divelab/Sys2Bench huggingface dataset:
Question: The probability of a team winning a match given Matt is playing the match is 0.65. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
Options:
A)0.8321
B)0.7
C)0.8571
D)0.7531
E)0.8387
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.65*80 = 52.
Out of 20 matches Matt does not play in, team wins 0.5*20 = 10.
So, out of 100 matches 52 + 10 = 62 are won.
It is known that the team has won the last match. Out of 62 matches won, Matt is in 52: 52/62 = 0.8387...
Answer: E.
Answer: E
Question: A dress on sale in a shop is marked at $X. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on thediscounted price. If a staff member buysthe dress what will she have to pay in terms of X?
Options:
A)0.560X
B)0.560X
C)0.765X
D)0.608X
E)0.895X
Rationale: If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85X = 0.765X
C
Answer: C
Question: A password consists of two letters of the alphabet followed by three digits chosen from 0 to 9. Repeats are allowed. How many different possible passwords are there?
Options:
A)492,804
B)650,000
C)676,000
D)1,757,600
E)757,600
Rationale: 26*26*10*10*10=676000
ANSWER:C
Answer: C
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer Q that must divide n is?
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer Q that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: B
Question: If 0 < x ≤ 6, then which one of the following is the maximum value of (x – 1)^2 + x ?
Options:
A)–2
B)–1
C)0
D)31
E)2
Rationale: the maximum value of (x – 1)^2 + x for 0 < x ≤ 6 is when x=6 --> (x – 1)^2 + x = 31
Answer: D.
Answer: D
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)16 sec
B)15 sec
C)48 sec
D)44 sec
E)21 sec
Rationale: Relative speed = 45 + 30
= 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500
= 1000 m.
Required time = 1000 * 6/125
= 48 sec.
Answer:C
Answer: C
Question: Machines P and Q are two different machines that make items in a factory. When Machine P works alone, it covers 15 items in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 15 items in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 15item?
Options:
A)m
B)n
C)15n/225-mn
D)m+n
E)m-n
Rationale: working rate p = 15/m ; working rate pq =( 1/p +1/q)* n =15 or mn/15 +n/q =15 0r n/q = 15-mn/15 = 225-mn/15
q = 15n/225-mn
C
Answer: C
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 9 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
Options:
A)25
B)32
C)36
D)48
E)67
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
9 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 56
b = 42
Number of freshmen who take Art = 42 + 20 + 5 = 67
Answer E
Answer: E
Question: A and B started business in partnership investing Rs. 18,000 and Rs. 16,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)A)7500
B)B)7389
C)C)7379
D)D)7453
E)E)7653
Rationale: A:B:C = (18000 * 24) : (16000 * 24) : (20000 * 18) = 18:16:15
B's share = 25000 *15/49 = Rs.7653
Answer: E
Answer: E
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 9% sugar. What percentage of the gallon is dye?
Options:
A) 6
B) 6.5
C) 7.2
D) 8
E) 24
Rationale: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/9
=> 4/5 = x/9 => x = 4*9/5 = 7.2.
Answer is C.
Answer: C
Question: City A to city B, Michael drove for 1 hour at 80 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)57
B)57.5
C)58.2
D)60
E)62
Rationale: The total distance is 1×80+3×60=240
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)=240/4=60
Answer : D
Answer: D
Question: If in a race of 80m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
Options:
A)20m
B)16m
C)11m
D)10m
E)15m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (80 * 5) / 25 = 16m
Hence, A beats B by 16m.
ANSWER B
Answer: B
Question: Kelsey travelled for 10 hours. He covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Kelsey?
Options:
A)583 km
B)400 km
C)670 km
D)360 km
E)234 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/25 + (x/2)/40 = 10 => x/50 + x/80
= 10 => (8x + 5x)/400 = 10 => x
= 400 km
Answer: B
Answer: B
Question: In how many ways can 6 boys and 3 girls sit around a table in such a way that no two girls sit together?
Options:
A)10000
B)14000
C)14400
D)18000
E)19000
Rationale: The 6 boys can be seated around a table in 5! Ways. In between them there are 6 places.
The 3 girls can be placed in the 6 places in 6P3 ways.
Therefore, Required number of ways= 5!* 6P3
=120*120
=14400
ANSWER:C
Answer: C
Question: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes $74000, what is their combined tax rate?
Options:
A)32%
B)34.4%
C)35%
D)35.6%
E)36.4%
Rationale: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 74000/128000 = 74/128 = 37/65 is a little above 1/2. Thus, our answer is just a little above 35.
Answer: D
Answer: D
Question: If two integers x,y (x>y) are selected from -3 to 4 (inclusive), how many cases are there?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: There are 8 integers from -3 to 4 inclusive.
8C2 = 28.
The answer is E.
Answer: E
Question: How many integers between 100 and 400 are there such that their unit digit is odd?
Options:
A)100
B)120
C)200
D)50
E)150
Rationale: 300 numbers between - 100 and 400
Out of which half would be even, half odd.
Number of odd unit digit number = 150.
correct option is E
Answer: E
Question: A ball is bought for Rs.400 and sold at a gain of 20% find its selling price
Options:
A)Rs.400/-
B)Rs.420/-
C)Rs.480/-
D)Rs.500/-
E)Rs.520/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
C)
Answer: C
Question: Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
Options:
A)2 kg
B)2.5 kg
C)2.4 kg
D)None of these
E)Cannot be determined
Rationale: Explanation :
Fresh grapes contains 10% pulp.
So, 20 kg fresh grapes contains 2kg pulp.
Dry grapes contain 80% pulp.
2kg pulp would contain 2/0.8 = 20/8 = 2.5 kg dry grapes.
Answer : B
Answer: B
Question: If "WATER" is given a code of 67, then what is the difference between "RIVER" and "LAKE"?
Options:
A)101
B)29
C)43
D)42
E)30
Rationale: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
RIVER: 72
LAKE: 29
Answer: C
Answer: C
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
II. xy^2 is an even negative integer
III. (y^2 ) is an odd negative integer
Options:
A)I only
B)II only
C)I
D)I and III
E)II and III
Rationale: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
3x - is always negative and odd
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always odd
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 ) is an odd negative integer
y can be 0 => III statement is not true
basing on above, only I statement will always be true
C
Answer: C
Question: Find large number from below question The difference of two numbers is 1200. On dividing the larger number by the smaller, we get 5 as quotient and the 4 as remainder
Options:
A)1234
B)1345
C)1456
D)1567
E)1499
Rationale: Let the smaller number be x. Then larger number = (x + 1200).
x + 1200 = 5x +4
4x = 1196
x = 299
Large number = 299+1200=1499
E
Answer: E
Question: Find 62976 ÷ ? = 123
Options:
A)412
B)502
C)512
D)522
E)None
Rationale: Answer
Let 62976/N = 123
Then N = 62976 / 123 = 512.
Option: C
Answer: C
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 1/3 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
Options:
A)16 2/3%
B)25%
C)33 1/3%
D)50%
E)66 2/3%
Rationale: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 1/3 *200X= 200/3X
%Change in 1995 from 1992 = [(400/3* X -200/3X) / (400/3 *X) ] *100 = 50%
Answer D
Answer: D
Question: The numerator of a fraction is 1 less than twice the denominator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
Options:
A)A)2/3
B)B)3/5
C)C)7/4
D)D)5/9
E)of these
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
n = 2d - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5(2d-1) + 5 = 4d + 4 => d = 4
n = 2d - 1 => n = 7
Hence the fraction is : 7/4
ANSWER:C
Answer: C
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 42, the how old is B?
Options:
A)16
B)9
C)8
D)11
E)10
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 42
⇒ 5x = 40
⇒ x = 8.
Hence, B's age = 2x = 16 years.
Answer: A
Answer: A
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)87 Kmph
B)68 Kmph
C)54 Kmph
D)15 Kmph
E)12 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: B
Question: Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and five times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket?
Options:
A)9
B)10
C)18
D)24
E)21
Rationale: E.
Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.
Total value = 15q(.05) + 3q(0.1) + .25q =1.3q
Given total value = 10.15
therefore, 1.3q=10.15 or q=8
Number of dimes = 3q or 24
Answer : D
Answer: D
Question: A train running at the speed of 40 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)120 metres
B)180 metres
C)324 metres
D)150 metres
E)100 meters
Rationale: Speed=40 x5/18m/sec=100/9	m/sec.
Length of the train = (Speed x Time).
Length of the train =	100/9 x 9m = 100 m.
ANSWER:E
Answer: E
Question: To reach her destination, Jeanette must drive 90 miles. If she drives 5 miles every 9 minutes, how much time will it take her to reach her destination?
Options:
A)2 hours and 2 minutes
B)2 hours and 42 minutes
C)2 hours and 10 minutes
D)2 hours and 12 minutes
E)2 hours and 15 minutes
Rationale: 9 minute for 5 miles how much for 90? minutes for 1(9/5) mile multiplied by 90 miles.
9*90/5= 162> 2 hours 42 min answer is B
Answer: B
Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 37, the mean is how much greater than the median?
Options:
A)6
B)1
C)2
D)4
E)7
Rationale: Mean = (x + x+2 + x+4 + x+7 + x+37)/5
=(5x+50)/5
=x+10
Median = x+4
Thus Mean - Median = x+10 - (x+4)
=6
Answer = A
Answer: A
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
Options:
A)1/2
B)2/3
C)3/5
D)3/7
E)4/9
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: A
Question: In how many different ways can the letters of the word ‘PROBE’ be arranged ?
Options:
A)120
B)130
C)150
D)110
E)160
Rationale: A
120
Required number of arrangements = 5! = 120
Answer: A
Question: Statement : Company X has marketed the product. Go ahead, purchase it if price and quality are your considerations.
Conclusions :
I. The product must be good in quality.
II. The price of product must be reasonable.
Options:
A) I only
B) II only
C) I and II only
D) I and III only
E) II and III only
Rationale: Explanation:
Both conclusions follow as per statement.
Option C
Answer: C
Question: If Nick gains 10 pounds, he will weigh 50% more than his brother. Currently, their combined weight is 340 pounds. What is Nick's current weight?
Options:
A)140
B)160
C)170
D)190
E)200
Rationale: Given: N+B = 340
N+10 = 1.5B
N+B = 340
Add 10 to both sides
(N+10) + B = 350
2.5B = 350
B = 140
N = 200
Correct answer is E
Answer: E
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Options:
A)233
B)877
C)100
D)286
E)181
Rationale: Explanation:
MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: C
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 250 more than A :
Options:
A)2348
B)7250
C)2767
D)1998
E)2771
Rationale: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 250
Total earning = \inline \frac{58xy}{100} = 7250
Answer: B) Rs.7250
Answer: B
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol?
Options:
A) 7/2
B) 5
C) 20/3
D) 100/19
E) 39/4
Rationale: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 24% of (100+x)
OR
20+x=(100+x)6/25
500+25x=600+6x
19x=100
x=100/19
Ans:D
Answer: D
Question: Area of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is:
Options:
A)2.5m
B)3.5m
C)1.5m
D)4.5m
E)5.5m
Rationale: 2(7.5+3.5)×h = 99
2(11)h = 99
22h = 99
h = 99/22 = 9/2 = 4.5 m
Answer is D.
Answer: D
Question: 3 OUT OF 2500 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
Options:
A)11/50
B)1/8
C)1/45
D)2/45
E)NONE OF THESE
Rationale: REQUIRED PERCENTAGE=(3/2500*100)%=1/8%
CORRECT OPTIONS: B
Answer: B
Question: How many multiples of 5 are there between 1 and 100 (both are inclusive)?
Options:
A)1.2
B)20.8
C)2.3
D)6.7
E)8.2
Rationale: the answer is (100-1)/5+1=20.8
Answer is B
Answer: B
Question: A truck covers the distance of 550 meters in 1 minute where as a bus covers a distance of 33kms in 45 minutes.Find the ratio of their speed?
Options:
A)3:1
B)4:3
C)5:2
D)3:4
E)2:2
Rationale: Formula: d=s*t
Ratio of speed=[(550/50)*(18/5)]:[33*(45*60)](1 minute=60 sec)
=(11*3):(11*4)
=33:44
=3:4
Ratio of speed in car and bus is 3:4
Answer: option D
Answer: D
Question: The area of a circular place is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 3/meter approximately.
Options:
A)Rs. 4233
B)Rs. 4350
C)Rs. 4457
D)Rs. 4670
E)Rs. 4756
Rationale: Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.
C
Answer: C
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
Options:
A)9179
B)3000
C)2997
D)2678
E)2682
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B
Answer: B
Question: As x increases from 111 to 112, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x
Options:
A)II only
B)I,II only
C)III only
D)I only
E)I,III only
Rationale: On Increasing the value of x from 111 to 112
I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit
II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)
III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)
Answer: B
Answer: B
Question: If the probability T of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
Options:
A)8/125
B)2/25
C)5/16
D)8/25
E)3/4
Rationale: 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
T= 5/16
Answer - C
Answer: C
Question: a father said to his son ,i was as old as your are at the present at the time of your birth. if the father's age is 38 years now. the son's age five years back was:
Options:
A)14
B)19
C)33
D)38
E)12
Rationale: son's age x years, then (38-x) = x
2x=38, x=19, therefore = son's age 5 years back (19-5)=14 years
correct answer(A)
Answer: A
Question: On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.15 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
Options:
A)0.027
B)0.386
C)0.417
D)0.657
E)0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.15
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.85 * 0.15 = 0.1275
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.85^2 * 0.15 = 0.1084
Total = 0.386
Ans B
Answer: B
Question: Three students appear at an examination of Mathematics. The probability of their success are 2/3, 1/4, 1/5 respectively. Find the probability of success of at least two.
Options:
A)17/60
B)2/50
C)3/40
D)13/50
E)14/60
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 2/3 x 1/4 x 4/5 + 1/4 x 1/5 x 1/3 + 2/3 x 1/5 x 3/4 + 2/3 x 1/4 x 1/5 = 17/60
ANSWER:A
Answer: A
Question: A train crosses a platform of 130 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)230
C)77
D)62
E)52
Rationale: Length of the train be â€˜Xâ€™
X + 130/15 = X + 250/20
4X + 520 = 3X + 750
X = 230m
Answer: B
Answer: B
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1:96
B)2:96
C)1:86
D)1:94
E)2:96
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer:A
Answer: A
Question: Two persons starting from the same place walk at a rate of 4kmph and 5.5kmph respectively. What time will they take to be 9km apart, if they walk in the same direction?
Options:
A)6 hrs
B)22 hrs
C)25 hrs
D)12 hrs
E)14 hrs
Rationale: The relative speed of the boys = 5.5kmph â€“ 4kmph
= 1.5 kmph
Distance between them is 9 km
Time= 9km / 1.5 kmph = 6 hrs
Answer : A.
Answer: A
Question: If 4a^4 − 41a^2 + 100 = 0, then what is the sum of the two greatest possible values of a ?
Options:
A)4
B)9/2
C)7
D)41/4
E)25
Rationale: just forget about the value of a^4 for the moment and let a^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so a^2 = 4 and 25/4
so a= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Answer: B
Question: Only a single rail track exists between stations A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south-bound passenger train S reaches
station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?
Options:
A)1 : 3
B)1 : 4
C)1 : 5
D)1 : 6
E)None of these
Rationale: Explanation :
If speed of N = 4, speed of S = 1.
=> Average speed = (2 X 4 x 1) / ( 4 + 1) = 1.6.
Because time available is 2/3, speed = 3/2.
Now Average speed = 2.4
Now speed of N = 8.
Speed of S = y.
=> (2 x 8 x y) / (8+y) = 2.4
=> y = 1.3
The required ratio is 1.3 : 8 i.e 1 : 6.
Answer : D
Answer: D
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 52, the dividend is:
Options:
A)5324
B)5334
C)6812
D)7356
E)7400
Rationale: Divisor = (5 * 52) = 260
= 10 * Quotient = Divisor
=> Quotient = 260/10 = 26
Dividend = (Divisor * Quotient) + Remainder
Dividend = (260 * 26) + 52 = 6812
C
Answer: C