divelab/Sys2Bench huggingface dataset:
Question: At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes?
Options:
A)2150
B)2600
C)3120
D)1500
E)1895
Rationale: Winner votes = 100-30 = 70
polled votes = [(100*1000)/2*70-100]+100 = 2600
Answer is B
Answer: B
Question: A class has a ratio of 3:6:7 of children with red hair, blonde hair and black hair respectively. If the class has 9 kids with red hair, how many kids are in the class?
Options:
A)99
B)48
C)16
D)22
E)60
Rationale: Since there are 9 children with red hair, and the class exists in a 3:6:7 ratio, there are 3 times more children than the unit ratio. Therefore
9 red-haired children
3*(6) blonde-haired children
3*(7) black-haired children
9+18+21 = 48
Alternatively, a part-to-whole ratio can be set up. Since the whole is 3+6+7=16,
9/3=X/16
3*16=48
Answer: B)
Answer: B
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 400 that is both a prime and a palindrome. What is the sum of the digits of p?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Given that p is smallest integer greater than 400 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
A
Answer: A
Question: 300 liters of a mixture contains milk and water in the ratio 3:2 If 15 liters of this mixture be replaced by 15 liters of milk, the ratio of milk to water in the new mixture would be?
Options:
A)12:8
B)12:4
C)13:8
D)14:5
E)13:5
Rationale: Quantity of milk in 300 liters if mix = 300*3/5 =180 liters
Quantity of milk in 315liters of new mix = 180+15 = 195 liters
Quantity of water in it = 315-195 = 120 liters
Ratio of milk and water in new mix = 90:20 = 13:8
Answer isC
Answer: C
Question: 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
Options:
A)334
B)377
C)495
D)766
E)261
Rationale: Explanation:
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is \inline {\color{Black}12C_4{}} = 495.
Therefore, we can draw 495 quadrilaterals
Answer: C) 495
Answer: C
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was
Options:
A)three times as much
B)twice as much
C)the same
D)half as much
E)a third as much
Rationale: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: (B)
Answer: B
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
Options:
A)7/9
B)5/4
C)15/4
D)2/5
E)7/18
Rationale: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
Ans:E
Answer: E
Question: By weight, liquid X makes up 2 percent of solution P and 7.5 percent of solution Q. If 400 grams of solution P are mixed with 600 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution?
Options:
A)4.5%
B)4.7%
C)4.9%
D)5.1%
E)5.3%
Rationale: The number of grams of liquid X is 2(400)/100 + 7.5(600)/100 = 8 + 45 = 53 grams.
53 / 1000 = 5.3%
The answer is E.
Answer: E
Question: If (|p|!)^p=|p|!, which of the following could be the value(s) of p ?
Options:
A)-1
B)0
C)1
D)-1 and 1
E)-1, 0, and 1
Rationale: Test Values
A. -1 ==> |−1|−1=|−||! ==> 1/1=1 ==> -1 is valid
B. 0 ==> |0|!0=|0|! ==> 1^0 ==> 1=1 ==> 0 is valid
C. 1 ==> 1^1 ==> 1 is valid
D. -1 and 1
E. -1, 0, and 1
Answer:E
Answer: E
Question: The probability that a convenience store has no iced tea is 50%. If Karl is stopping by 4 convenience stores on his way to work, what is the probability thatat least oneof the stores will not have a can of iced tea?
Options:
A)1/8
B)1/4
C)1/2
D)3/4
E)15/16
Rationale: p=1-1/2^4(all stores have iced tea)=15/16
E
Answer: E
Question: A man gains 20% by selling an article at a certain price. If the sells it at double the price, the percentage of profit will be?
Options:
A)288%
B)882%
C)388%
D)140%
E)382%
Rationale: Let C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
Answer:D
Answer: D
Question: A rectangular circuit board is designed to have width w inches, perimeter p inches, and area M square inches. Which of the following equations must be true?
Options:
A)w^2 + pw + M = 0
B)w^2 - pw + 2M = 0
C)2w^2 + pw + 2M = 0
D)2w^2 - pw - 2M = 0
E)2w^2 - pw + 2M = 0
Rationale: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.
Now, assume:
Width =w = 1 inchand length = 1 inch;
Perimeter =p = 4 inches;
Area =M = 1 square inches.
Plug the values of w, p, and M into the answer choices: only for E 2w^2 - pw + 2M = 2 - 4 + 2 = 0.
Answer: E.
Answer: E
Question: In a factory, there are 30% technicians and 70% non-technicians. If the 30% of the technicians and 70% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
Options:
A)62%
B)57%
C)52%
D)22%
E)48%
Rationale: Total = 100
T= 30 NT= 70
30*(70/100)=21 70*(30/100)=21
21 + 21= 42 => 100 - 42 = 58%
Answer:E
Answer: E
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
Options:
A)1/5
B)3/4
C)3/7
D)3/5
E)3/7
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: B
Question: Find the percentage gain if a shop owner sells 40 mtr of fabric and gains Cost Price of 15 meters?
Options:
A)38.50%
B)39.50%
C)27.50%
D)37.50%
E)17.90%
Rationale: Let cost of each metre be Rs. 100.
Therefore, cost price of 15m cloth = 15*100 =1500
cost price of 40m cloth = 40*100 = 4000
Since the trader made the CP of 15m from the sale of 40m therefore
Profit on sale of 40m = cost price of 15 m cloth = 1500
Selling price of 40m = 4000+1500 = 5500
Profit % = 37.50%
D
Answer: D
Question: Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 40 feet across and 7 feet deep?
Options:
A)700
B)1500
C)3000
D)5000
E)9000
Rationale: Answer Should be E.
V= \pir^2h= \pi*20^2*7= approximately 9000
Answer: E
Question: Ramu bought an old car for Rs. 38000. He spent Rs. 12000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)17%
B)19%
C)18%
D)14%
E)29.8%
Rationale: Total CP = Rs. 38000 + Rs. 12000
= Rs. 50000 and SP
= Rs. 64900
Profit(%) = (64900 - 50000)/50000 * 100
= 29.8%
Answer: E
Answer: E
Question: In 1990 the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?
Options:
A) 1992
B) 1993
C) 1994
D) 1995
E) 1996
Rationale: Let the no of years it takes is x.
540+30x = 780-10x --> 40x = 240 and x=6.
Thus, it happens in 1996.
E.
Answer: E
Question: If s is the product of the integers from 30 to 40 inclusive, and if t is the product of the integers from 30 to 41 inclusive, what is 1/s + 1/t in terms of t?
Options:
A)40/t
B)42/t
C)38/t
D)36/t
E)34/t
Rationale: Similarly in the actual problem
s =t/41. 1/s = 1/(t/41) or 1/s = 41/t
1/s + 1/t = 41/t + 1/t = 42/t
B
Answer: B
Question: How many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph?
Options:
A)26
B)72
C)25
D)23
E)27
Rationale: Explanation:
D = 100 + 130 = 230
S = 36 * 5/18 = 10 mps
T = 230/10 = 23 sec
Answer: Option D
Answer: D
Question: Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed ?
Options:
A)1000
B)2430
C)3402
D)3006
E)None of these
Rationale: Explanation :
Let's check the number of ways for the first telephone number.
6 3 5 - - - -
a) 6 3 5 9 - - -
4 choices for last digit (1,3,5,7).
9 * 9 choices for 5th and 6th digits together.
So, 9 * 9 * 4 choices = 324 ways.
Similarly,
b.) 6 3 5 - 9 - - = 324 ways.
c.) 6 3 5 - - 9 - = 324 ways.
d.) 6 3 5 - - - 9 = 9 * 9 * 9 =729 ways.
Total= (324 + 324 + 324 + 729) = 1701.
It will be also the case with the phone number starting with 674.
Hence, the minimum number of trial required is 2 x 1701 = 3402.
Answer : C
Answer: C
Question: A contractor undertook to finish a job in 150 days and employed 200 men. After 50 days he found that only 1/4 of work was finished. How many extra days are needed if he employs 50 more men?
Options:
A)20
B)25
C)30
D)35
E)45
Rationale: work part A=25% and work part B= 75%
25% work done by 200 people in 50 days
if only one employee works then he takes 200*50=10000 days
and if work(B) is triple more ten he will take =10000*3 =30000 days
if employees are 250 then days = 30000/250=120days
then total days = 50+120 = 170 days
how many extra days taken = 170-150 = 20 days
ANSWER:A
Answer: A
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 4 : 2?
Options:
A)16
B)45
C)277
D)92
E)11
Rationale: Let the distances between city A to B and B to C be 4x km and 2x km respectively.
Total time taken to cover from A to C
= (4x)/40 + (2x)/60 = (4x + 12x)/120 = 16x/120 = 2x/15 Average speed = (4x + 2x)/(x/10) = 45 kmph.
Answer:B
Answer: B
Question: 14, 35, 56, 91, 126, 238
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?
Options:
A)161
B)250
C)322
D)686
E)847
Rationale: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7
clearly the answer is 250 because if we divide 250 by 7 we get a remainder of 1
Correct answer - B
Answer: B
Question: Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 789 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
Options:
A)1711
B)2209
C)2878
D)1210
E)1560
Rationale: As expected, this question boils down to 2 equation,
Consider total number of Balls in Triangle = T and number of balls in last row = x.
1+2+3+...+x = T
x(x+1)/2 = T ----(a)
As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+789)
(x-8)^2 = T+789 -----(b)
Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.
We can see that option A fits this criteria in eq (b). Add - 1711+789 = 2500 = 50^2 = (x-8)^2 Hence, x = 58.
Cross check by putting in eq (a) = x(x+1)/2 = T = > 58*59/2=1711
Hence, answer is A.
Answer: A
Question: The price of 5 kilograms of Wheat was $3 in 1995. In 2015, the price had increased to $5. What was the percent increase in the price of the 5 kilograms of Wheat?
Options:
A)66.6%
B)76.4%
C)67.7%
D)38.3%
E)78%
Rationale: Increase = 5 - 3 = 2
% increase = 2*100/3 = 66.6%
Answer: option A
Answer: A
Question: Joe invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 3 years and to $500 at the end of another 5 years. What was the rate of interest in which he invested his sum?
Options:
A)4.76%
B)5.88%
C)6.33%
D)7.75%
E)8.33%
Rationale: In 5 years, the value grew $100, so the simple interest was $20 per year.
In 3 years, the total interest was 3*$20 = $60
The principal is $400 - $60 = 340.
The interest rate is $20/$340 = 1/17 which is about 5.88%
The answer is B.
Answer: B
Question: Which of the following numbers is two more than the square of an odd integer?
Options:
A)14,173
B)14,361
C)15,627
D)15,737
E)15,981
Rationale: If a square has an odd unit's digit, then its ten's digit must be even.
Only 15,627-2 = 15,625 satisfies this condition.
The answer is C.
Answer: C
Question: In an exam, Bright scored 60 percent, Bivi scored 65 percent and Lisa 45 percent. The maximum score awarded in the exam is 900. Find the average mark scored by all the three boys?
Options:
A)490
B)530
C)520
D)500
E)510
Rationale: Average mark scored by all the three boys =
[60/100 (900) + 65/100 (900) + 45/100 (900)] / 3
(540+585+405)/3= 510
Answer: E
Answer: E
Question: What is value of (P + Q)/(P - Q) if P/Q = 7 ?
Options:
A)1/3
B)2/3
C)4/3
D)5/3
E)None of these
Rationale: Explanation:
(P + Q)/(P - Q) = (P/Q+1)/(P/Q - 1) = (7 +1)/(7 - 1) = 4/3.
Answer: C
Answer: C
Question: 97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?
I. At least 49 students’ score are equal to or more than 87.
II At least 49 students’ score are equal to or more than 85.
III. At most 49 students’ score are equal to or more than 85.
Options:
A)I
B)II
C)III
D)III
E)IIII
Rationale: If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.
The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions thatmustbe correct.
Answer B.
Answer: B
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.10000?
Options:
A)6620
B)3310
C)2776
D)2997
E)2718
Rationale: A = 10000(11/10)^3
= 13310
= 10000
----------
3310. Answer: B
Answer: B
Question: In a box of 9 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
Options:
A)3/10
B)4/11
C)5/12
D)6/13
E)7/15
Rationale: P(neither pen is defective) = 6/9*5/8 = 5/12
The answer is C.
Answer: C
Question: Light glows for every 32 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.
Options:
A)180 times
B)381 times
C)155 times
D)392 times
E)150 times
Rationale: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/32)=15582 times.
ANSWER:C
Answer: C
Question: If 30! × 30!/30^n is an integer, what is the largest possible value of n?
Options:
A)20
B)14
C)8
D)4
E)1
Rationale: 30! × 30!/30^n is an integer.
Or 30! × 30!/(3^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 30! = [30/5] + [30/25] = 7
Since there are 2 20!'s, power of 7 in the numerator = 2*7 = 14
Hence the largest value of b for which 30! × 30!/30^n is integer = 14
Correct Option : B
Answer: B
Question: While working alone at their constant rates, computer X can process 240 files in 8 hours, and computer Y can process 240 files in 6 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?
Options:
A)3
B)3.4
C)3.8
D)4
E)4.5
Rationale: Both computers together process files at a rate of 240/8 + 240/6 = 30+40 = 70 files per hour.
The time required to process 240 files is 240/70 which is about 3.4 hours
The answer is B.
Answer: B
Question: Evaluate :
28% of 400 + 45 % of 250
Options:
A)224.8
B)224.9
C)224.5
D)224.6
E)224.1
Rationale: Explanation:
28% of 400 + 45 % of 250
= (28/100 *400 + 45/100 * 250)
= (112 + 112.5)
= 224.5
ANSWER:C
Answer: C
Question: If r = 2^3 * 5^2 * 7 and s = 2^3 * 3^2 * 5^3, which of the following is equal to the greatest common divisor of r and s?
Options:
A)2 * 5
B)2^2 * 5
C)2^3 * 5^2
D)2*3*5*7
E)2^3 * 3^2 *5^2 * 7
Rationale: GCD = product of prime factors raised to the least power = 2^3 * 5^2
The answer is C.
Answer: C
Question: If the digit in the unit’s place of a two-digit number is halved and the digit in the ten’s place is doubled, the number thus, obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?
Options:
A)Digits in the unit’s place and the ten’s place are equal.
B)Sum of the digits is a two-digit number.
C)Digit in the unit’s place is half of the digit in the ten’s place.
D)Digit in the unit’s place is twice the digit in the ten’s place.
E)None of these
Rationale: Suppose the two-digit number is
10 x + y
Then, 10 y + x = 20x + y⁄2
or 20y + 2x = 40x + y or, y = 2x
Answer D
Answer: D
Question: Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5days extra by reading 10 pages a day less, how many days did Tom spend reading the book?
Options:
A)13
B)15
C)14
D)13.19
E)16
Rationale: Actually u can set up 2 equation
P--stands for the pages
D--stands for the days
1) P*D=480 (we want to find the Days, soP=480/D)
2) (P-10)(D+5)=480 => PD+5P-10D-50=480
as the 1) stated u can put 1) into 2)
=> 480+5P-10D-50=480 => 5P-10D=50
put the bold one into it => 5*480/D-10D=50
the we get the final equation 2400/D-10D=50
=> D^2+5D-240=0
(D-15)(D+10)=0 so D=13.19days. Ans: D
Answer: D
Question: On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 3 attempts?
Options:
A)3/4
B)5/8
C)7/8
D)9/16
E)15/16
Rationale: P(missing all 3)=(1/2)^3=1/8
P(success on at least one attempt)=1-1/8=7/8
The answer is C.
Answer: C
Question: A can do a piece of work in 40 days; B can do the same in 20 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Options:
A)24 days
B)60 days
C)86 days
D)40 days
E)17 days
Rationale: 10/40 + 10/20 + 10/x = 1
x = 40 days
Answer:D
Answer: D
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)12819
B)12800
C)12801
D)92801
E)12802
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
AnswerB
Answer: B
Question: A man engaged a servant on the condition that he would pay him Rs.500 and a uniform after one year service. He served only for 9 months and received uniform and Rs.250, find the price of the uniform?
Options:
A)s.80
B)s.85
C)s.90
D)s.500
E)s.120
Rationale: 9/12 = 3/4 * 500 = 375
250
-------------
125
1/4 -------- 125
1 --------- ? => Rs.500
ANSWER:D
Answer: D
Question: Last year, for every 100 million vehicles that travelled on a certain highway, 100 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
Options:
A)288
B)320
C)3,000
D)3,200
E)28,800
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 100 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. Creating a proportion we have:
100/100 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 100
x = 30 * 100 = 3,000
Correct answer is C.
Answer: C
Question: P and Q started a business investing Rs. 25,000 and Rs. 20,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)5:4
B)5:6
C)4:3
D)6:5
E)17:4
Rationale: P:Q = 25000 : 20000
= 5:4.
Answer:A
Answer: A
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 2x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 1.5x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
Options:
A)35.75
B)36
C)37
D)38
E)39
Rationale: James worked for 41 hours hence he earned 40*x+1*1.5x=41.5x dollars;
We know that Harry also earned the same 41.5x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 11.5x additional dollars. Since for each additional hour he gets 3x dollars then he worked for 11.5x/2x= 5.75 additional hours, so Harry worked for total of 30+5.75=35.75 hours.
Answer: A.
Answer: A
Question: Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture?
Options:
A)1 : 9
B)1 : 5
C)1 : 7
D)1 : 3
E)1 : 1
Rationale: Selling price of the mixture = 70 and profit = 20%
Cost price of the mixture = 70×100120=70×5670×100120=70×56
By applying alligation rule:
So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5
Answer:B
Answer: B
Question: A train 300 m long can cross an electric pole in 30 sec and then find the speed of the train?
Options:
A)76 Kmph
B)54 Kmph
C)72 Kmph
D)36 Kmph
E)91 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 300/30
S = 10 M/Sec
Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 36 Kmph
Answer: D
Answer: D
Question: Find the quotient when total no. Of divisors of 16! is divided by right most non-zero digit of 15!
Options:
A)672
B)682
C)692
D)745
E)845
Rationale: first find the factors of 16!
and then divide with non zero digit of 15!
factors of 16!
prime no below 16 are 2 3 5 7 11 13
now highest power of 2 in 16! is 15
3is 6,5 is 3,7 is 2,11,is 1,13 is 1
so no of factors is 16*7*4*3*2*2=5376
now last digit in 15!
it can be written as 2^11*3^6*5^3*7^2*11^1*13*1
5^3*2^3 gives 0 so remaining is 2^3 =8
therefore 5376/8=672
ANSWER:A
Answer: A
Question: The product of the digits of the four-digit number R is 36. No two digits of are identical. How many different numbers are possible values of R ?
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: The main question here is how can you arrange 4 different digits R. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C
Answer: C
Question: A deer takes 3 leaps for every 5 leaps of a fox. If one leap of the deer is equal to 3 leaps of the fox, the ratio of the speed of the deer to that of the fox is :
Options:
A)8:5
B)9:5
C)8:7
D)9:7
E)None of these
Rationale: Explanation :
Deer : Fox = (3*3) leaps of fox : 5 leaps of fox = 9 : 5.
Answer : B
Answer: B