divelab/Sys2Bench huggingface dataset:
Question: The food in a camp lasts for 40 men for 30 days. If ten more men join, how many days will the food last?
Options:
A)32days
B)30days
C)28days
D)26days
E)24days
Rationale: one man can consume the same food in 40*30 = 1200 days.
10 more men join, the total number of men = 50
The number of days the food will last = 1200/50 = 24 days.
Answer: E
Answer: E
Question: 2 corner most boxes of a chess board(diagonally opposite) haven been cut out
there's a rectangular block = 2 sqaures of chess board , how many such blocks can be placed on the chess board ?”
Options:
A)27
B)28
C)29
D)30
E)31
Rationale: chess board has 64 squares.so we can place 32 rectangular blocks,but 2 are cut off from the corner.
hence 32-2=30 blocks
ANSWER:D
Answer: D
Question: A can finish a piece of work in 5 days. B can do it in 15 days. They work together for two days and then A goes away. In how many days will B finish the work?
Options:
A)3 days
B)5 days
C)4 days
D)6 days
E)7 days
Rationale: 2/5 + (2 + x)/15 = 1 => x = 7 days
ANSWER:E
Answer: E
Question: In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $60,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?
Options:
A)$80,000
B)$130,000
C)$240,000
D)$290,000
E)$220,000
Rationale: For sake of ease, let's say there are 10 employees: 7 marketers, 2 engineers, and 1 manager.
Average company salary * Number of employees = Total company salary
>>> $80,000 * 10 = $800,000
Subtract the combined salaries for the marketers (7 * $60,000) and the engineers (2 * $80,000)
>>> $800,000 - $420,000 - $160,000 = $220,000.
The correct answer is E.
Answer: E
Question: If |x - 20| = 40 what is the sum of all the values of x.
Options:
A)0
B)60
C)-80
D)40
E)80
Rationale: There will be two cases
x-20 = 40 and x-20 = -40
Solve for x => x=40+20=> x=60 or x= -40 + 20 => x= -20
The sum of both values will be 60 + -20 =40
Answer is D
Answer: D
Question: If your mother asked you to bring her 7 water bottles, and one bottle costs 1.5 $, how much money should she give you?
Options:
A)9 $
B)9.5 $
C)10 $
D)10.5 $
E)11 $
Rationale: Simply multiply the cost of one bottle by its number you would buy.
The cost=7*1.5=10.5 $
So the correct choice is D
Answer: D
Question: At what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years?
Options:
A)11%
B)8%
C)10%
D)9%
E)7%
Rationale: C.I=P(1+R/100)^N
12100=10000(1+R/100)^2
121/100=(1+R/100)^2
(11/10)^2=(1+R/100)
R=10%
ANSWER:C
Answer: C
Question: 15 and 5 are the first two terms in a geometric sequence. What is the arithmetic difference between the 7th term and the 9th term?
Options:
A)(40/3) * (1/3)^7
B)(40/6) * (1/3)^7
C)(40/9) * (1/3)^7
D)(1/3)^7
E)(100/3) * (1/3)^7
Rationale: Common ratio = 5/15 =1/3
7th term = 15*(1/3)^7
9th term = 15*(1/3)^9
Difference = 15 * ((1/3)^7 - (1/3)^9)
= 15 * (1/3)^7 *(1 - (1/3)^2)
= 15 * (1/3)^7 * (8/9)
= (120/9) * (1/3)^7....
= (40/3) * (1/3)^7
A
Answer: A
Question: The mean of 1^3,2^3,3^3,4^3,5^3 is?
Options:
A)30
B)45
C)50
D)60
E)75
Rationale: 1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2
1^3+2^3+3^3+-----+5^3 = (5*6/2)^2 = 225
Required average is = 225/5 = 45
Answer is B
Answer: B
Question: Convert the 18/42 m/s into kilometers per hour?
Options:
A)3.5 kmph.
B)2.5 kmph.
C)1.2 kmph.
D)1.54 kmph.
E)1.9 kmph.
Rationale: 18/42 m/s = 18/42 * 18/5 = 1 (27/50) = 1.54 kmph.
ANSWER:D
Answer: D
Question: The ratio of salary of a worker in July to that in June was 21⁄2 : 21⁄4, by what % the salary of July more than salary of June. Also find by what %, salary of June was less than that of July.
Options:
A)11 1⁄9% and 10%
B)10% and 11 1⁄9%
C)Both 10%
D)Both 11 1⁄9%
E)None of these
Rationale: Let the salary of July be 5⁄2 x
and the salary of June be 9⁄4 x
Required percentages
= 5/2x−9/4x /9/4x×100 and 5/2x−9/4x /5/2x×100
= 100⁄9% and 100⁄10% = 11 1⁄9% and 10%
Answer A
Answer: A
Question: In expressing a length of 77.470 km as nearly as possible with the three significant digits, find the percentage error
Options:
A)0.39%
B)0.34%
C)0.039%
D)0.035%
E)None of these
Rationale: Explanation:
Error = (77.5 - 77.470) = 0.03
Required percentage =
0.03/ 77.470Ã—100=0.039
Option C
Answer: C
Question: The average of 40 numbers is 32. If two numbers namely 34 and 39 are discarded, The average of
remaining numbers is?
Options:
A)31.7
B)37.5
C)39.5
D)34.5
E)38.5
Rationale: Total of 50 numbers = 40 * 32 = 1280
Average of 38 numbers = 1280-(34+39) / 38
= 1207 / 38 = 31.7
Answer is A.
Answer: A
Question: The cube root of .000343 is
Options:
A)0.7
B)0.07
C)0.007
D)7
E)None of these
Rationale: Explanation:
(.000343)1/3
= (343/106)1/3
= (7*7*7/ 102*102*102)1/3
= 7/102
= 7/100 = 0.07
ANSWER B
Answer: B
Question: The probability that a arrow fired from a point will hit the target is 1/4. Three such arrows are fired simultaneously towards the target from that very point. What is the probability that the target will be hit?
Options:
A)19/64
B)23/64
C)23/67
D)37/64
E)37/50
Rationale: Explanation :
Probability of a arrow not hitting the target =3/4.
Probability that none of the 3 arrow will hit the target:
=>(3/4)3.
=>27/64.
Probability that the target will hit at least once
=>1−(27/64).
=>37/64.
Answer : D
Answer: D
Question: A and B together can do a piece of work in 3 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
Options:
A)0.28 days
B)0.45 days
C)0.55 days
D)0.25 days
E)0.15 days
Rationale: B = 1/2 – 1/20 =0.28 days
ANSWER:A
Answer: A
Question: By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Options:
A)30 kmph
B)28 kmph
C)26 kmph
D)24 kmph
E)22 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km
He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x
=30 kmph.
Answer: A
Answer: A
Question: Find the invalid no.from the following series 10, 17, 22, 29, 34, 36
Options:
A)36
B)18
C)40
D)37
E)25
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 36 is wrong.
Answer : A
Answer: A
Question: Present ages of X and Y are in the ratio 4:5 respectively. 6 years hence this ratio will become 5:6 respectively. What is X's present age in years?
Options:
A)35
B)24
C)37
D)39
E)40
Rationale: Let the present ages of X and Y be 4x and 5x years respectively.
Then, (4x + 6)/(5x + 6) = 5/6
6(4x + 6) = 5(5x + 6) => 24x+36 = 25x+30 => x=6
X's present age = 4x = 4*6 = 24
ANSWER: B
Answer: B
Question: In a 2000 m race, A beats B by 100 meters or 50 seconds. Find the speed of B?
Options:
A)10m/s
B)2m/s
C)5m/s
D)7m/s
E)3m/s
Rationale: Since A beats B by 100 m or 50 seconds,
it implies that B covers 100 m in 50 seconds.
Hence speed of B = 100/50 = 2 m/s.
Answer: B
Answer: B
Question: Two isosceles Triangles have equal vertical angles and their areas are in the ratio 16:36. Find the ratio of their corresponding heights .
Options:
A) 4/6
B) 5/4
C) 3/2
D) 5/7
E) 2/3
Rationale: We are basically given that the triangles are similar.
In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.
Therefore, area/AREA=height^2/HEIGHT^2=16/36 --> height/HEIGHT=4/6.
Answer: A.
Answer: A
Question: 65% of x = 20% of 422.50. Find the value of x?
Options:
A)100
B)130
C)150
D)180
E)199
Rationale: 65% of x = 20% of 422.50
Then, 65/100 * x = 20/100 * 4225/10
x = 845/10 * 100/65 = 130
Answer is B
Answer: B
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=2P+48, what is the perimeter of the garden in feet?
Options:
A)36
B)40
C)44
D)48
E)52
Rationale: Let x be the length of one side of the square garden.
x^2 = 8x + 48
x^2 - 8x - 48 = 0
(x-12)(x+4) = 0
x = 12, -4
P = 4(12) = 48
The answer is D.
Answer: D
Question: The perimeter of a triangle is 24 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)30 cm2
B)85 cm2
C)65 cm2
D)45 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 24/2 = 30 cm2
Answer:A
Answer: A
Question: What is the rate percent when the simple interest on Rs.9100 amount to Rs.455 in 3 Years?
Options:
A)3.7%
B)5.7%
C)6.7%
D)8.7%
E)9.7%
Rationale: 455 = (4100*3*R)/100
R = 3.7%
Answer: A
Answer: A
Question: How many digits are in the number 50^8 × 8^3 × 11^2?
Options:
A)22
B)20
C)19
D)18
E)17
Rationale: calculate the Number of 0's through the powers of 10
50^8 × 8^3 × 11^2 = (5^2*2)^8*2^9*11^2 = 5^16*2^17*11^2 = 2*11^2*10^16 = 242*10^16
Hence we would have 16 trailing 0's and the three digits from 242
Total digits = 3 + 16 = 19
Correct Option: C
Answer: C
Question: . If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?
Options:
A)3:2
B)9:5
C)9:1
D)9:9
E)9:7
Rationale: Explanation:
a1 : a2 = 3 : 1
6 a12 : 6 a22 = 9: 1
Answer: Option C
Answer: C
Question: If mn > 0, which of the following must be negative?
Options:
A)mn
B)mn^2
C)m/-n
D)m/n
E)m+n
Rationale: Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive.
Answer :C
Answer: C
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
Options:
A)2 hours
B)9 hours
C)6 hours
D)3 hours
E)12 hours
Rationale: Explanation:
|-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: Option A
Answer: A
Question: If the radius of a circle is increased by 20% then the area is increased by:
Options:
A)44
B)219
C)16
D)18
E)11
Rationale: Explanation:
Let say radius = πr2πr2 = π102π102 = 100π100π
New radius = 10 × 120% = 12
New area = π122π122 = 144π144π
Increment = 144π−100π100π×100144π−100π100π×100 = 44%
Answer: A
Answer: A
Question: A certain fruit stand sold apples for $0.70 each and guava for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?
Options:
A)12
B)13
C)11
D)14
E)5
Rationale: Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.
63 is a direct multiple of 7, however in this case there won't be any guava. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 .
C
Answer: C
Question: Cathy and Jim begin running at the same time and they start at the same place on a straight path. Cathy runs at 10 miles per hour, and Jim runs at 6 miles per hour. After 18 minutes, Cathy stops to stretch. If it takes Cathy 27 minutes to stretch and Jim continues to run during this time, how many minutes will it take Cathy to catch up to Jim?
Options:
A)20.5
B)21.5
C)22.5
D)23.5
E)24.5
Rationale: In 18 minutes, Cathy runs 3 miles.
In 45 minutes, Jim runs 4.5 miles.
Cathy can catch Jim at a rate of 4 miles per hour.
Since Jim is ahead by 1.5 miles, it will take Cathy 1.5 / 4 hours = 22.5 minutes to catch Jim.
The answer is C.
Answer: C
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
Options:
A)2880.
B)4320.
C)5780.
D)5760.
E)6380.
Rationale: Efficiency per machine = 600 watt/hr
Efficiency due to increase in wind speed = 600*120% => 720 watt/hr
Production by each machine in 2 hours is 720*2 => 1440 watt
Production by 3 machines => 1440 watt * 3 = 4320 watt
Answer will be (B)
Answer: B
Question: A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Options:
A)130
B)360
C)500
D)540
E)580
Rationale: L = 800 m
S = 78kmph = 65/3 mps
Time to pass tunnel = 1min = 60 sec
t.f (800+X)/(60) = (65/3)
=500
ANSWER:C
Answer: C
Question: Find the sum of all 2 digit numbers divisible by 3.
Options:
A)99
B)199
C)1665
D)2452
E)2547
Rationale: All 2 digit numbers divisible by 3 are :
12, 51, 18, 21, ..., 99.
This is an A.P. with a = 12 and d = 3.
Let it contain n terms. Then,
12 + (n - 1) x 3 = 99 or n = 30.
Required sum = 30 x (12+99) = 1665.
ANSWER C 1665
Answer: C
Question: The speed of a boat in still water is 60kmph and the speed of the current is 40kmph. Find the speed downstream and upstream?
Options:
A)87 kmph
B)40 kmph
C)16 kmph
D)20 kmph
E)18 kmph kmph
Rationale: Speed downstream = 60 + 40
= 100 kmph
Speed upstream = 60 - 40
= 20 kmph
Answer:D
Answer: D
Question: 49 Ã— 49 = 7^?
Options:
A)4
B)7
C)8
D)16
E)None of these
Rationale: 49 Ã— 49 = 7?
or, 7(2) Ã— 7(2) = 7?
or 7(4) = 7? or, ? = 4
Answer A
Answer: A
Question: If pipe A can fill the tank in 45 minutes and pipe B in 30 minutes, find the time to fill the tank if both the pipes are opened together.
Options:
A)12 minutes
B)20 minutes
C)18 minutes
D)15 minutes
E)None of these
Rationale: Explanation:
In 1 minute pipe A can fill 1/45th part of the tank and pipe B can fill 1/30th part of the tank. If they are opened simultaneously then in 1 minute they can fill (1/45
+ 1/30) part of the tank = 1/18th part of the tank.
Hence, in 18 minutes the tank gets filled if pipes A & B are opened together.
ANSWER C
Answer: C
Question: The average of 5 quantities is 11. The average of 3 of them is 4. What is the average of remaining 2 numbers?
Options:
A)21.5
B)10.6
C)8
D)9.5
E)None of these
Rationale: ANSWER: A
(5x11-3x4)/2=21.5
Answer: A
Question: How many cubes of 5cm edge can be cut out of a cube of 15cm edge
Options:
A)36
B)232
C)27
D)48
E)None of these
Rationale: Explanation:
number of cubes=(15 x 15 x 15) / (5 x 5 x 5) = 27
Answer: C
Answer: C
Question: Sum of the squares of three numbers is 431 and the sum of their products taken two at a time is 265. Find the sum?
Options:
A)32
B)35
C)25
D)31
E)29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 431 + 2* 265
a + b + c = √961 = 31
D
Answer: D
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 63 as quotient. What is the correct quotient ?
Options:
A)0
B)36
C)13
D)20
E)25
Rationale: 12*63=756
756%21=36
ANSWER:B
Answer: B
Question: Suresh drives his car to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. What is his average speed for the whole journey ?
Options:
A)32.5 km/hr
B)35 km/hr
C)37.5 km/hr
D)40 km/hr
E)42 km/hr
Rationale: Explanation:
If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,
average speed of the whole journey = 2xy/x+y kmph.
Therefore, average speed
=2×50×30/50+30=2×50×30/80
=2×50×3/8=50×3/4
=25×3/2=75/2=37.5
Answer: Option C
Answer: C
Question: The average height of 30 students in a class was calculated as 175 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm. What was the actual average height of the students in the class?
Options:
A)174.5
B)173.5
C)172.5
D)171.5
E)170.5
Rationale: The total height was 15 cm too much.
The average height should be reduced by 15 cm/30 = 0.5 cm
The answer is A.
Answer: A
Question: What is the value of n if the sum of the consecutive odd intergers E from 1 to n equals 169?
Options:
A)47
B)25
C)37
D)33
E)29
Rationale: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.
Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.
a=1 (first term)
d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2
*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.
But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.
Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.
It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Answer: B
Question: A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?
Options:
A)115
B)117
C)116
D)114
E)113
Rationale: Explanation:
Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.
ANSWER IS B
Answer: B
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
Options:
A)1/4
B)1/2
C)3/4
D)3/5
E)None of these
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer : B
Answer: B
Question: How many terms are there in 2, 4, 8, 16,..., 16384?
Options:
A)14
B)11
C)12
D)10
E)8
Rationale: 2, 4, 8, 16, ..., 16384 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 16384
or 2^n-1 = 8192 = 2^13
Thus n - 1 =13
n= 14
ANSWER:A
Answer: A
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)18/38
C)18/36
D)16/35
E)18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability
= 3/5 * 2/7 + 2/5 * 5/7
= 6/35 + 10/35
= 16/35
Answer: D
Answer: D
Question: If the TV is selling for $1200 its cost price is $800. Then what is the profit percentage
Options:
A)60%
B)70%
C)80%
D)90%
E)50%
Rationale: Explanation:
Let the S.P = 1200
then C.P. = 800
Profit = 400
Profit% = (400/800) * 100 = 50%. Answer: E
Answer: E
Question: A hotel has 4 available rooms. One room has a view to the garden and the others has a view to the pool. If you sleep in the hotel, what is the probability that you get a room in the side of the garden?
Options:
A)1/4
B)1/2
C)1/3
D)none
E)2
Rationale: the total number of rooms is 4
and the number of rooms in the side of the garden is 1
then, in one chance the probability to pick a room in the side of the garden is
1/4
Answer A
Answer: A
Question: If 425/999=0.125, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
Options:
A)0
B)2
C)3
D)4
E)5
Rationale: 0.[u]125[/u = 0.425425425.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E
Answer: E
Question: In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.0 sec
B)2.8 sec
C)7.5 sec
D)2.3 sec
E)1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 80/40
= 2.0 sec.
Answer:A
Answer: A
Question: A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 300,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
Options:
A)a) 500
B)b) 750
C)c) 1,000
D)d) 1,250
E)e) 1,500
Rationale: Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 300,000 = 75,000
So required ratio = 75,000/75 = 1000
Answer C
Answer: C
Question: If 2^(2w) = 8^(w−6), what is the value of w?
Options:
A)12
B)15
C)18
D)21
E)24
Rationale: 2^(2w) = 8^(w−6)
2^(2w) = 2^(3*(w−6))
2^(2w) = 2^(3w-18)
Let's equate the exponents as the bases are equal.
2w = 3w-18
w = 18
The answer is C.
Answer: C
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
Options:
A)15
B)25
C)35
D)45
E)55
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 20) = 90(x - 5)
350 = 10x => x = 35
ANSWER:C
Answer: C
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 2 muffins remained. How many guests did Monica plan on?
Options:
A)3.
B)4.
C)5.
D)6.
E)7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 2 = 5x + 2
6x - 4 = 5x + 2
x = 6
Answer: D
Answer: D
Question: The average weight of three men A, B and C is 84 Kg. The average weight becomes 80 Kg when D joins them. If E whose weight is 3 Kg more than D joins the group replacing A, then the average weight of B, C, D and E becomes 79 Kg. The weight of A is:
Options:
A)65kg
B)70kg
C)75kg
D)80kg
E)85kg
Rationale: Wt of ABC = 84*3= 252 kg
wt of ABCD= 80*4=320 kg
wt of D= 68 kg
wt of E = 71 kg
wt of ABCDE = 320+71=391 kg
wt of BCDE = 79*4=316 kg
wt of A = 391-316=75 kg
ANSWER:C
Answer: C
Question: Choose the missing terms out of the given alternatives.
AD, EH, IL, ?, QT
Options:
A)MP
B)LM
C)MN
D)OP
E)OM
Rationale: A
MP
The letters move four steps forward.
Answer: A