mathewhe/aqua_rat huggingface dataset:
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
(A) 150
(B) 278
(C) 100
(D) 776
(E) 191
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter
Answer:C
Answer: (C) 100
Question: Ram completes 60% of a task in 15 days and then takes the help of Rahim and Rachel. Rahim is 50% as efficient as Ram is and Rachel is 50% as efficient as Rahim is. In how many more days will they complete the work?
(A) 5(5/7) days
(B) 6(5/7) days
(C) 7(5/7) days
(D) 5(4/7) days
(E) 3(5/7) days
Rationale: ram completes 60% of work in 15 days
so ram 1 day work is 60% / 15= 4%
rahim is 50%efficient than ram
so rahim 1 day work is 2%
rachel is 50% efficient than rahim
so rachil 1day work is 1%
total work done by ram rahim and rachel in 1 day is 4%+2%+1%= 7%
7%----- 1 day
40%---------?
40/7
so 5.7=6 days needed to complete the 40%of work
ANSWER:A
Answer: (A) 5(5/7) days
Question: Two numbers are in ratio 7:11. If 7 is added to each of the numbers, the ratio becomes 2:3. The smaller number is
(A) 39
(B) 49
(C) 66
(D) 77
(E) None
Rationale: Solution: Let the numbers be 7x and 11x.
According to question,
(7x+7)/(11x+7) = 2/3;
Or, 22x+14 = 21x+21;
Or, x = 7;
Smaller number = 49.
Answer: Option B
Answer: (B) 49
Question: At what rate percent on simple interest will a sum of money double itself in 20 years?
(A) 2%
(B) 6%
(C) 3%
(D) 4%
(E) 5%
Rationale: P = (P*20*R)/100
R = 5%
ANSWER:E
Answer: (E) 5%
Question: 6x – 5y + 3z = 22
4x + 8y – 11z = 7
5x – 6y + 2z = 12
Given the equations above, x + y + z = ?
(A)  10
(B)  12
(C)  13
(D)  14
(E)  15
Rationale: (6x – 5y + 3z) - (5x – 6y + 2z ) = 22-12
or, x+y+z = 10
Option A is the ans
Answer: (A)  10
Question: If the two hands in a clock are 8 minutes divisions apart,then the angle between them is
(A) 3Â°
(B) 18Â°
(C) 24Â°
(D) 60Â°
(E) None of these
Rationale: In a clock, each minute makes 6Â°
âˆ´ 8 minutes will make 6 Ã— 8 = 24Â°
Answer C
Answer: (C) 24Â°
Question: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance e before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%
Rationale: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance e before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.
If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15 = 5 hours to reach john. If John had not stopped, their combined rate would 10+15 = 25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.
ANSWER: A) 25%
Answer: (A) 25%
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430 ?
(A) s. 832
(B) s. 830
(C) s. 822
(D) s. 812
(E) s. 810
Rationale: Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
A's share in the profit of Rs. 2430 = 20 (2430/60) = Rs. 810.
Answer: E
Answer: (E) s. 810
Question: Josh spends a total of $5.5 buying Q items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then Q may be which of the following?
(A) 99
(B) 100
(C) 101
(D) 112
(E) 113
Rationale: Q items in the convenience store $5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
Answer: (C) 101
Question: A can do a piece of work in 5 hours. B and C together can do it in 4 hours, while A and C together can do it in 3 hours. How long will B alone take to do it?
(A) 8hr
(B) 6hr
(C) 9hr
(D) 10hr
(E) 12hr
Rationale: A's 1 hour work = 1/5
B+C 1 hour work = 1/4
A+C 1 hour work = 1/3
A+B+C 1 hour work = 1/5 + 1/4 = 9/20
B's 1 hour work = 9/20 - 1/3 = 7/60 = 9hr (approximately)
B alone will take 9 hours approximately to do the work
Answer is C
Answer: (C) 9hr
Question: If a and b are the roots of the equation x2 - 4x + 4 = 0, then the value of a2 + b2 is:
(A) 36
(B) 24
(C) 17
(D) 8
(E) 5
Rationale: Sol.(b) The sum of roots = a+ b = 4
Product of roots = ab = 4
Now, a2 + b2 = (a + b)2 - 2ab = 16 - 8 = 8
Answer D
Answer: (D) 8
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.13600 after a year?
(A) 3630
(B) 9232
(C) 8828
(D) 2387
(E) 4080
Rationale: 6300:4200:10500
3:2:5
3/10 * 13600 = 4080
Answer: E
Answer: (E) 4080
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 50 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
(A) 93%
(B) 96%
(C) 100%
(D) 107%
(E) 120%
Rationale: Say Arthur's fortune was $100. Then:
A = 20*1.5*1.1 = 33
B = 20*1.5*1.1 = 33
C = 20*1.5*0.4 = 12
D = 20*0.6*1.50 = 18
E = 0
Total 33 + 33 + 12 + 18 = 96.
Answer: B.
Answer: (B) 96%
Question: The sum of two consecutive integers is 15. Find the numbers.
(A) 17, 18
(B) 7, 8
(C) 5, 6
(D) 1, 2
(E) 8, 9
Rationale: n + (n + 1) = 15
2n + 1 = 15
2n = 14
n = 7
Answer: B
Answer: (B) 7, 8
Question: A car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for the rest of the trip. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip?
(A) 6.5
(B) 7.5
(C) 8.5
(D) 9.5
(E) 10.5
Rationale: Let T be the total time of the trip.
30*5 + 42(T-5) = 34T
8T = 210-150
T = 7.5
The answer is B.
Answer: (B) 7.5
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 2/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
(A) 2/35
(B) 2/3
(C) 7/35
(D) 5/7
(E) 7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 2/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 2/7 x 1/5 = 2/35
ANSWER:A
Answer: (A) 2/35
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
(A) 8877
(B) 3000
(C) 7787
(D) 1799
(E) 1711
Rationale: 4 --- 2000
5 --- ? => 3000
Answer: B
Answer: (B) 3000
Question: A cistern 8 m long and 6 m wide contains water up to a breadth of 1 m 85 cm. Find the total area of the wet surface.
(A) 102 m sqaure
(B) 100 m sqaure
(C) 152 m sqaure
(D) 164 m sqaure
(E) None of these
Rationale: Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(6*1.85+8*1.85)]+8*6 = 100 m square
Option B
Answer: (B) 100 m sqaure
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability W that the new color will be one of theJaunecolors?
(A) 5/42
(B) 37/42
(C) 1/21
(D) 4/9
(E) 5/9
Rationale: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune W= (40 + 34)/84 = 37/42
Answer: (B) 37/42
Question: Three years ago the average of A and B was 18 Years. With C joining them now, the average becomes 22 years. How old is C now?
(A) 24 years
(B) 27 years
(C) 28 years
(D) 30 years
(E) 32 years
Rationale: (a+b)/2=18
(a+3+b+3+c)/3=22
(3+3+36+c)/3=22
c=24
ANSWER:A
Answer: (A) 24 years
Question: If a Half kg of potato costs 40 paise, how many paise does 400 gm cost?
(A) 84 paise
(B) 44 paise
(C) 28 paise
(D) 16 paise
(E) 18 paise
Rationale: Cost of 1/2 kg potato = 40 Paise
=> Cost of 500 gm potato = 40 Paise
=> Cost of 200 gm potato = (40*200)/500=80/5=16 Paise
ANSWER:D
Answer: (D) 16 paise
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 144 km/hr
(A) 8.5 seconds
(B) 2.8 seconds
(C) 3.5 seconds
(D) 2.5 seconds
(E) 2.6 seconds
Rationale: First convert speed into m/sec
Speed = 144*(5/18) = 40 m/sec
Time = Distance/speed
= 100/40 = 2.5 seconds
Answer: D
Answer: (D) 2.5 seconds
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) Rs.250
(B) Rs.256
(C) Rs.252
(D) Rs.258
(E) Rs.253
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? =>
Rs.250
Answer:A
Answer: (A) Rs.250
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 8
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: Option B
Answer: (B) 10
Question: If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word
"GONE" would be
(A) 3569
(B) 1552
(C) 4573
(D) 4735
(E) 5235
Rationale: G-4
O-7
N-3
E-5
so for mango the code is 4735
ANSWER:D
Answer: (D) 4735
Question: Q is a set of eight distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19= 77 (Discard as sum is ODD)
3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 98 (Sum is even)
Least number = 3
B
Answer: (B) 3
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 45%
(B) 26%
(C) 12%
(D) 19%
(E) 37%
Rationale: Option C
Explanation:
Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: (C) 12%
Question: A flat of plants consists of 6 flowers and 6 ground covers. If a basket is created with 3 flowers and 1 ground cover, in how many ways can the basket be formed?
(A) 12
(B) 120
(C) 450
(D) 800
(E) 576
Rationale: Choose 3 flowers from 6 flowers and choose 1 ground cover from 6 ground cover:
3C6 * 1C6 = 20*6 = 120
Ans: B
Answer: (B) 120
Question: A train 110 m long is running with a speed of 50 km/h. In how many seconds will the train pass a man who is running at 5 km/h in the direction opposite to that in which the train is going?
(A) 6.1
(B) 7.2
(C) 8.3
(D) 9.4
(E) 10.5
Rationale: The speed of the train relative to the man = 50 + 5 = 55 km/h.
55000 m/h * 1h/3600 s = (550/36) m/s
(110 m) / (550/36 m/s) = (110 * 36) / 550 = 36/5 = 7.2 seconds
The answer is B.
Answer: (B) 7.2
Question: A three-person committee must be chosen from a group of 10 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
(A) A)70
(B) B)1020
(C) C)630
(D) D)1,260
(E) E)1,980
Rationale: Total number of ways to select at least one professor = Number of ways to select 3 people from 10 students and 10 professors - Number of ways to select 3 people from 10 student (i.e. without including any professor)
= 20C3 - 10C3 = 1140 - 120 = 1020
ANSWER:B
Answer: (B) B)1020
Question: Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 7 even numbers. His mother immediately worked out the answer. How much had he scored in Math?
(A) 80
(B) 90
(C) 56
(D) 70
(E) 60
Rationale: C
56
Sum = (n x n) + n
Hence, 7 x 7 = 49 + 7 = 56
Answer: (C) 56
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 4, 2008?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Friday
(E) Sunday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 4 days beyond Monday
Hence, It will be Friday. answer : D
Answer: (D) Friday
Question: The average of temperatures at noontime from Monday to Friday is 30; the lowest one is 20, what is the possible maximum range of the temperatures?
(A) 20
(B) 25
(C) 40
(D) 45
(E) 10
Rationale: Average=30, Sum of temperatures=30*5=150
As the min temperature is 20, max would be 150-4*20=30 --> The range=30(max)-20(min)=10
Answer: E
Answer: (E) 10
Question: A and B can do a piece of work in 9 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 11.25 days
(B) 19.5 days
(C) 17.5 days
(D) 16.5 days
(E) 18.5 days
Rationale: C = 1/5 – 1/9 = 4/45 => 11.25 days
ANSWER:A
Answer: (A) 11.25 days
Question: If p,q ,and r are positive real numbers such that p(q+r) = 152, q(r+p) =162 , and r(p+q) = 170, then pqr is
(A) a) 672
(B) b) 688
(C) c) 704
(D) d) 720
(E) e) 750
Rationale: pq+pr = 152 --------------------------------------1)
qr+qp = 162---------------------------------------2)
pr+rq = 170---------------------------------------3)
Re-writing equation 3 as follows:
pr+rq = 162 + 8
pr+rq = qr+qp + 8
pr = qp + 8 ............... (4)
Adding (1)(4)
2pr = 160
pr = 80
pqr has to be multiple of 80, only 720 fits in
Answer = D
Answer: (D) d) 720
Question: Jeremy challenges his friends Asafa, Yohan, Nestor and Usain to a 400 metre race, with a difference. Jeremy will run the entire 400 metres and the others will run 100 metres each and then combine their times. If their combined time is quicker than Jeremy's they will have won the race. Asafa runs his stage in 10 seconds, Yohan runs his stage in 11 seconds but Nestor trips over and runs his stage in 16 seconds. Jeremy has run the first 300 metres at an average speed of 10.5 seconds per 100 metres. However when Jeremy runs 400 metre races, his final 100 metres is always 1.5 seconds slower than his average speed over the first 300 metres. If Usain's team is to have a chance of winning how quickly must he run his 100 metres?
(A) 5
(B) 5.5
(C) 6
(D) 6.5
(E) 7
Rationale: Jeremy has run the first 300 metres at an average speed of 10.5 seconds per 100 metres and so his time for 300 metres is 31.5 seconds (10.5 x 3 = 31.5).
Jeremy's final 100 metres is always 1.5 seconds slower than his average 300 metre speed and so he will run it in 12 seconds (10.5 + 1.5 = 12).
Jeremy's total time for 400 metres is 43.5 seconds (31.5 + 12 = 43.5).
Usain's team has run the first 300 metres in 37 seconds (10 + 11 + 16 = 37).
To be in with a chance of winning Usain must close the gap of 6.5 seconds (43.5 - 37 = 6.5).
ANSWER: D
Answer: (D) 6.5
Question: In a mixture of milk and water, the proportion of milk by weight was 70%. If, in a 200-gram mixture, 40 grams of pure milk is added, what would be the percentage of milk in the resulting mixture?
(A) 71%
(B) 72%
(C) 73%
(D) 74%
(E) 75%
Rationale: The amount of milk is 0.7(200) + 40 = 180 grams.
The proportion is 180/240 = 0.75 which is 75%
The answer is E.
Answer: (E) 75%
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 68% of the required amount. What is the net difference in the expenditure on that product?
(A) 12.5%
(B) 13%
(C) 16%
(D) 15%
(E) 19%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.68 x 1.25 = 0.85
Decrease in price = (0.15/1) × 100 = 15%
D)
Answer: (D) 15%
Question: If S> 0 and S is divisible by the product of the first nine positive integers, all of the following must be factors of S except
(A) 35
(B) 40
(C) 63
(D) 315
(E) 704
Rationale: The question states taht S is divisible by 9!,which is 1*2*3*4*5*6*7*8*9
S=(9!) * some number
A. 35 = 5*7 so will divide S
B. 40 =5*8 so will divide S
C. 63 =9*7 so will divide S
D. 315 =5*7*9 so will divide S
E. 704 =8*8*11 This will not divide S
Ans E
Answer: (E) 704
Question: A Truck drives 80 miles on local roads at 30 mph, and 50 miles on the highway at 60 mph, the truck also take a hour lunch break. what is the average speed of the entire trip?
(A) 30 mph
(B) 29 mph
(C) 28 mph
(D) 31 mph
(E) 23 mph
Rationale: So The Answer is Plainly A....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=80 miles , and v= 30 mph so we can obtain time : 30*t = 80 Or t= 80/30 = 2.6 hours the needed time to cover 80 miles
in the same way we should divide 50 to 60 to find the needed time to cover 50 miles ,so t= 0.8 hours
so the total time for covering total distance would be 2.6+0.8+1 (lunch time) = 4.4 hours and total distance is 80+50= 130 miles
Final stage : average speed is total distance divide to total time : 130/4.4 = 29.5 miles per hour rounding up to 30....
Answer: (A) 30 mph
Question: A can do a work in 9 days. B can do the same work in 18 days. If both A & B are working together in how many days they will finish the work?
(A) 3
(B) 5
(C) 4
(D) 2
(E) 6
Rationale: A rate = 1/9
B rate = 1/18
(A+B) rate = (1/9)+(1/18) = 1/6
A & B finish the work in 6 days
correct option is E
Answer: (E) 6
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
(A) 20
(B) 21
(C) 22
(D) 23
(E) NONE
Rationale: Sol.
Let the total number of workers be x. Then,
8000x = (12000 × 7) + 6000 ( x – 7)
‹=› 2000x = 42000
‹=› x = 21.
Answer B
Answer: (B) 21
Question: Which number need to add to 7844213 to get a number exactly divisible by 549?
(A) 418
(B) 148
(C) 448
(D) 248
(E) 348
Rationale: 7844213 / 549 = 14288 and reminder = 101.
549-101 = 448
So, the next number divisible by 549 is 448 places in front of 7844213
Which means 448 + 7844213 =7844661
448 should be added to 7844213
C
Answer: (C) 448
Question: Find The Next Number In Sequence ?
100 365 24 60 ?
(A) 55
(B) 60
(C) 80
(D) 90
(E) 65
Rationale: B
60.
100 years in a century, 365 days in a year, 24 hours in a day, 60 minutes in an hour, & 60 seconds in a minute.
Answer: (B) 60
Question: in how many ways u can form a group of 11 members from 5 men and 11 women if the men member not more than 3?
(A) 2256
(B) 2356
(C) 3456
(D) 4456
(E) 1554
Rationale: we need team members=11 such that there should not be more than 3 men
so the conditions are (3M,8W),(2M,9W),(1M,10W)
Now, no. of ways=11c11+5c3*11c8+5c2*11c9+5c1*11c10=2256
ANSWER:A
Answer: (A) 2256
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 18° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 5%
(B) 25%
(C) 30%
(D) 35%
(E) 72%
Rationale: ANSWER: A 18° divided by 360° equals 0.05, therefore the sector is equal to 5% of the total
Answer: (A) 5%
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 5 (B + G) is ?
(A) Equal to 3
(B) Less than 5
(C) More than 5
(D) Less than 1/5
(E) none of these
Rationale: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
5(B + G) = 5[(x/y) + (y/x)] = 5[(x2 + y2)/xy] > 5
ANSWER:A
Answer: (A) Equal to 3
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
(A) 9600
(B) 3337
(C) 2368
(D) 2688
(E) 2611
Rationale: Explanation:
Greatest number of 4-digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600. On dividing 9999 by 600, the remainder is 399. Required number (9999 - 399) = 9600.
Like this ?
Answer:A
Answer: (A) 9600
Question: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders R will be:[/b]
(A) 3, 3, 2
(B) 3, 4, 2
(C) 5, 4, 3
(D) R=5, 5, 2
(E) 6, 4, 3
Rationale: Let the original number be X. Then by the successive dividing we have followings :
X=5A+2
A=7B+3
B=8C+4.
So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.
Now by dividing X by 8, 7, 5 successively we have followings :
X=8*(5*7C+19)+5
5*7C+19=7*(5C+2) + 5
5C+2=5C+2.
The remainders are, therefore, 5, 5, 2.
The answer is (D).
Answer: (D) R=5, 5, 2
Question: If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is ?
(A) 1/25
(B) 1/20
(C) 1/27
(D) 1/26
(E) 1/212
Rationale: We have 1, 8, 27 and 64 as perfect cubes from 1 to 100.
Thus, the probability of picking a perfect cube is
4/100 = 1/25.
Answer: A
Answer: (A) 1/25
Question: An bus covers a certain distance at aspeed of 240 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 560 km/h
(B) 567 km/h
(C) 779 km/h
(D) 723 km/h
(E) 720 km/h
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
5
E
Answer: (E) 720 km/h
Question: A rectangular photograph is surrounded by a border that is 2 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 94) square inches. What is the perimeter of the photograph, in inches?
(A) 34
(B) 36
(C) 23
(D) 40
(E) 42
Rationale: Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)
According to the question:
(L+4)(B+4) = m ----(2)
and
(L+8)(B+8) = m + 94 ---------> (L+8)(B+8) - 94 = m ------(3)
Equating (2) and (3)
(L+4)(B+4) = (L+8)(B+8) - 94
LB + 4L + 4B + 16 = LB + 8L + 8B + 64 -94
Simplify
4L + 4B = 46 ------> 2(L+B) =23 (Check eq (1))
Answer is C
Answer: (C) 23
Question: How many integerskgreater than 100 and less than 1100 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Numbers will be like 102 => 201 = 102 + 99
203 => 302 = 103 + 99
so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit.
There will be ninet pairs of such numbers
for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.
Total = 9 *10 = 90 hence E.
Answer: (E) 90