divelab/Sys2Bench huggingface dataset:
Question: A standard Veggiematik machine can chop 40 carrots in 4 minutes. How many carrots can 4 standard Veggiematik machines chop in 5 minutes?
Options:
A)50
B)100
C)150
D)200
E)250
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 40 Carrots - 4 minutes,
1 standard Veggiematik machine - 10 Carrots - 1 minute,
Now
4 standard Veggiematik machine - ? Carrots - 5 minutes,
Hence = 10X4X5 =200 Carrots
Answer D
Answer: D
Question: {10,9,3,4,2}
Of the following value which value should be inserted in the set of 5 values to get a median of 4?
Options:
A)3
B)5
C)6
D)8
E)7
Rationale: Median is the middle number of a sorted distribution. In case of even number of items, Median will be the average of middle two values.
The question asks fora new number that will cause the median of new set at 4.
Mentionable that given set is already sorted and number of items of new set will be 5+1 = 6.
To get median 4,the sum of 3th4th Term should be 8.
So to keep the median 4,the new item should be >=5.
The answer is B
Answer: B
Question: Set A contains three different positive odd integers and five different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?
Options:
A)3/5
B)7/10
C)11/20
D)17/20
E)33/40
Rationale: There can be an odd product only if both integers are odd.
P(odd product) = 3/8*2/5 = 3/20
P(even product) = 1 - 3/20 = 17/20
The answer is D.
Answer: D
Question: Right triangle XYZs the base of the prism in the figure above. If XY=XZ=âˆš9 and the height of the prism is 6, what is the volume of the prism?
Options:
A)3
B)27
C)13
D)12
E)15
Rationale: Volume of prism = Area of base * height = 1/2* (square root of 9) * (square root of 9)*6=27
Answer: B
Answer: B
Question: Missing number in the series
4 9 20 43 90 185 376 759 1526 3061 ?
Options:
A)6132
B)6185
C)6190
D)6195
E)6180
Rationale: 4*2+1=9
9*2+2=20
20*2+3=43
43*2+4=90
185*2+6=376
376*2+7=759
759*2+8=1526
1526*2+9=3061
3061*2+10=6132
ANSWER:A
Answer: A
Question: The product of all the prime numbers less than 15 is closest to which of the following powers of 10 ?
Options:
A) 10^9
B) 10^8
C) 10^7
D) 10^6
E) 10^4
Rationale: P = 2*3*5*7*11*13
= 21 * 11 * 13*10
~ 10^ 4
Answer : E
Answer: E
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Options:
A)Rs. 2100
B)Rs. 2200
C)Rs. 2400
D)Rs. 2500
E)Rs. 2550
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
C)
Answer: C
Question: A and B invested some money such that capital of A is 20% more than that of B. If after one year they get profit of Rs.22000 then profit share of B is
Options:
A)Rs.7500
B)Rs.8000
C)Rs.9000
D)Rs.10,000
E)None of the above
Rationale: A:B=120:100= 6:5
then B share =5/11*(22000)
=10,000
ANSWER:D
Answer: D
Question: The diagonal of a cube is 8√3. find its volume and surface area.
Options:
A)354
B)384
C)324
D)344
E)364
Rationale: √3.a = 8 √3 => a = 8
Volume = a(power)3 => (8 × 8 × 8) Cm(power)3 => 512 Cm(power)3
Surface area => 6 a(power)2 => (6 × 8 × 8) Cm(power)2 => 384 Cm(power)2
Answer is B.
Answer: B
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 126 km/hr
Options:
A)8.5 seconds
B)2.86 seconds
C)3.5 seconds
D)2.5 seconds
E)2.6 seconds
Rationale: First convert speed into m/sec
Speed = 126*(5/18) = 35 m/sec
Time = Distance/speed
= 100/35 = 2.86 seconds
Answer: B
Answer: B
Question: A shopkeeper has 280 kg of apples. He sells 45% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.
Options:
A)24%
B)25%
C)27%
D)28%
E)35%
Rationale: If the total quantity was 100
Then 45X 20% + 60 X30%= 27
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'C' is the answer
Answer: C
Question: Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
Options:
A)65, 15
B)64, 16
C)62, 18
D)60, 20
E)61, 22
Rationale: Explanation:
x + y = 80
x – 4y = 5
x = 65 y = 15
ANSWER IS A
Answer: A
Question: A water tank which could be filled in 5 hours takes one more hour to be filled as a result of a leak in its bottom. If the tank is full calculate the time it will take for the leak empty it?
Options:
A)32 hours
B)30 hours
C)34 hours
D)31 hours
E)33 hours
Rationale: Part filled without leak in 1 hour = 1/5
Part filled with leak in 1 hour = 1/6
Work done by leak in 1 hour
=1/5âˆ’1/6=30 hours
Answer:B
Answer: B
Question: 117 x 217 + 83 x 83=?
Options:
A)79698
B)20578
C)80698
D)81268
E)None of them
Rationale: =(117)^2 + (83)^2
=(100+17)^2 + (100-17)^2
=2[(100)^2+(17)^2]
=2[10000+289]
=2 x 10289 = 20578
Answer is B
Answer: B
Question: When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.18
II.18.17
III. 17.16
Options:
A) I only
B) II only
C) III only
D) I and II only
E) I and III only
Rationale: Problem statement was difficult to parse. but some how I managed to understand what we can do.
1) x/y = 15 + 0.18
2) x/y = 18 + 0.17
3) x/y = 17 + 0.15
w.k.t x = yn (i.e Q) + yk=60 (i.e remainder)
therefore :
1) y*0.18=60 -- we can't get y an integer.
2) y*0.17=60 -- we can't get y an integer.
3) y*0.16=60 -- we can get y an integer.
Therefore 3 are possible answers.
Ans C.
Answer: C
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 90 mph. What is his average speed of travel for the entire journey?
Options:
A)60 mph
B)56.67 mph
C)53.33 mph
D)70 mph
E)66.67 mph
Rationale: Answer
Average speed of travel = Total distance travelled/Total time taken
Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.
Distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles.
Distance covered in the next 3 hours = speed * time = 90 * 3 = 270 miles.
Therefore, total distance covered = 80 + 270 = 350 miles.
Total time taken = 2 + 3 = 5 hours.
Hence, average speed = Total distance travelled/Total time taken=350/5 = 70 miles per hour.
Choice D
Answer: D
Question: Integer X represents the product of all integers between 1 to 24 (inclusive). The smallest prime factor of (x+1) must be
Options:
A)Between 1 to 10
B)Between 11 to 15
C)Between 15 to 20
D)Between 20 to 25
E)Greater than 24
Rationale: Answer = E = Greater than 24
This problem is asking smallest prime factor of (24!+1)
25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)
Just adding 1 to 24! will remove all the factors stated above;
so the smallest possible prime factor has to be greater than 24
Answer = E
Answer: E
Question: Three people (1 couple and 1 single) are seated at random in a row of 8 chairs. What is the probability that the couple does not sit together?
Options:
A)2/3
B)2/5
C)3/8
D)3/4
E)4/5
Rationale: The total number of arrangements of 3 people is 8*7*6 = 336
Let's think of the couple as a single unit.
The number of arrangements when the couple sits together is 7*6*2 = 84.
Note that we multiply by 2 because the couple can switch places with each other.
The number of ways the couple won't sit together is 336 - 84 = 252
P(couple won't sit together) = 252/336 = 3/4
The answer is D.
Answer: D
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options:
A)100
B)110
C)120
D)130
E)140
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: A
Question: A student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 18 more than the correct answer. Find the number.
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: Let the number be x.
(5/4) * x = (4/5)*x + 18
25x = 16x + 360
9x = 360
x = 40
The answer is C.
Answer: C
Question: Rohit walked 25 m towards south. Then he turned to his left and walked 20 m. He then turned to his left and walked 25 m. He again turned to his right and walked 15 m. At what distance is he from the starting point and in which direction?
Options:
A)35 m East
B)35 m North
C)30 m West
D)45 m East
E)55 m East
Rationale: ! 20 !--->15
! !
!--->!
20+15=35
ANSWER:A
Answer: A
Question: If the selling price is hexatrupled, the profit is septupled, what is the percentage of profit??
Options:
A)50%
B)100%
C)150%
D)200%
E)250%
Rationale: we can make two equations from the given info..
let selling price be S and cost price be C..
so profit=P=S-C...
if S is doubled profit is tripled..
so 7P=6S-C..
or S=6P...
therefore C=P..
% of profit=P/P=100%
B
Answer: B
Question: What is the total number of P integers between 100 and 200 that are divisible by 3?
Options:
A) 33
B) 32
C) 31
D) 30
E) 29
Rationale: yes there is a different way of arriving at that answer ....
u can also use airthmetic progression to get the answer
since the first term to be divisble by 3 is 102 ..take that as A .. the starting no
and since 198 is the last digit to be divisible by 3 take that as N ...
since the difference is 3 take that as D
no u have to find what term is 198 take that as nth term
the formula for that is N = A + (n-1) * d
198 = 102 +(n-1) * 3
from this u get n =33
Answer: A
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options:
A)20
B)80
C)100
D)200
E)120
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10
x - y = 20 .... (i)
and x + 20 = 2(y - 20)
x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
ANSWER:C
Answer: C
Question: Which one of the following numbers is the greatest positive integer x such that 4^x is a factor of 64^5?
Options:
A)5
B)8
C)10
D)15
E)19
Rationale: 64 = 4*4*4= 4^3
64^5 =(4^3)^5
=4^15
we have to find the greatest positive integer value for x
when x=15, it divides exactly once and that is the least positive integer value of the quotient
therefore, the correct option is D
Answer: D
Question: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
Options:
A)15 cm
B)25 cm
C)35 cm
D)42 cm
E)45 cm
Rationale: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.
Answer: Option C
Answer: C
Question: In a friendship gang Kala has 11 gang, in how many ways can he invite one or more of the gang to his house?
Options:
A)1244
B)2047
C)3698
D)5789
E)78895
Rationale: Kala can select one or more than one of his 8 gang.
=> Required number of ways = 2^11 – 1= 2047.
B
Answer: B
Question: A train moves past a house and a river bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?
Options:
A)79.2 km/hr
B)60.5 km/hr
C)65 km/hr
D)62.5 km/hr
E)75.2 km/hr
Rationale: length of the train be p metres and its speed - q m/sec.
p/q = 8 => p = 8q
p+264/20 = q
8q+264 = 20q
q = 22
speed = 22 m/s = (22*18/5) = 79.2 km/hr
ANSWER A
Answer: A
Question: If s is the smallest positive integer such that 3,150 multiplied by s is the square of an integer, then s must be
Options:
A) 2
B) 5
C) 6
D) 7
E) 14
Rationale: Solution:
This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number.
Let’s start by prime factorizing 3,150.
3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2
3,150 = 2^1 x 3^2 x 5^2 x 7^1
(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)
We also are given that 3,150 multiplied by s is the square of an integer. We can write this as:
2^1 x 3^2 x 5^2 x 7^1 x s = square of an integer
According to our rule, we need all unique prime factors' exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, s = 7 x 2 = 14
Answer is E.
Answer: E
Question: The last day of a century cannot be
Options:
A)Monday
B)Wednesday
C)Tuesday
D)Friday
E)None of these
Rationale: Explanation :
We know that number of odd days in 100 years = 5
Hence last day of the first century is Friday
Number of odd days in 200 years = 5 x 2 = 10 = 3 (As we can reduce multiples of 7
from odd days which will not change anything)
Hence last day of the 2nd century is Wednesday
Number of odd days in 300 years = 5 x 3 = 15 = 1 (As we can reduce multiples of 7
from odd days which will not change anything)
Hence last day of the 3rd century is Monday
We know that umber of odd days in 400 years = 0. (? 5 x 4 + 1 = 21 = 0)
Hence last day of the 4th century is Sunday
Now this cycle will be repeated.
Hence last day of a century will not be Tuesday or Thursday or Saturday
Answer : Option C
Answer: C
Question: What is the product of all positive factors of 21?
Options:
A)39
B)324
C)441
D)451
E)551
Rationale: Positive factors of 21 are 1, 3, 7, 21.
Positive factors of 21 is: 21*7*3 =441
Answer: C
Answer: C
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?
Options:
A)360
B)227
C)268
D)198
E)176
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
12/29 * 870 = 360
Answer:A
Answer: A
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)16
B)17
C)18
D)19
E)14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: Option B
Answer: B
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options:
A)175
B)195
C)180
D)160
E)140
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x * 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer is A.
Answer: A
Question: A shipment of 220 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
Options:
A)1/250
B)1/84
C)11/76
D)1/9
E)1/3
Rationale: Probability of chosing one defective phone from a lot of 220 which ontains 84 defective phones is = (84/220)
Probability of chosing one defective phone from a lot of 219(we already picked one) which ontains 83(we already picked one) defective phones is = (83/219)
Combined probability of series of events = product of the probabilities = (84/220)*(83/219)
84/220 is close to (21/55) and (83/219)= (36/95)
so answer is (21/55)*(36/95) = (11/76)
So, answer will be C
Answer: C
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)277
B)277
C)261
D)860
E)267
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: D
Question: Integer n is a four digit number such that it is made exactly of 2 distinct digits. If n is divisible by 9, how many possible values does n have?
Options:
A)59
B)60
C)61
D)68
E)69
Rationale: Then the additional combinations would be, 9000(1), 8883(4), 7776(4), 6669(4), 6660(3), 5553(4), 4446(4), 3339(4), 3330(3), 2221(4), 1116(4), 9990(3).
8*4 = 32
3*3 = 9
1*1 = 1
total = 42
Previous was 27. So total 27+42 = 69.
ANSWER:E
Answer: E
Question: In a certain town, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 330 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
Options:
A)72
B)88
C)95
D)120
E)135
Rationale: The ratio of Yankees:Mets:Red Sox = 6:4:5
The Mets fans are 4/15 of the population.
(4/15)*330 = 88
The answer is B.
Answer: B
Question: pqrs is a rectangle having area 50. rx=1/4sr.what is the area of pqxs?
Options:
A)41.75
B)42.75
C)43.75
D)44.75
E)45.75
Rationale: given pqrs is a rectangle and x located on sr whivh is having length rx=1/4sr.
from this we get right angle traingle qrx.
area of qrx=1/2*l/4*b=lb/8= 50/8 =6.25.
therefore area of pqxs= 50-6.25 = 42.75
ANSWER:B
Answer: B
Question: A runs 1 2⁄3 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
Options:
A)200 m
B)250 m
C)450 m
D)350 m
E)270 m
Rationale: Speed of A : Speed of B = 5⁄3 : 1 = 5 : 3
i.e., In a race of 5 m, A runs 5 m and B runs 3 m
i.e., A gains 2 m over B in a race of 5 m
=> A gains 80 m over B in a race of 52×80 = 200 m
Hence, winning point should be 200 m away from the starting point.
ANSWER:A
Answer: A
Question: Johnny bought six peanut butter cans at an average price (arithmetic mean) of 35¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans?
Options:
A)5.5
B)43
C)47.5
D)66
E)67.5
Rationale: Total price of six cans = 6*35 = 210
Total price of 4 cans = 4*31 = 124
Total rice of two cans = 210 - 124 = 86
Average price of two cans = 86/2 = 43 c
Another way to do it is this:
Assume that the four leftover cans were of 31c each. The avg was 35c initially because the two cans were 35c each and were providing another 4c of cost to other 4 cans.
So cost of the two cans = 2*35 + 4*4 = 86
Avg cost of the two cans = 86/2 = 43c
Answer (B)
Answer: B
Question: A rope of which a calf is tied is increased from 5m to 9 m, how much additional grassy ground shall it graze?
Options:
A)1218
B)180
C)176
D)200
E)291
Rationale: π (92 – 52) = 176
Answer: C
Answer: C
Question: 5% of a number is more than 20% of 650 by 190. Find the number?
Options:
A)288
B)278
C)800
D)267
E)6400
Rationale: (5/100) * X â€“ (20/100) * 650 = 190
1/20 X = 320
X = 6400
Answer:E
Answer: E
Question: For all numbers a and b, the operation is defined by ab = (a + 2)(b – 3).
If 3x = –20, then x =
Options:
A) –15
B) –6
C) 3
D) 6
E) -1
Rationale: (3+2)(x-3)=-20..
x-3=-4..
x=-1
E
Answer: E
Question: (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = ?
Options:
A)1
B)1 / 5
C)15 / 11
D)3 / 11
E)None
Rationale: Answer
Given expression = (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5)
= (14 + 1) / (10 + 1)
=15 / 11
Option: C
Answer: C
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 3,500, how much money did investors B and C earn in total?
Options:
A)$4,000
B)$4,900
C)$5,600
D)$9,500
E)$10,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 3500
5x = 3500
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 5x * 3 = 3500 * 3 = 10,500
Answer E
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150
B)776
C)555
D)257
E)812
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train(Distance) = Speed * Time
=50/3∗9=150meter
Answer: A
Answer: A
Question: In a certain province in France there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
Options:
A)30
B)105
C)330
D)14!
E)15!
Rationale: 1 city needs 14 roads to connect directly to the rest => 15 city needs 15*14 roads.
One road is counted twice => the number of road needed is 15*14/2 = 105
Answer B
Answer: B
Question: The value of (8x10^7)(8x10^8) is closest to which of the following?
Options:
A)10^17
B)10^14
C)10^18
D)10^19
E)10^20
Rationale: multiplying these we get,
64 x 10^7 x 10^8
= 6.4 x 10^16
which is closer to 10^17
Answer: A
Answer: A
Question: If the number65947*8 is completely divisible by 8, then the smallest whole number in place of * will be?
Options:
A)1
B)2
C)3
D)4
E)None of these
Rationale: The number 7x8 must be divisible by 8.
x=2 as 728 is divisible by 8.
Correct Option : B
Answer: B
Question: A sum of money place at compound interest doubles itself in 7 years. In how many years will it amount to eight times itself?
Options:
A)21
B)25
C)31
D)35
E)41
Rationale: 100 ---- 200 ---- 7
400 ---- 7
800 ---- 7
------
21 years
Answer: A
Answer: A
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)180%
B)189%
C)100%
D)109%
E)120%
Rationale: MP = 100
CP = 75
SP = 150
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75 ---- 75
100 ---- ? => 100%
Answer: C
Answer: C
Question: The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.
Options:
A)195
B)196
C)197
D)198
E)199
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient × divisor + remainder = 15 × 13 + 2 = 197
correct answer is C)197
Answer: C
Question: Solution A is 30% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
Options:
A)6:4
B)6:14
C)4:4
D)4:6
E)3:2
Rationale: Forget the volumes for the time being.
You have to mix 30% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 30) = 3/2
So the volume of the two solutions will be equal. Answer has to be 3:2
E
Answer: E
Question: A train running at the speed of 36 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)150 meter
B)299 meter
C)666 meter
D)90 meter
E)144 meter
Rationale: Speed = 36*(5/18) m/sec = 10 m/sec
Length of Train (Distance) = Speed * Time
(10) * 9
= 90 meter
Answer: D
Answer: D
Question: Which of the following best approximates the value of q if 6^44+3^11=6^q ?
Options:
A)55
B)50
C)45
D)44
E)43
Rationale: We have: 6^44+3^11=6^q
==> because 3^11 > 0 --> 6^q MUST be equal or greater than 6^44 ==>q MUST be equal or greater than 44
==> Option E is out immediately.
Divide both sides by 6^q and q >= 44
We have:
6^(44-q) + 3^11/6^q = 1
Because q >= 44 ==>3^11/6^q = 0.0000xyz, that is very small,we can ignore it.
Thus, 6^(44-q) must be approximately 1
==> 44-q = 0 ==> q is approximately 44
D is the answer.
Answer: D