how many ways can he choose the questions?
(A) 50
(B) 100
(C) 152
(D) 150
(E) 55
Rationale: There 3 questions in part A out of which 4 question can be chosen as = 5C3.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 5C4.
Hence, total number of ways,
=5C3*5C4
=[5!/(2!3!)]*[5!/(4!*1)]
= {10}*{5*4!/(4!)}
= 10*5=50.
A
Answer: (A) 50
Question: The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 14.56 years. What was the average age of five new men?
(A) 15.5
(B) 15.4
(C) 15.25
(D) 10.4
(E) 15.6
Rationale: Total age of 20 men = 15.6 x 20 = 312
Now, total age of 25 men = 364.
Total age of five men added later = 364 - 312 = 52.
Hence, the total average of five men = 52/5 = 10.4
ANSWER:D
Answer: (D) 10.4
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.865 per pound?
(A) 1:3
(B) 1:2
(C) 1:1
(D) 2:1
(E) 3:1
Rationale: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.865
0.9 – 0.1x = 0.865
x = 0.35
Thus ratio of both flours is 1:2
B
Answer: (B) 1:2
Question: The average number of printing error per page in a book of 512 pages is 4. If the total number of printing error in the first 302 pages is 1,208, the average number of printing errors per page in the remaining pages is
(A) 0
(B) 4
(C) 840
(D) 90
(E) 80
Rationale: Remaining pages = 512 – 302 = 210
Let average printing error in remaining pages = x
Then, 1208+210×x /512=4
⇒ 210x = 840 ⇒ x = 4
Answer B
Answer: (B) 4
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 60 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is :
(A) 45
(B) 43
(C) 40
(D) 38
(E) 29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*60*36 / 60+36
= 45
Answer : A
Answer: (A) 45
Question: If c and d are unique prime integers, which of the following must be odd?
(A) a−b
(B) a−2b
(C) 2c−2d
(D) 2c/2d
(E) c-d
Rationale: The answer is C. Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.
Answer C
Answer: (C) 2c−2d
Question: When the positive integer C is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer Dis divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of C-D?
(A)  12
(B)  24
(C)  35
(D)  16
(E)  30
Rationale: If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5c + 3
n = 7d + 4
I will need to check for the smallest such number.
I put d= 1. n = 11. Is it of the form 5c + 3? No.
Put d= 2. n = 18. Is it of the form 5c + 3? Yes.
When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.
Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder
Next will be 35*2 + 18
and so on...
Difference between such numbers will be a multiple of 35 so
your answer is C
Answer: (C)  35
Question: What is the difference between the compound interests on $5000 for 1 years at 4% per annum compounded yearly and half-yearly?
(A) $2.04
(B) $3.06
(C) $4.80
(D) $8.30
(E) $9.30
Rationale: A.
$. 2.04
B.
$. 3.06
C.
$. 4.80
D.
$. 8.30
Answer: Option A
Explanation:
C.I. when interest
compounded yearly = $ 5000 x 1 +	4 x 1 + x 4
100 100
= $. 5000 x	26	x	51
25 50
= $. 5304.
C.I. when interest is
compounded half-yearly	= $ 5000 x 1 +	2 3
100
= $ 5000 x	51	x	51	x	51
50 50 50
= $5306.04
Difference = $. (5306.04 - 5304) =$. 2.04
ANSWER : A $2.04
Answer: (A) $2.04
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
(A) 18
(B) 19
(C) 27
(D) 29
(E) 31
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: (C) 27