divelab/Sys2Bench huggingface dataset:
Question: The difference between two angles of a triangle is 24o. The average of the same two angles is 54o. Which one of the following is the value of the greatest angle of the triangle
Options:
A)45o
B)45o
C)66o
D)72 degree
E)None of these
Rationale: Solution:
Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24o.
=> a – b = 24.
Since the average of the two angles is 54o, we have (a+b)/2 =54.
Solving for b in the first equation yields b=a–24, and substituting this into the second equation yields,
[{a+(a−24)}/2] =54
2a−24 = 54*2
2a−24 = 108
2a = 108 +24
2a =132
a =66
Also,
b=a−24=66−24=42.
Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is
180o, a+b+c =180.
Putting the previous results into the equation yields 66+42+c =180.
Solving for c yields c =72
Hence, the greatest of the three angles a, b and c is c, which equ
Answer: Option D
Answer: D
Question: Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B,
each at a constant rate of speed. Their first meeting is 90 miles from city A. After reaching their
respective destinations and immediately turning around, their second meeting is 30 miles from city B.
What is the distance in miles between city A and city B?
Options:
A)90
B)120
C)125
D)150
E)240
Rationale: let d=distance between cities A and B
bus 1 distance to first meeting=90 miles
bus 1 distance from first to second meeting=(d-90)+30=d-60 miles
bus 2 distance to first meeting=d-90 miles
bus 2 distance from first to second meeting=90+(d-30)=d+60 miles
because both buses take the same time for the pre-meeting leg, and
the same time for the inter-meeting leg, and their speeds remain
constant, their ratios between pre-meeting distance and inter-meeting
distance should be the same
therefore, 90/(d-60)=(d-90)/(d+60)
d^2=240d
d=240 miles
E
Answer: E
Question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 420 feet in circumference.After how many minutes are the three of them together again?
Options:
A)5 mins
B)10 mins
C)15 mins
D)3 mins
E)7 mins
Rationale: The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 7 mins.
E
Answer: E
Question: (0.66)(power 3) - (0.1)(power 3)/ (0.66)(power 2) + 0.066 + (0.1)(power 2) is:
Options:
A)0.86
B)0.56
C)0.96
D)0.69
E)0.76
Rationale: Given expression
= (0.66) (power 3) - (0.1)(power 3) / (0.66)(power 2) + (0.66 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.66 - 0.1)
= 0.56
Answer is B
Answer: B
Question: 144 choclates are distributed to children with the same number. What can’t be the range including the number of children?
Options:
A)1~10
B)50~60
C)20~30
D)10~20
E)70~80
Rationale: -> In 144=1*144=2*72=4*36=6*24=8*18=9*16, you can come up with 4 cases.
Amongst these cases, what is not included is B. 50~60. Therefore, the answer is B.
Answer: B
Question: Two friends A, B decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share 4 time, no apples were left.How many apples were there?
Options:
A)250
B)255
C)254
D)253
E)251
Rationale: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 8 times. So answer is (2^8)-1=255
ANSWER:E
Answer: E
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 0.25 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)0.09
C)0.417
D)0.578
E)0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.25
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.75 * 0.25 = 0.1875
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.75^2 * 0.25 = 0.1406
Total = 0.578
Ans D
Answer: D
Question: The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is :
Options:
A)15
B)16
C)18
D)20
E)None of these
Rationale: Let the larger number be x.
Then, x -12 = 20% of x<>x-(x/5)=12
4x/5=12<=> x=(12∗5)/5=15.
Answer :A
Answer: A
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 33 years, then find the age of the person sitting in the middle of the row?
Options:
A)9 years
B)22 years
C)18 years
D)19 years
E)17 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (33 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 33 * 3 = 196 - 75 - 99 = 22 years.
ANSWER:B
Answer: B
Question: One type of liquid contains 20% of water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of 1st liquid and 4 parts of 2nd liquid. The percentage of water in the new mixture in the glass is?
Options:
A)22.15%
B)23.5%
C)24.3%
D)25%
E)29.6%
Rationale: Required percentage = (20% of 10 + 35% of 4)/10+4 *100
= 3.4/14 * 100 = 24.3%
Answer is C
Answer: C
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
A)3100
B)210
C)21300
D)25200
E)24400
Rationale: Number of ways of selecting 3 consonants from 7 =7C3
Number of ways of selecting 2 vowels from 4 = 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
= 210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
=5! = 5*4*3*2*1 = 120
Hence, required number of ways=210×120=25200
option - D
Answer: D
Question: A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 450 bolts?
Options:
A) 36
B) 72
C) 120
D) 144
E) 108
Rationale: Old Machine
100 bolts in 60 mins
so,
5/3 bolts in 1 min
New Machine
150 bolts in 60 mins
so,
5/2 bolts in 1 min
together,
5/3 + 5/2 =
25/6 bolts in 1 min
so, for 450 bolts
450 * 6 / 25 = 108 mins
Ans E
Answer: E
Question: In a box, there are 9 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
Options:
A)2/3
B)8/21
C)3/7
D)9/22
E)10/21
Rationale: Explanation:
Total number of balls = (9 + 7 + 6) = 22
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 9/22.
Answer: Option D
Answer: D
Question: Two sides of a triangle have length 5 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24
Options:
A)I, II, and III
B)I and II only
C)II and III only
D)I and III only
E)I only
Rationale: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Answer: A
Question: The sum of first five prime numbers is:
Options:
A)11
B)18
C)26
D)28
E)35
Rationale: Explanation:
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
ANSWER IS D
Answer: D
Question: Mixture S is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture S, how many kilograms of mixture S must be added to make a 70% material B in the new mixture?
Options:
A)A)6
B)B)7
C)C)8
D)D)9
E)E)10
Rationale: Can be done with weighted avg method.
if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil .
S1=20(initial mix.)
Avg. is what we need..ie 70% of material B means 30% of oil
S2=36(36% of 10 kg mix)
w1/w2=(S2-Avg)/(Avg-S1)
(36-30)/(30-20)
6/10
means for every 10 kg of new mix. we need 6 kg of mix S
Ans A
Answer: A
Question: You collect baseball cards. Suppose you start out with 21. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
Options:
A)17
B)18
C)19
D)20
E)27
Rationale: Solution
Start with 21 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 21 + 1 which is 11,
so you're left with 21 - 11 = 10.
Peter takes 1 baseball card from you: 10 - 1 = 9 baseball cards.
Paul triples the number of baseball cards you have: 9 Ã— 3 = 27 baseball cards.
So you have 27 at the end.
Correct answer : E
Answer: E
Question: What number times (1⁄2)^2 will give the value of 2^3?
Options:
A)2
B)4
C)8
D)16
E)32
Rationale: x*(1/2)^2 = 2^3
x = 2^2*2^3 = 2^5 = 32
The answer is E.
Answer: E
Question: Randy'sbar serves customers every weeknight from 4 pm to 1 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?
Options:
A)Monday, 7:30 pm
B)Monday, 9 pm
C)Monday, 7 pm
D)Monday, 6:45 pm
E)Monday, 9:30 pm
Rationale: Let the keg be a 150 Litre keg
At 5 pm.. There are 75 litres
At 6:30 pm there are 50 litres.
So, consumption rate is 25 litres per 1.5 hours.
So it will take 3 hours to finish 50 litres at this rate.
During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.
So, keg becomes empty at 6:30 + 1 hour = 7 pm
Answer is C
Answer: C
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 55 meters. How many times did the ball bounce?
Options:
A)5
B)6
C)3
D)8
E)9
Rationale: Going down = 20 m
Going Up = 10 --> Total = 30
Going down = 10 --> Total = 40
Going Up = 5 --> Total = 45
Going down = 5 --> Total = 50
Going up = 2.5 --> Total = 52.5
Going down = 2.5 --> Total =55(Caught)
No of bouncing = 3
Answer : C
Answer: C
Question: The difference between the compound interest and simple interest accrued on an amount at the end of three years at the rate of 12% is Rs.381.888. What is the amount?
Options:
A)Rs. 9500
B)Rs. 8400
C)Rs.8500
D)Rs.8200
E)Rs.7200
Rationale: Explanation:
C.I = P[(1+R/100)T - 1]
= P[(1+12/100)3 - 1] = P[(28/25)3 - 1]
= P[(21952/15625) - 1]
= 6327P/15625
S.I = (P x 3 x 12)/100 = Rs. 9P/25
6327P/15625 - 9P/25 = 381.888
=> 702P/15625 = 381.888
=> P = (381.888 x 15625)/702
= Rs. 8500
Answer: Option C
Answer: C
Question: 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term Y of the sequence?
Options:
A)360
B)365
C)369
D)374
E)383
Rationale: First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term Y, t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Answer: D
Question: For all integers a and b, a%b = (a + b)(a - b). If 4%x = 7, then which of the following could be a value of x?
Options:
A)-4
B)-3
C)2
D)4
E)6
Rationale: 4%x = (4+x)(4-x)
16-x^2 = 7
x^2 = 9
x=-3,3
Ans: B
Answer: B
Question: A invested $400 in a business after 6 months B invested $200 in the business. End of the year if they got $100 as profit. Find A shares?
Options:
A)$100
B)$75
C)$20
D)$120
E)$80
Rationale: A:B = 400*12:200*6
A:B = 4:1
A's share = 100*4/5 = $80
Answer is E
Answer: E
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Options:
A)480
B)487
C)481
D)729
E)268
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer:A
Answer: A
Question: A full-time employee’s hourly wage was increased by 10%. He decided to decrease the number of hours worked per week so that his total income did not change. By approximately what percent should the number of hours worked be decreased?
Options:
A)7%
B)9%
C)25%
D)50%
E)100%
Rationale: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 10% wage increase, the employee makes $1.10/hour
We want the employee's income to remain at $100/week.
So, we want ($1.10/hour)(new # of hours) = $100
Divide both sides by 1.10 to get:
new # of hours = 100/1.10
≈ 90 hours
So, the number of hours decreases from 100 hours to (approximately) 90 hours.
This represents a 10% decrease (approximately) .
Answer choice B is the closest answer.
Answer: B
Question: A train passes a station platform in 37 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)248 m
B)240 m
C)277 m
D)255 m
E)176 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/37 = 15 ==> x + 300 = 555 ==> x
= 255 m.
Answer: D
Answer: D
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
Options:
A)55 kmph
B)45 kmph
C)54 kmph
D)35 kmph
E)65 kmph
Rationale: B
45 kmph
Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
Answer: A
Question: Double of Quarter of 2 percent written as a decimal is :
Options:
A)0.01
B)0.0005
C)0.25
D)0.005
E)None of these
Rationale: Explanation :
Solution: (2)*(1/4)*2% = 2*(1/4 * 2/100) = 0.01.
Answer : A
Answer: A
Question: A shopkeeper sells 200 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
Options:
A)12
B)27
C)29
D)55
E)95
Rationale: SP per metre = 18000/200 = Rs. 90 Loss per metre = Rs. 5 CP per metre = 90 + 5 = Rs. 95.Answer: E
Answer: E
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Options:
A)635.5
B)635.59
C)635.51
D)635.56
E)635.52
Rationale: Explanation:
4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer:A
Answer: A
Question: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 60 km more than the other. What is the distance between the two stations?
Options:
A)540 km
B)767 km
C)276 km
D)178 km
E)176 km
Rationale: Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 60 km more than the other,
25x – 20x = 60
5x = 60
x = 12 hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*12 = 540 km.
ANSWER: A
Answer: A
Question: John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount Q of dollars he could have spent for the $12 tickets?
Options:
A)$48
B)$60
C)$84
D)$96
E)$120
Rationale: 60 ..... 12 *5 Q= 60. (min). Thus answer .B
Answer: B
Question: If p^2 – 13p + 40 = s, and p is a positive integer between 1 and 10, inclusive, what is the probability that s < 0?
Options:
A)1/10
B)1/5
C)2/5
D)3/5
E)3/10
Rationale: p2 – 13p + 40 = s
so (p – 8)(p – 5) = s
For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
Answer: B
Question: Dacid obtained 61, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)29
B)72
C)39
D)37
E)75
Rationale: Average = (61 + 65 + 82 + 67 + 85)/5
= 72
Answer: B
Answer: B
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62 percent of those who attended the meeting were stockholders and 42 percent were employees, what percent were stockholders who were not employees?
Options:
A) 34%
B) 58%
C) 45%
D) 53%
E) 62%
Rationale: Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M
were stockholders and 42% of M or 0.42M were employees, it follows that 0.62M +
0.42M = 1.04M were either stockholders, employees, or both. Since 1.04M exceeds
M, the excess 1.04M − M = 0.04M must be the number of attendees who were both
stockholders and employees, leaving the rest 0.62M − 0.04M = 0.58M, or 58%, of
the meeting attendees to be stockholders but not employees.
The correct answer is B.
Answer: B
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is?
Options:
A)70 km/hr
B)75 km/hr
C)84 km/hr
D)87.5 km/hr
E)90.5 km/hr
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = [ 400/4] = 100
x = [100/8] = 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Answer is D
Answer: D
Question: John and David can finish a job together in 4 hours. If John can do the job by himself in 5 hours, what percent of the job does David do?
Options:
A)20%
B)25%
C)24%
D)23%
E)22%
Rationale: You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 20 donuts which is the job ( I picked this as a SMART number).
John on his own works 20/5 = 4 donuts per hour.
John and David work 20/4 = 5 donuts per hour so David works 1 donuts/hour
To find out the percentage, David works 1 donuts/hr x 4 hours = 4 donuts per hour.
Therefore 4 donuts/20donuts = 1/5 = 20%
Answer : A
Answer: A
Question: Mario and Nina each have a bag of marbles, each of which contains 18 blue marbles, 10 red marbles, and 12 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?
Options:
A)3/4
B)2/4
C)1/4
D)1/8
E)1/16
Rationale: Mario and Nina each select one marble from their respective bags.
Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble
Probability that either Mario or Nina select a red marble = (10/40)*(10/40) + (10/40)*(10/40) = 2*(1/16)
Probability that either Mario or Nina select a red marble = 1/8
Answer would be D.
Answer: D
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
Options:
A)5%
B)10%
C)15%
D)20%
E)25%
Rationale: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Answer: B
Question: Solve below Sequence problem ?
7, 8, 10, 12, 16, 18 ?
Options:
A)22
B)18
C)29
D)32
E)52
Rationale: A
22
Its is sequence of prime numbers and adding 5 to theb number
As we know, 1st seven Prime numbers are :
2 , 3 , 5 , 7 , 11 , 13 , 17
Adding 5 to each number =>
7 , 8 , 10 , 12 , 16 , 18 , 22(Ans)
Answer: A
Question: The average of first six multiples of 4 is :
Options:
A)14
B)9
C)12
D)15
E)17
Rationale: Solution
Average = 4(1+2+3+4+5+6)/6 =84/6 =14 Answer A
Answer: A
Question: Month	Average Price
per Dozen
April $1.10
May $1.20
June $1.08
The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
Options:
A)1.12
B)1.16
C)1.17
D)1.18
E)1.19
Rationale: Say x dozen eggs were sold in May.
Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.
Total x+2x/3+4x/3=3x dozen eggs were sold in three months.
Total sales: 2x/3*1.1+x*1.2+4x/3*1.08=$3.373x. The average price per dozen 3.37x/3x=$1.124.
A
Answer: A
Question: A 12% stock yielding 10% is quoted at:
Options:
A)Rs. 83.33
B)Rs. 110
C)Rs. 112
D)Rs. 120
E)Rs. 130
Rationale: Let the Face value of the stock:Rs.100
Yield=Rs.12
Market value quoted at (12/10)*100=Rs.120
ANSWER:D
Answer: D
Question: A train 180 m long running at 70 kmph crosses a platform in 20 sec. What is the length of the platform?
Options:
A)208
B)277
C)350
D)881
E)271
Rationale: D = 70 * 5/18 = 20 = 388 – 180 = 208
Answer: A
Answer: A
Question: The following questions are based on the information given. Choose the appropriate answer that suits the question based on the information. A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then colored red on the two larger faces and green on remaining. While the other is colored green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up. 21. How many cubes have only one colored face each?
Options:
A)32
B)8
C)16
D)24
E)0
Rationale: 16 =2^3 each cube will have 2^3 cubes painted 1 side.
ANSWER:C
Answer: C
Question: What least number should be subtracted from 1,439 so that the remainder when divided by 5, 11, and 13 will leave in each case the same remainder 3 ?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The LCM of 5, 11, and 13 is 715. The next multiple is 2*715 = 1,430.
1,430 + {remainder} = 1,430 +3 = 1,433, which is 6 less than 1,439.
Answer: E.
Answer: E
Question: If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?
Options:
A)5:12
B)7:12
C)3:11
D)5:11
E)None of these
Rationale: Explanation:
a/d = (3/4)*(7/9)*(5/7) => 5/12
Answer is A
Answer: A
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)10
B)99
C)787
D)62
E)22
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer: A
Answer: A
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age five years back was?
Options:
A)17years
B)18years
C)19years
D)20years
E)21years
Rationale: Let the son's present age be x years. Then, (44 - x) = x
2x = 44.
x = 22.
Son's age 5 years back (22 - 5) = 17 years.
A)
Answer: A