mathewhe/aqua_rat huggingface dataset:
Question: If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A- B is also a odd number.
(A) 1 only.
(B) 2 only.
(C) 3 only.
(D) 1 and 3 only.
(E) 2 and 3. Only
Rationale: (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A x B is also a prime number. : Beats the property of primes, so false
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans E
Answer: (E) 2 and 3. Only
Question: The average of first 10 natural numbers is?
(A) 5.2
(B) 5.5
(C) 5.3
(D) 5.9
(E) 5.1
Rationale: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer:B
Answer: (B) 5.5
Question: The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?
(A) 17000
(B) 12000
(C) 19000
(D) 14000
(E) 18000
Rationale: For 2 years = (100(power 2)D)/R(power 2)
= (100(power 2) × 45)/(5 × 5) = (10000 × 45)/25 = Rs.18000/-
Answer is E.
Answer: (E) 18000
Question: A reduction of 30% in the price of oil enables a house wife to obtain 9 kgs more for Rs.1800, what is the reduced price for kg?
(A) Rs.55
(B) Rs.60
(C) Rs.65
(D) Rs.70
(E) Rs.75
Rationale: Explanation:
1800*(30/100) = 540 ---- 9
? ---- 1 => Rs.60
Answer: B
Answer: (B) Rs.60
Question: The speed at which a man can row a boat in still water is 15 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 110 meters?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 28
Rationale: The speed of the boat downstream = 15 + 3 = 18 km/hr
18 km/hr * 5/18 = 5 m/s
The time taken to cover 110 meters = 110/5 = 22 seconds.
The answer is B.
Answer: (B) 20
Question: The sum of three consecutive numbers is 102. The greatest among these three number is:
(A) 26
(B) 35
(C) 29
(D) 30
(E) 31
Rationale: Let the numbers be x, x + 1 and x + 2
Then,
x + (x + 1) + (x + 2) = 102
3x = 102
x = 33
Greatest number, (x + 2) = 35.
ANSWER:B
Answer: (B) 35
Question: If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions G represents the final price of the item?
(A) G=(10,000z + 100z(x – y) – xyz)/10,000
(B) G=(10,000z + 100z(y – x) – xyz)/10,000
(C) G=(100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: -A-
z=Original Price
x= MU
y=MD
New price with MU:
z(x/100+1)
New price with MD:
z[(x/100+1)(-y/100+1)]
Solvingâ€¦
=z[((x+100)/100)((-y+100)/100)]
=z(x100-xy+10000-100y)/10000
=(zx100-xyz+10000z-100yz)/10000 --> similar to A
Answer: (A) G=(10,000z + 100z(x – y) – xyz)/10,000
Question: A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
(A) 19/20
(B) 17/20
(C) 21/40
(D) 8/10
(E) 9/40
Rationale: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.
Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.
P(A) = (5/8) x (6/10) = 3/8.
P(B) = (3/8) x (4/10) = 3/20.
Hence, the required probability is P(A) + P(B) which is nothing but 21/40.
ANSWER:C
Answer: (C) 21/40
Question: If P is a prime number greater than 5, what is the remainder when P^2 is divided by 8.
(A) 4
(B) 3
(C) 2
(D) 1
(E) Cannot be determined
Rationale: Here is the algebraic approach..
these prime numbers are of teh form 6n+1 or 6n-1..
so P= 6n+1..
P^2=(6n+1)2=36n^2+12n+1
Now 36n^2+12n=4n(9n+3)
if n is even... 4n will be div by 8....
if n is odd.. 4n will be div by 4 and 9n+3 will become even and be div by 2,hence 4n*(9n+3) will be div by 4*2=8..
so in P^2=36n^2+12n+1 only 1 is left, Remainder = 1.
ANSWER:D
Answer: (D) 1
Question: Two cars were driven by C and B. They were 580 miles apart when they started driving towards each other.C's car had traveled at a speed of 20 miles per hour, 4 hours per day for 5 days when it had met B's car. If B had driven 3 hours per day for 5 days, what was B's speed in miles per hour?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: 1. At 20mph for 4 hours a day, then driver C was traveling 80 miles per day. When C met with B, C had already traveled 400 miles.
2. This means that driver B had traveled 580-400 = 180 miles upon meeting up with C. B traveled a total of 3 x 5 = 15 hours (3hrs/day for 5 days). 180 miles / 15 hours = 12mph
3. Answer E!
Answer: (E) 12
Question: If the price of a certain computer increased 30 percent from x dollars to 351 dollars, then 2x =
(A) 540
(B) 570
(C) 619
(D) 649
(E) 700
Rationale: Before Price increase Price = x
After 30% Price increase Price = x+(30/100)*x= 1.3x = 351 (Given)
i.e. x= 351/1.3 = $270
i.e. 2x = 2*270 = 540
Answer: option A
Answer: (A) 540
Question: A train 440 meters long is running with a speed of 55 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 40.58 sec
(B) 41.33 sec
(C) 42.33 sec
(D) 40 sec
(E) 44.33 sec
Rationale: D = 440 + 180 =620
S = 55 * 5/18 = 15.27778 mps
T = 620/15.27778 =40.58182 sec
ANSWER:A
Answer: (A) 40.58 sec
Question: Rahul take a loan of sum Rs.550.This is to be repaid in two equal annual installments. If the rate of interest be 20% compounded annually,then find the value of each installment?
(A) 360
(B) 420
(C) 230
(D) 540
(E) 610
Rationale: Let the value of each installment be Rs.x
[x/(1+(20/100))]+[x/(1+(20/100))2]=550
(100x/120)+(10000x/14400)=550
(5x/6)+(25x/36)=550
x=360
Option A
Answer: (A) 360
Question: Mr. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck
(A) $145
(B) $250
(C) $300
(D) $175
(E) $150
Rationale: Let the 1st paycheck be x(integer).Mr. Rodger got a weekly raise of $145. so after completing the 1st week she will get $ (x+145).similarly after completing the 2nd week she will get $(x+145)+$145.=$(x+145+145=$(x+290). so in this way end of every week her salary will increase by $145. correct answer will be (A)
Answer: (A) $145
Question: A person can row at 9 kmph and still water. He takes 5 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 32
(B) 28
(C) 29
(D) 24
(E) 20
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 5.5
=> x/10 + x/8 = 11/2 => (4x + 5x)/40 = 11/2 => x
= 24 km.
Answer:D
Answer: (D) 24
Question: In a kilometer race, A beats B by 60 meters or 15 seconds. What time does A take to complete the race?
(A) 221
(B) 235
(C) 245
(D) 289
(E) 260
Rationale: Time taken by B run 1000 meters = (1000 * 15)/60 = 250 sec.
Time taken by A = 250 - 15 = 235 sec.Answer:B
Answer: (B) 235
Question: How many positive integers less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72
Rationale: 210 = 2x5x3x7 = 5x6x7x1 = 5x6x7
Those are the only sets of digits we can use to for the numbers (any other combination of factors will have two digit factors).
Numbers using 2,5,3,7 = 4!
Numbers using 5,6,7,1 = 4!
Numbers using 5,6,7 (3-digit numbers) = 3!
Answer = 24+24+6 = 54
Answer is (D)
Answer: (D) 54
Question: How many multiples of 2 are there between 1 and 56, exclusive?
(A) 21
(B) 22
(C) 27
(D) 26
(E) 28
Rationale: 27
multiples of 2 between 1 and 56 exclusive.
from 2 * 1 upto 2*27, (1,2,3,4,...,27). Hence, 27 multiples !
correct option is C
Answer: (C) 27
Question: A Rent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
(A) 5%
(B) 7%
(C) 7.5%
(D) 10%
(E) None of these
Rationale: Answer: D
Answer: (D) 10%
Question: Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?
(A) 15
(B) 14
(C) 17
(D) 18
(E) 19
Rationale: In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.
ANSWER A
Answer: (A) 15
Question: The manufacturing cost of a shoe is Rs.210 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
(A) s 222
(B) s 216
(C) s 258
(D) s 210
(E) s 217
Rationale: Explanation :
Total cost of a watch = 210 + (500/100) = 215.
Gain = 20% => SP = 1.2CP = 1.2 X 215 = 258
Answer : C
Answer: (C) s 258
Question: suppose that 10 teams participated in a soccer tournament where each
team played exactly one game with each of the other teams. The winner
of each game received 3 points, while the loser received 0 points. In case
of a tie, both teams received 1 point. At the end of the tournament, the
10 teams received a total of 130 points. How many games ended in a tie?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: There were 45 games played in the tournament (10 2 )games.
Now, the total
number of points awarded in one game is either 3 (if one team wins), or 2 (when the
teams tie the game). So, the total number of points received is 3 × 45−(the number of
games ended in a tie). Thus, exactly 5 games ended in a tie.
correct answer E
Answer: (E) 5
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 33
(B) 77
(C) 18
(D) 99
(E) 66
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18.
Answer: C
Answer: (C) 18
Question: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 25, and 30 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
(A)  4/11
(B)  1/2
(C)  15/22
(D)  150/11
(E)  11/4
Rationale: P1 takes 12 hrs
Rate for P2P3 together = 1/25 + 1/30 = 11/150
Therefore they take 150/11
Ratio = 150/11 = D
Answer: (D)  150/11
Question: If x, y, and z are positive integers such that x^2 + y^2 + z^2 = 3460, which of the following could be the values of x, y, and z?
I. x=21,y=42,z=36
II.x=20,y=41,z=30
III.x=20,y=42,y=36
(A) I only
(B) II only
(C) III only
(D) I​ and II
(E) I and III
Rationale: 10 sec answer if you know how to find the units digit of a number
The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0
x = 20, so x^2 will have units digit 0
y = 42, so y^2 will have units digit 4
z = 36, so z^2 will have units digit 6
Calculate the units digit , the units digit will be 0
Test with options II and I, only option III will satisfy the condition , hence this will be our answer is option C.
Answer: (C) III only
Question: 20 men do a work in 20days. How many men are needed to finish the work in 10days?
(A) 50
(B) 20
(C) 30
(D) 10
(E) 40
Rationale: men required to finish the work in 10days = 20*20/10 = 40
Answer is E
Answer: (E) 40
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 7 1/2 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/9 sec
Rationale: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 1/2 sec
Answer: D
Answer: (D) 8 1/2 sec
Question: The sum of three consecutive even numbers is 36. Find the middle number of the three?
(A) 14
(B) 16
(C) 18
(D) 24
(E) 36
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 36
6P = 36 => P = 6.
The middle number is: 6P = 36.
ANSWER:E
Answer: (E) 36
Question: Tough and Tricky questions: Combinations.
six contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 7
(C) 18
(D) 16
(E) 24
Rationale: Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
We have 2 slots to be filled using 6 contestants:6 options for slot1*3 option for slot2
= 6* 3
= 18
Ans. C) 18
Answer: (C) 18
Question: Pipe A fills a tank of capacity 950 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?
(A) 57 minutes
(B) 14 minutes
(C) 39 minutes
(D) 40 minutes 20 seconds
(E) None of these
Rationale: In one cycle they fill 40+30-20 = 50 liters
950 = 50*n => n = 19
here n = number of cycles.
total time = 19*3 = 57 as in one cycle there are 3 minutes.
thus 57 minutes
ANSWER:A
Answer: (A) 57 minutes
Question: A certain college party is attended by both male and female students. The ratio of male to female students is 4 to 5. If 9 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 46
(B) 50
(C) 54
(D) 58
(E) 62
Rationale: The ratio is 4:5 = 8:10, so there are 8k males and 10k females.
If 9 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.
8k-5k = 9
k = 3
8k + 10k = 24 + 30 = 54
The answer is C.
Answer: (C) 54
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 15 kmph
(B) 11 kmph
(C) 88 kmph
(D) 18 kmph
(E) 12 kmph
Rationale: 90 * 10/60
= 15 kmph
Answer:A
Answer: (A) 15 kmph
Question: Robert's salary was decreased by 40% and subsequently increased by 40%. how much percentage does he lose?
(A) 16%
(B) 20%
(C) 25%
(D) 30%
(E) 50%
Rationale: let original salary be $100
Salary after decreasing 40% = 100 - 100 x 40/100 = $60
Salary after increasing 40% on $60 = 60 + 60 x 40/100 = $84
Percentage of loss = 100 - 84 = 16%
Answer : A
Answer: (A) 16%
Question: The average height of 12 girls out of a class of 20 is 161 cm. and that of the remaining girls is 158 cm. The average height of the whole class is :
(A) 142.3 cms
(B) 162.3 cms
(C) 160.5 cms
(D) 142.8 cms
(E) 159.8 cms
Rationale: Explanation:
Average height of the whole class =(12×161+8×158/20)=159.8 cms
Answer E
Answer: (E) 159.8 cms
Question: Tracy's mum gave her $64 to go shopping. She bought a jumper for $20, a T-shirt for $10, and a pair of shoes for $9. How much money does Tracy have left?
(A) $33
(B) $54
(C) $25
(D) $60
(E) $10
Rationale: Step 1: Find the total cost of the clothes.
$20 + $10 + $9 = $39
Step 2: Find the amount of money left.
$64 – $39 = $25
Tracy has $25 left.
Answer is C.
Answer: (C) $25
Question: Patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon. If she made no stops during the run and her average speed for the entire marathon was 5 mph, for what fraction of the total time did she run at 3 mph?
(A)  1/5
(B)  2/3
(C)  2/5
(D)  3/5
(E)  1/3
Rationale: We don't need to get into calculations for solving this question. We can use the concept of weighted averages.
We know that if the average speed for the entire marathon was 5 mph, she ran at 6 mph for a longer duration.
2 1
3--5----6
This shows that you can divide the entire journey in 3 equal parts. Thus, 2/3 part she ran at 6 mph and 1/3 part she ran at 3 mph.
Answer: E
Answer: (E)  1/3
Question: If 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
(A) 41
(B) 28
(C) 43
(D) 44
(E) 45
Rationale: n(n-1)/2 =8*7/2
=28
ANSWER:B
Answer: (B) 28
Question: We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value R of the ratio A/B?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 1/4
(E) 1/5
Rationale: R-> A/B=20*21*……*39/21*22*….*39*40=20/40=1/2.
Therefore, the answer is A.
Answer: (A) 1/2
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 7m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 54
(B) 32
(C) 75
(D) 28
(E) 11
Rationale: A/8 = 7 * 7 => A = 7 * 7 * 8
x * 2x = 7* 7 * 8
x = 14 => 2x = 28
Answer:D
Answer: (D) 28
Question: A train 150 meters long completely crosses a 320 meters long bridge in 40 seconds. What is the speed of the train is?
(A) 32
(B) 42
(C) 54
(D) 66
(E) 09
Rationale: S = (150 + 320)/40 = 470/40 * 18/5 = 42
Answer: B
Answer: (B) 42
Question: If x is a sum of all even integers on the interval 13...63 and y is their number, what is the GCD (x, y)?
(A)  1
(B)  13
(C)  26
(D) 25
(E)  1014
Rationale: x = 14 + 16 + ... + 62 = (largest + smallest)/2 *(# of terms) = (14 + 62)/2*25 = 38*25.
GCD of 25 and 39*25 is 25.
Answer: D.
Answer: (D) 25
Question: If 10power2y=25, the 10power-y equals:
(A) -1/5
(B) 1/625
(C) 1/50
(D) 1/25
(E) 1/5
Rationale: 10power2y=25, (10powerY)power2= 5power2, 10powerY= 5, 1/10powerY=1/5, 10power-Y=1/5, correct answer will be (E)
Answer: (E) 1/5
Question: The missing term in the sequence 2, 3, 5, 7, 11, ... 17, 19 is
(A) 11
(B) 13
(C) 15
(D) 17
(E) 18
Rationale: Sequence is contain prime numbers.
Final sequence : 2,3,5,7,11,13,17,19
ANSWER:B
Answer: (B) 13
Question: Two employees M and N are paid a total of Rs. 550 per week by their employer. If M is paid 120 percent of the sum paid to N, how much is N paid per week?
(A) Rs.220
(B) Rs.250
(C) Rs.280
(D) Rs.300
(E) Rs.320
Rationale: Let the amount paid to M per week = x
and the amount paid to N per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
B)
Answer: (B) Rs.250
Question: A grocer has 400 pounds of coffee in stock, 40 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
(A) 28%
(B) 30%
(C) 32%
(D) 34%
(E) 44%
Rationale: 1. 40% of 400=160 pounds of decaffeinated coffee
2. 60% of 100=60 pounds of decaffeinated coffee
3. Wt have 220 pounds of decaffeinated out of 500 pounds, that means 220/500*100%=44%. The correct answer is E.
Answer: (E) 44%
Question: A man can do a piece of work in 4 days, but with the help of his daughter, he can do it in 3 days. In what time can his daughter do it alone?
(A) 12
(B) 28
(C) 26
(D) 19
(E) 112
Rationale: Explanation:
Daughter’s 1 day’s work = (1/3 – 1/4) = 1/12
Daughter alone can do the work in 12/1 = 12 days
ANSWER: A
Answer: (A) 12
Question: Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999?
(A) 50,029
(B) 50,000
(C) 50,019
(D) 50,128
(E) 50,191
Rationale: Sekar: Rajeev: jatin = (25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's Share =Rs.(150000×2/6)
=Rs.50000.
Answer: B
Answer: (B) 50,000
Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 18 times as heavy as water?
(A) 1:2
(B) 3:2
(C) 9:1
(D) 5:2
(E) 6:5
Rationale: G = 19W
C = 9W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
19W+9Wx = x+1 * 18W
19+9x = 18(x+1)
x = 1/9
Ratio of gold with copper = 1:1/9 = 9:1
Answer is C
Answer: (C) 9:1
Question: What is the greatest positive integer x such that 3^x is a factor of 9^6?
(A) 5
(B) 12
(C) 10
(D) 20
(E) 30
Rationale: What is the greatest positive integer x such that 3^x is a factor of 9^6?
9^6 = (3^2)^6 = 3^12
B. 12
Answer: (B) 12
Question: In a certain country, 60 percent of the population likes basketball, and 31 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?
(A) 20%
(B) 33%
(C) 40%
(D) 52%
(E) 67%
Rationale: Correct Answer: (D).
Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 31 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 31/60 = 52%, or choice D.
Answer: (D) 52%
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 18. By how much do the two digits differ?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: we are given that if the integer N has its digits reversed the resulting integer differs from the original by 18. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original by 18 we can say:
10B + A – (10A + B) = 18
10B + A – 10A – B = 18
9B – 9A = 18
B – A = 2
Since B is the tens digit and A is the units digit, we can say that the digits differ by 2.
The answer is A.
Answer: (A) 2
Question: A young and energetic cobbler fixes 3650 pairs of shoes every year, while an old yet experienced cobbler fixes 20% less than the young cobbler. In a shoe factory there are two old and one young cobblers working together. How many shoes can the factory fix every day assuming that there are 365 days a year?
(A) 26.
(B) 34.
(C) 36.
(D) 44.
(E) 48
Rationale: Number of shoes/day the young cobbler fixes= 3650/365= 10
Number of shoes old cobbler fixes= 3650*80/100
Number of shoes 2 old cobbler fixes in one day= 2* 3650 *80/100 *1/365= 16
Total shoes fixed in one day= 10+16= 26
A is the answer
Answer: (A) 26.
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 150 m
(B) 200 m
(C) 170 m
(D) 100 m
(E) 250 m
Rationale: D
100 m
Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 200 - 100 = 100 m
Answer: (D) 100 m
Question: A train of length 250 m crosses a bridge of length 150m in 25 seconds. What is the speed of train?
(A) 57.6
(B) 27
(C) 25
(D) 22
(E) 72
Rationale: Sol : (length of train+ length of bridge) = speed of train x Time
(250+150) = 25 x Speed
Speed = 400/25= 16 m/s =57.6 km/h
ANSWER=A
Answer: (A) 57.6
Question: 30% of a number when subtracted from 91, gives the number itself. Find the number
(A) 60
(B) 65
(C) 75
(D) 70
(E) NONE
Rationale: Solution: Let the number be x
According to the question,
91 - (30x/100) = x
9100 - 30x = 100x
Or, 9100 = 130x
Or, x = 9100/130
Hence, x = 70.
Answer: Option D
Answer: (D) 70
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
(A) 11.11 km/hr
(B) 21.11 km/hr
(C) 71.11 km/hr
(D) 81.11 km/hr
(E) 41.11 km/hr
Rationale: Explanation:
Total time taken = (160/64 + 160/8)hrs
= 9/2 hrs.
Average speed = (320 x 2/9) km.hr
= 71.11 km/hr.
Answer: C
Answer: (C) 71.11 km/hr
Question: If the average of 10,11,12,13,14,15,16,17,18 and x is 23, what is the value of x?
(A) 90
(B) 89
(C) 123
(D) 104
(E) 110
Rationale: Given (10+11+12+13+14+15+16+17+18+x)/10=23
126+x/10=23
126+x=230
x=230-126
x=104
Answer is D
Answer: (D) 104