divelab/Sys2Bench huggingface dataset:
Question: A fellow borrowed a certain sum of money at 8% per annum at simple interest and in 8 years the interest amounted to Rs.900 less than the sum lent. What was the sum lent?
Options:
A)1050
B)1220
C)2500
D)1060
E)1110
Rationale: P - 900 = (P*8*8)/100
P = 2500
Answer: C
Answer: C
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What isthe probability that first is white and second is black?
Options:
A)31/111
B)36/145
C)21/115
D)11/154
E)None of these
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: B
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
Options:
A)1/3
B)2/3
C)2/5
D)2/7
E)2/9
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: C
Question: A math teacher has 26 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 26 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 26 - 17 = 9
Answer (A)
Answer: A
Question: Sunanth is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Options:
A)20 years
B)23 years
C)21 years
D)22 years
E)24 years
Rationale: Let present age of the son =c years
Then, present age of the sunanth =(c+22) years
Given that, in 2 years, sunanth's age will be twice the age of his son
=>(c+22)+2=2(c+2)
=>x=20
ANSWER:A
Answer: A
Question: A constructor estimates that 3 people can paint Mr. Gokhle's house in 10 days. If he uses 5 people instead of 3,how long will they take to complete the job?
Options:
A)6
B)5
C)10
D)5
E)4
Rationale: Explanation:
Use formula For a work Members Ã— days = constant
3 Ã— 10 = 5Ã— a
a = 6
so answer is 6days
Answer:A
Answer: A
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options:
A)A) 6.24
B)B) 4.1
C)C) 10
D)D) 15
E)E) 24
Rationale: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/40 = 10*3/2 = 15
Time difference = 4.1
Ans:B
Answer: B
Question: Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?
Options:
A)37.5 mph
B)40 mph
C)50 mph
D)44 mph
E)None of these
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by Jim = Distance covered in the first 3 hours + Distance covered in the next 5 hours.
Distance covered in the first 3 hours = 3×60=180 miles
Distance covered in the next 5 hours= 5×24=120 miles
Therefore, total distance travelled = 180+120=300 miles.
The total time taken = 3+5=8 hours.
Hence, the average speed = 300/8= 37.5 mph.
Answer : A
Answer: A
Question: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 18 members of this sequence?
Options:
A)878
B)900
C)788
D)810
E)1022
Rationale: I would split them up like this.
23 28 33 and so on (9 terms)....the 10th term = 23+8*5 = 63
27 32 37 and so on (9 terms)......the 9th term = 27+8*5 = 67
Since the distance between any two numbers is the same we can use arithmetics
first+last/2 times no of numbers = the sum
(23+63)/2 * 9= 387
(27+67)/2 * 9 = 423
= 810
D
Answer: D
Question: If A = 2B+1 where A is an Integer then which of the following is true?
Options:
A)A is always Odd
B)A is always Even
C)A is a non multiple of 2
D)A is even if B is a non integer and a multiple of 0.5
E)A=1
Rationale: D
Answer: D
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
Options:
A)Rs.81.60
B)Rs.160
C)Rs.172
D)Rs.727
E)Rs.728
Rationale: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer:A
Answer: A
Question: . A man pays off 3/20 of his debt every month.At the end of 6 months, his remaining debt is $A.How much amount has he cleared off every month?
Options:
A)3A/20
B)9A/10
C)A/10
D)3A/10
E)3A/2
Rationale: Let his total debt be T
Every month he pays off 3/20 of his debt = 3/20∗T3/20∗T
After 6 months he would have paid = 3/20∗6∗T3/20∗6∗T
His remaining debt after 6 months is A.
Hence Total debt = Remaining debt + Paid debt
T=A+3/20∗6∗TT=A+3/20∗6∗T
T−18/20∗T=AT−18/20∗T=A
T∗2/20=AT∗2/20=A
T=10AT=10A
Every month he pays off 3/20 of his debt = 3/20∗T=3/20∗10A=3A/2
Answer : E
Answer: E
Question: Which of the options is a multiple of 3!+6
Options:
A)4!-12
B)4!+2
C)4!-2
D)3!+20
E)4!+20
Rationale: When expanded 3!+6 equal (3*2) +6
Therefore (3*2) +6=6+6=12
Looking at the options the only one that gives a multiple of 12 is option A)
Answer: A
Question: The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
Options:
A)50
B)60
C)None of these
D)70
E)100
Rationale: C
100
2C + 3T = 1300 --- (1)
3C + 3T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T - C = 100
Answer: C
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
Options:
A)24007
B)24000
C)24028
D)240011
E)240121
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer:B
Answer: B
Question: The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ?
Options:
A)4.5
B)4.2
C)4.7
D)4.8
E)None of these
Rationale: solution:
Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)]
=23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4.
∴ Required average =8.4/2 = 4.2 Answer B
Answer: B
Question: If x/2 years ago Roger was 18 years old and x/2 years from now he will be 4x years old, how old will he be 5x years from now?
Options:
A)32
B)35
C)30
D)51
E)28
Rationale: Assume the current age = a
a - x/2 = 18 (i)
a + x/2 = 4x
Or a = 7x/2 (ii)
Putting the value of a from (ii) in (i)
7x/2 - x/2 = 18
Or 6x/2 = 18 Therefore x = 6 and a = 21
5x years from now, age will be 21 + 5*6 = 51
Option D
Answer: D
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Options:
A)224km
B)233km
C)277km
D)256km
E)297km
Rationale: distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x
Distance covered in the the second half = 24(10 - x)
But distance covered in the the first half = Distance covered in the the second half
=> 21x = 24(10 - x)
=> 21x = 240 - 24x
=> 45x = 240
=> 9x = 48
=> 3x = 16
⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km
Answer :A
Answer: A
Question: For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <3>*<4>?
Options:
A) 60
B) 116
C) 710
D) 756
E) 478
Rationale: Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.
Hence <3> is the sum of all integers from 1 to 2*3=6 and <4> is the sum of all integers from 1 to 2*4=8--> <3>=21 and <4>=36 --> <3>*<4>=21*36=756.
Answer: D
Answer: D
Question: The average age of an adult class is 40years. 12new students with an avg age of 32years join the class. Therefore decreasing theaverage by 4year. Find what was theoriginal strength of class?
Options:
A)11
B)12
C)17
D)19
E)21
Rationale: Let original strength = y
Then , 40y + 12 x 32 = ( y + 12) x 36
⇒ 40y + 384 = 36y + 432
⇒ 4y = 48
∴ y = 12
B
Answer: B
Question: A company has $329,864 in its account. What is the least amount of money (in whole number of dollars) that it must add to the account if the money is paid evenly among 9 of its vendors?
Options:
A)$1
B)$2
C)$3
D)$4
E)$6
Rationale: To find the least amount that must be added to the Account to split the money evenly among 9 of its vendors,
the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: D
Question: A beekeeper has 600,000 bees living in four beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
Options:
A)20,000
B)176470
C)10000
D)13000
E)56600
Rationale: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+3*(0.8)*x = 600,000 => 3.4x = 600,000 => x = 176470.
B is the answer.
Answer: B
Question: The cross section of a canal is a trapezium in shape. If the canal is 7 metres wide at the top and 9 metres at the bottom and the area of cross-section is 1280 square metres, find the length of the canal.
Options:
A)160 metres
B)172 metres
C)154 metres
D)165 metres
E)None of these
Rationale: None of these
Let the length of canal = h m.
Then,area of canal = 1⁄2 × h(9 + 7)
or 1280 = 1⁄2h(16)
∴ h = 1280×2/16=160m
Answer A
Answer: A
Question: If n is a positive integer, which one of the following numbers must have a remainder of 1 when
divided by any of the numbers 4, 5, and 6?
Options:
A)125n + 1
B)240n + 1
C)275n + 1
D)290n + 1
E)320n + 1
Rationale: The numbers 4, 5, and 6 all divide 240 so they all divide 240n.
When we divide (240n + 1) by 4, 5, or 6, the remainder must be 1.
The answer is B.
Answer: B
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5?
Options:
A)10
B)20
C)34
D)54
E)28
Rationale: Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5 = 20.
Answer:B
Answer: B
Question: A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
Options:
A)90
B)106
C)110
D)120
E)130
Rationale: sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C
Answer: C
Question: In the manufacture of a certain product, 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
Options:
A)0.125%
B)0.32%
C)0.8%
D)1.25%
E)2.0%
Rationale: Percent of defective produced = 8%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(8/100)*100%
= (32/10000)*100%
= (32/100)%
= .32 %
Answer B
Answer: B
Question: If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability Q that N is divisible by 3?
Options:
A)1/3
B)¼
C)9/25
D)5/16
E)0
Rationale: Prime digits are : 2, 3, 5, 7
Total number of 2 digit #s with both digits prime are: 4*4 = 16
out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.
=> prob = 5/16.
Ans D. Took me 3:20 mins.
Answer: D
Question: Find the constant k so that : -x2 - (k + 9)x - 8 = -(x - 2)(x - 4)
Options:
A)11
B)12
C)15
D)14
E)19
Rationale: -x2 - (k + 9)x - 8 = -(x - 2)(x - 4) : given
-x2 - (k + 9)x - 8 = -x2 + 6x - 8
-(k + 9) = 6 : two polynomials are equal if their corresponding coefficients are equal.
k = -15 : solve the above for k
correct answer C
Answer: C
Question: A train running at the speed of 48 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)286
B)120
C)255
D)150
E)287
Rationale: Speed=(48 * 5/18) m/sec = (40/3) m/sec Length of the train
= (Speed x Time) = (40/3 * 9) m
= 120 m.
Answer:B
Answer: B
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 45% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
Options:
A) 5%
B) 10%
C) 15%
D) 35%
E) 30%
Rationale: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 60 + 50 + 45 - n (Exactly 2 products) - 2*10
100 = 135 - n (Exactly 2 products) => n (Exactly 2 products) = 35.
Answer: D
Answer: D
Question: Calculate the time it will take for a train that is 250 meter long to pass a bridge of 150 meter length, if the speed of the train is 35 km/hour ?
Options:
A)56 seconds
B)3515 seconds
C)41.15 seconds
D)30 seconds
E)36 seconds
Rationale: Speed = 35 Km/hr = 35*(5/18) m/sec = 9.72 m/sec
Total distance = 250+150 = 400 meter
Time = Distance/speed
= 400 * (1/9.72) = 41.15 seconds
Answer: C
Answer: C
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 20 different models of televisions, what is the minimum number of letters that must be used to make the codes?
Options:
A)5
B)7
C)8
D)9
E)10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥20. The smallest n which fulfills this condition is n = 5.
Answer A
Answer: A
Question: what is the smallest number by which 3600 be divided to make it a perfect cube ?
Options:
A)9
B)50
C)300
D)450
E)550
Rationale: Solution
3600 = 23 * 52 * 32 * 2.
to make it a perfect cube, it must be divided by 52 * 32 * 2 i.e., 450 .
Answer D
Answer: D
Question: A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.4
C)1.2
D)1.5
E)3
Rationale: M = 9
S = x
DS = 9 + x
US = 9 + x
9 + x = (9 - x)2
9 + x = 18 -2x
3x = 9
x = 3
Answer: E
Answer: E
Question: If p and q are prime numbers, how many divisors does the product p^4 * q^5 have?
Options:
A)30
B)40
C)45
D)50
E)56
Rationale: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)
Therefore, the answer is A. 5*6=30
Answer: A
Question: Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 61.3 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
Options:
A)0.08
B)1.0
C)1.1
D)10.5
E)1.4
Rationale: Change in production of motor vehicles = 61.3 - 3.9 = 57.4 million in 41 years (1987 - 1946)
average increase per year = 57.4/41 = 1.4 million (apporx.)
Answer (E)
Answer: E
Question: Two pipes can fill a tank in 14 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
Options:
A)5.5 Hours
B)7.5 Hours
C)8.5 Hours
D)9.5 Hours
E)6.5 Hours
Rationale: In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19
So fill tank fill up in 19/2= 9.5 Hours
ANSWER:D
Answer: D
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 10 minutes?
Options:
A)40
B)100
C)150
D)240
E)300
Rationale: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 10 minutes the population increases by 10 x 4 = 40 people.
Answer. A.
Answer: A
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
Options:
A)1.5
B)2.4
C)3.6
D)4.0
E)4.6
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E
Answer: E
Question: remy bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?
Options:
A)50RW/Q
B)50QR/W.
C)25RQ/W
D)25RW/Q
E)RW/(4Q)
Rationale: Cost of 1 steaks = W/2Q dollars or 100W/2Q cents
Cost of R steaks at no discount = 100RW/2Q = 50RW/Q
Cost of R steaks at 50% discount = 1/2 * 50RW/Q = 25RW/Q
Hence, answer will be D.
Answer: D
Question: In what ratio P:Q should the Mixture P of milk and water in the ratio of 4:1 be mixed with another Mixture Q of milk and water in the ratio 2:3 so that the resultant mixture contains equal quantities of milk and water?
Options:
A)1:3
B)2:3
C)1:4
D)3:4
E)3:5
Rationale: (4/5)*P +(2/5)*Q = (1/5)*P+(3/5)*Q
3P=Q
P/Q = 1/3
The answer is A.
Answer: A
Question: In how many ways the letters of the word RAIMBON be arranged?
Options:
A)6468
B)9667
C)5040
D)9865
E)4687
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
C)
Answer: C
Question: For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6, -5 ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Given sequence: {1, -3, 2, 5, -4, -6}
The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.
So there are 4 pairs of consecutive terms of the sequence for which the product is negative.
Answer: D.
Answer: D
Question: A student can select one of 6 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
Options:
A)22
B)72
C)99
D)37
E)01
Rationale: 6C1×3C1×4C16C1×3C1×4C1 = 6x3x4=72 ways
Answer:B
Answer: B
Question: A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.
Options:
A)6,18,6
B)6,18,0
C)6,18,7
D)6,18,2
E)6,18,1
Rationale: Explanation:
Let breadth = x metres, length = 3x metres, height = H metres.
Area of the floor=(Total cost of carpeting)/(Rate) = (270/5)= 54
So, breadth = 6 m and length = = 9 m.
Now, papered area = (1720/10) = 172
Area of 1 door and 2 windows = 8
Total area of 4 walls = (172 + 8) = 180
Answer: A) b=6;l=18;H=6
Answer: A
Question: A man taking the census walks up to the apartment of a mathematician and asks him if he has any children and how old they are. The mathematician says "I have three daughters and the product of their ages is 72." The man tells the mathematician that he needs more information, so the mathematician tells him "The sum of their ages is equal to our apartment number." The man still needs more information so the mathematician tells him "My oldest daughter has her own bed and the other two share bunk beds."
How old are his daughters?
Options:
A)5-2-3
B)6-4-4
C)9-5-4
D)8-3-3
E)7-2-2
Rationale: His daughters are 8, 3, and 3. The prime factorization of 72 is 2 * 2 * 2 * 3 * 3, so the possible ages are 2, 3, 4, 6, 8, 9, 12, and 18. Using the prime factorization and these numbers the only combinations of numbers that work for the first clue are:
18, 2 and 2.
9, 4 and 2.
6, 6 and 2.
6, 4 and 3.
8, 3, and 3.
Since he doesn't know the ages after this piece of information the sum of the three numbers must not be unique. The sum of 8, 3, and 3; and 6, 6, and 2 are the same. Now the final clue comes in handy. Since we know that the oldest daughter has her own bed it is likely that she has the bed to herself and is older than the other two so there ages are 8, 3, and 3 rather than 2, 6 and 6.
Answer: D
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Options:
A)1.04
B)2.04
C)3.04
D)4.04
E)None of these
Rationale: Explanation:
100 cm is read as 102 cm.
A1 =(100 × 100)cm2 and A2= (102 × 102)cm2
(A2 - A1) = [1022 - 1002]
= (102 + 100) x (102 - 100) = 404 cm2 Answer: D
Answer: D
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
Options:
A)81 min
B)108 min
C)144 min
D)192 min
E)120 min
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
ANSWER:C
Answer: C
Question: If Finn was 16 months old one year ago, how old was he, in months, x months ago?
Options:
A)x − 30
B)x − 12
C)28 − x
D)24 − x
E)30 − x
Rationale: Age Today = 16 months + 12 months (1year) = 28 months
X months ago- Today's Age - X = 28 - X
Ans- C
Answer: C
Question: On the xy co-ordinate plane, point C is (5,-2) and point D is (-2,2.5). The point on line segment CD that is twice as far from C as from D is:
Options:
A)(1,-1)
B)(1,1)
C)(2,0.25)
D)(3,-0.5)
E)(3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,-0.5)
Answer: D
Answer: D
Question: Two bullet train s 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Options:
A)15.8 sec.
B)12.8 sec.
C)11.8 sec.
D)10.8 sec.
E)08.8 sec.
Rationale: D
10.8 sec.
Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = 300x9/250 = 54/5 = 10.8 sec.
Answer: D