divelab/Sys2Bench huggingface dataset:
Question: Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 4 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?
Options:
A)9
B)14
C)17
D)23
E)26
Rationale: My take is Option D (23)
I followed a simple approach (explained below):
Test 1: Ada's score = Paul's score + 10
Test 2: Ada's score = Paul's score + 4
Avg. of Paul's score = 4 points higher than Avg. of Ada's score
This implies that : Sum of Paul's score [3 Tests] = 12 points higher than Sum of Ada's score [3 Tests] (12 points higher since 3 points were given in terms of average of 3 scores)
So, Paul needs to score 23 points higher than Ada in Test 3, since Paul needs to compensate for the lower score in test 1 and Test 2 ( 26 = 10 + 4 + 12)
E
Answer: E
Question: For integers x and y, if 91x = 8y, which of the following must be true?
I. The cube root of x is an integer
II. y > x
III. y/7 is an integer
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: Statement 2: y>x
When y=x=0, equation holds but y is not greater than x
When x=-8 and y=-91, equation again holds but x>y
NOT TRUE
Statement 3: y/7 is an integer
Since x and y are integers, 91x and 8y must also be integers.
It is given that 91x=8y
or 13*7*x = 8 y
or 13x = 8y/7
To balance the equation, y/7 must be an integer
TRUE
Statement 1: The cube root of x is an integer
x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3
So, x may or may not be a cube root.
NOT TRUE
Answer:-C
Answer: C
Question: George is 8 years more than Christopher and Ford is 2 years younger than Christopher. The sum of their ages is 60. Find the ages of George.
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Christopher age = x
George age, y = x + 8---------->(1)
Ford age, z = x - 2------------>(2)
Sum of their ages, x+y+z=60---->(3)
Substitute z and y values in equation (3)
Therefore, x+(x+8)+(x-2)=60
=> 3x+8-2=60
=> 3x=60-6
=> 3x=54 =>x=54/3
x=18(Christopher's age)
Substitute x value in equation 1 & 2
y=x+8
y=18+8
y=26
ANSWER:B
Answer: B
Question: A rectangular football field is fenced on all four sides. The length of the football field is twice the length of its breadth. The cost of fencing the field was $300. The football management has decided to change the dimensions of field by increasing the breadth by 50% of its original value and reducing the length by 25% of its original value and fence the field again.. What will be the cost of the new fencing?
Options:
A)$300
B)$180
C)$425
D)$405
E)$415
Rationale: Let's take x to be the breadth. Then the length of the football field is 2x.
The perimeter of the old football field is x + 2x + x + 2x = 6x.
Now, for the new football field:
The new breadth = 1.5 times old breadth = 1.5x
The new length is 0.75 times old length = (.75)2x = 1.5x
So the new perimeter is 1.5x + 1.5x + 1.5x + 1.5x = 6x.
The new perimeter is the same as the older perimeter! So presumably the cost is the same at $300.
Ans - A
Answer: A
Question: 325325 is a six digit number.It is divisible by
Options:
A)7 only
B)11 only
C)13 only
D)all 7,11,and 13
E)none
Rationale: Solution
Clearly,325325 is divisible by all 7,11,and 13.
Answer D
Answer: D
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: Option B
Answer: B
Question: A clock shows the time as 10 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 4 p.m.?
Options:
A)30 min
B)35 min
C)45 min
D)50 min
E)55 min
Rationale: there are 6 hours in between 10 a.m. to 4 p.m.
6*5=30 minutes.
ANSWER:A
Answer: A
Question: person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: A
Question: A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B's contribution in the capital is
Options:
A)6000
B)7000
C)8000
D)9000
E)5000
Rationale: Ratio in which profit is divided =2:3
Assume that B's contribution to the capital =b
3500×12:b×7=2:3
⇒3500×12×3=2×b×7
⇒b=(3500×12×3)/(2×7)
=500×6×3=9000
Answer is D.
Answer: D
Question: A certain club has 10 members, including Parry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that parry will be either the member chose to be secretary or the member chose to be treasurer?
Options:
A)1/720
B)1/80
C)1/10
D)1/9
E)1/5
Rationale: In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8
probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10
Since, the problem is saying parry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E
Answer: E
Question: If q and y are different prime numbers less than ten, what must be true about the sum of q and y?
Options:
A)the sum is even
B)the sum is odd
C)the sum is less than ten
D)the sum is greater than ten
E)the sum is less than 13
Rationale: This has to be solved by checking for each option:
Prime numbers less that 10 = 2, 3, 5, 7
A. the sum is even
May or may not be true. q = 3, y, = 5 -> True.
q = 2, y = 3 - True
B. the sum is odd
May or may not be true. q = 3, y, = 5 -> False.
q = 2, y = 3 - True
C. the sum is less than ten
May or may not be true q= 5, y = 7, Sum = 12
q = 2, y = 3. Sum = 5
D. the sum is greater than ten
May or may not be true q= 5, y = 7, Sum = 12
q = 2, y = 3. Sum = 5
E. the sum is less than 13
This will always be true.
Maximum sum = 7 + 5 = 12.
This is always less than 13.
Correct Option: E
Answer: E
Question: An exam consists of 7 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?
Options:
A)1/16
B)37/256
C)1/2
D)219/256
E)15/16
Rationale: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.
If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.
So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.
The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 219/256.
D
Answer: D
Question: Statement: "You are appointed as a programmer with a probation period of 1 year and your performance will be reviewed at the end of the period for confirmation."
Assumptions:
The performance of an individual generally is not known at the time of appointment offer.
Generally an individual tries to prove his worth in the probation period.
Options:
A)Only assumption I is implicit
B)Only assumption II is implicit
C)Either I or II is implicit
D)Neither I nor II is implicit
E)Both I and II are implicit
Rationale: The performance of the individual has to be tested over a span of time as the statement mentions. So, I is implicit. The statement mentions that the individual's worth shall be reviewed (during probation period) before confirmation. So, II is also implicit.
E
Answer: E
Question: a sales person was starting a business and giving everyone that worked there a salary of 50000 for the first 6 years and giving them 65000 after 12 years. what would the interest rate for each year?
Options:
A)7%
B)10%
C)15%
D)25%
E)20%
Rationale: for 6 years = (65000 - 50000 ) = 15000.
for 12 years = (15000x6)/6= 15000
Principal = (50000 - 15000) = 35000.
Hence, rate = (100 x 15000)/(35000x6) = 7% ANSWER: A
Answer: A
Question: If 25% of x is 15 less than 15% of 1500, then x is?
Options:
A)188
B)216
C)156
D)840
E)121
Rationale: 25% of x = x/4 ; 15% of 1500 = 15/100 * 1500 = 225
Given that, x/4 = 225 - 15 => x/4 = 210 => x = 840.
Answer: D
Answer: D
Question: Find the average of first 15 natural numbers.
Options:
A)10
B)120
C)15
D)8
E)16
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 15 natural numbers = (15 x 16)/2 = 120
Therefore, required average of = 120/15 = 8
ANSWER: D
Answer: D
Question: What is |-26|?
Options:
A)(a) -26
B)(b) 26
C)(c) 0
D)(d) 1
E)(e) 25
Rationale: |-26|
= 26.
the answer is (B)
Answer: B
Question: A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% C.I. The sum borrowed was?
Options:
A)Rs. 1620
B)Rs. 1640
C)Rs. 1680
D)Rs. 1700
E)Rs. 1800
Rationale: Principal = (P.W. of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)
= [882/(1 + 5/100) + 882/(1 + 5/100)2]
= (882 * 20)/21 + (882 * 400)/441 = Rs. 1640.
ANSWER:B
Answer: B
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?
Options:
A)19
B)20
C)21
D)23
E)25
Rationale: Number = (12 x 35)
Correct Quotient = 420 ÷ 21 = 20
B)
Answer: B
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 16 days. In how many days Peter complete the work separately.
Options:
A)26 days
B)27 days
C)23 days
D)35 days
E)40 days
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 16 days which means that the whole job(1) can be completed in X days.
<=> 8/20->16 <=> X=16/(8/20)=40 Thus the answer is E.
Answer: E
Question: Anita, Indu and Geeta can do a piece of work in 18 days, 27 days and 36 days respectively. They start working together. After working for 4 days. Anita goes away and Indu leaves 7 days before the work is finished. Only Geeta remains at work from beginning to end. In how many days was the whole work done?
Options:
A)13 days
B)16 days
C)18 days
D)11 days
E)12 days
Rationale: B
16 days
4/18 + (x -7)/27 + x/36 = 1
x = 16 days
Answer: B
Question: The sale price sarees listed for Rs.560 after successive discount is 20% and 30% is?
Options:
A)321
B)314
C)316
D)265
E)162
Rationale: Explanation:
560*(80/100)*(70/100) = 314
Answer: B
Answer: B
Question: For a positive integer n, define S(n) to be the sum of the positive divisors of n. Which of the
following is the smallest?
Options:
A)S(2010)
B)S(2011)
C)S(2012)
D)S(2013)
E)S(2014)
Rationale: 2011 is prime, so that S(2011) = 1 + 2011 = 2012, the smallest.
But this answer can be verified without checking that 2011 is prime. Observe that
S(2010) > 2010 + 1005 > 3000
S(2013) > 2013 + 671 > 2600
and S(2012) and S(2014) are also larger than 3000.
Check by hand that 2, 3, 5, 7, and 11 do not divide 2011, and so if 2011 is not prime, then it
is a product of two primes p and q. If p 6= q, then
S(2011) = 2011 +
2011/p
+
2011/q
+ 1;
and p and q are greater than 11, so that this is smaller than 2600. If p = q then this is smaller
still.
correct answer B
Answer: B
Question: If the cost price of 15 articles is same as the selling price of 25 articles. Find the gain or loss percentage?
Options:
A)30% Gain
B)30% Loss
C)40% Gain
D)40% Loss
E)50% Loss
Rationale: Explanation:
15 cp = 25 sp
Cost price CP = 25
Selling price SP = 15
Formula = (SP-CP)/CP * 100 = (15 - 25)/25 * 100 = 40 % Loss
Answer: Option D
Answer: D
Question: What is the sum of the multiples of 4 between 63 and 151 inclusive?
Options:
A)2240
B)2250
C)2310
D)2330
E)2332
Rationale: the fastest way in an AP is to find the average and multiply with total integers..
between 63 and 151, the smallest multiple of 4 is 64 and largest =148..
average=(64+148)/2=106..
total numbers = (148-64)/4 + 1= 21+1=22..
sum=22*106=2332
ans E
Answer: E
Question: If a sum of money at simple interest doubles in 6 years, it will become 4 times in
Options:
A)15years
B)16years
C)11years
D)18years
E)12years
Rationale: Explanation:
let sum =x . s.i.=x
rate =(100*x)/(x*6)=50/3%
now ,sum =x, s.i= 3x, rate =50/3%
time =(100*3x)/(x*50/3) = 18 years
Answer: D
Answer: D
Question: A photograph measuring 8.5 by 7.5 cm is to be enlarged. If the enlargement of the longer side is 13.6 cm, what is the length of the smaller side?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Sol.
= (13.6 ÷ 8.5) × 7.5
= 12 cm.
Answer : C
Answer: C
Question: In how many ways the letters of the word RAIMBON be arranged?
Options:
A)4678
B)8754
C)5040
D)8658
E)8754
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
C)
Answer: C
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6.6 m x 22.5 cm?
Options:
A)6400
B)6410
C)6440
D)6500
E)7040
Rationale: Number of bricks = Volume of Wall/Volume of Bricks
=800x660x22.5/25x11.25x6= = 7040
answer :E
Answer: E
Question: Two cylinders of the radius in the ratio 3 : 5 and heights in the ratio 10 : 9. Then find the volumes ratio?
Options:
A)4:5
B)1:5
C)3:5
D)1.5:5
E)2:5
Rationale: πR(power2)H : πr(power2)h
9 × 10 : 25 × 9
90 : 225
2 : 5
Answer is E.
Answer: E
Question: ind the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2?
Options:
A)18 kmph
B)19 kmph
C)24 kmph
D)17 kmph
E)16 kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8)
= 24 kmph
Answer: C
Answer: C
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
Options:
A)39:40
B)39:30
C)39:47
D)39:45
E)39:41
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: A
Question: Maru obtained 66, 65, 82, 67 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)71
B)38
C)39
D)37
E)75
Rationale: Average = (66 + 65 + 82 + 67 + 75)/5
= 71.
Answer: A
Answer: A
Question: A is twice as good as B. And together they finish a piece of work in 18days. In how many days will A alone finish the work
Options:
A)25
B)27
C)15
D)18
E)21
Rationale: (A's 1day work):(B's 1day work) = 2:1
A+B 1day work = 1/18
A's 1day work = (1/18)*(2/3) = 1/27
A alone can finish the work in 27 days
Answer is B
Answer: B
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
Options:
A)22777
B)28877
C)26888
D)28800
E)67881
Rationale: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
Answer:D
Answer: D
Question: In track last week, the boys ran 27 laps. The girls ran 9 more
laps. Each lap is a three-fourth of a mile. How many miles did the girls run?
Options:
A)24 miles
B)25 miles
C)26 miles
D)27 miles
E)28 miles
Rationale: The girls ran 27 + 9 = 36 laps. 36 x3/4 = 108/4, which reduces to 27.
The girls ran 27 miles
correct answer D
Answer: D
Question: Dan can do a job alone in 15 hours. Annie, working alone, can do the same job in just 10 hours. If Dan works alone for 3 hours and then stops, how many hours will it take Annie, working alone, to complete the job?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Dan can complete 1/15 of the job per hour.
In 3 hours, Dan completes 3(1/15) = 1/5 of the job.
Annie can complete 1/10 of the job per hour.
To complete the job, Annie will take 4/5 / 1/10 = 8 hours.
The answer is D.
Answer: D
Question: Hannah and Glen will throw three dice each. The score is the sum of points on all three dice. If Hannah scores 3 in her attempt, what is the probability that Glen will outscore Hannah in his attempt?
Options:
A)5/6
B)35/36
C)71/72
D)215/216
E)431/432
Rationale: The total number of ways the dice can land is 6*6*6=216.
There is only 1 way that Glen can get a score of 3 = 1+1+1
Glen wins for any other outcome.
P(Glen wins)=1-1/216=215/216
The answer is D.
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train.
Options:
A)150
B)278
C)179
D)250
E)191
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 15 = 250 meter
Answer:D
Answer: D
Question: If each year the population of the country grows by 40%, how many years will elapse before the population of the country doubles?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Till Year 2000, population is 100 .
Year 2001: Population becomes 140 ............. 1 Year elapsed
Year 2002: Population becomes 196 ............. 2 Year elapsed
Year 2003: Population > 200 .................. 3 year elapsed
Answer:A
Answer: A
Question: If 0.75 : x :: 5 : 8, then x is equal to:
Options:
A)1.12
B)1.2
C)1.25
D)1.3
E)none
Rationale: (x * 5) = (0.75 * 8)
x = 6/5
x = 1.20
Answer = B
Answer: B
Question: The average age of a group of n people is 14 years old. One more person aged 32 joins the group and the new average is 15 years old. What is the value of n?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: 14n + 32 = 15(n+1)
n = 17
The answer is E.
Answer: E
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)37 km/hr
B)53 km/hr
C)36 km/hr
D)26 km/hr
E)87 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 8 = 45 => x = 53 km/hr.
Answer:B
Answer: B
Question: If in coded language
23 = 10
72 = 63
65 = 66
84 = 96
Then
97 = ?
Options:
A)141
B)142
C)143
D)144
E)145
Rationale: 2x(2+3)=10
7x(7+2)=63
6x(6+5)=66
8x(8+4)=96
9x(9+7)=144
ANSWER:D
Answer: D
Question: A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?
Options:
A)140
B)388
C)238
D)119
E)112
Rationale: when folded along the breadth
we have 2(l/2 +b) = 34 or l+2b = 34...........(1)
when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2)
from 1 &2 we get l=14 and b=10
Area of the paper = 14*10 = 140 sq cmV
Answer: A
Answer: A
Question: Sequence of numbers are 1, 11, 21, 1211, 111221.
What will be the next one in the above sequence?
Options:
A)223461
B)443576
C)532457
D)126434
E)312211
Rationale: E
312211
It is a strange sequence. Each number describes the resemblance of the previous one, except the first one.
11 describes the previous '1' which contains one '1'
21 describes the previous '11' which contains two '1'
1211 describes the previous '21' which contains one '2' and one '1'
111221 describes the previous '1211' which contains one '1', one '2' and two '1'.
So the next sequence will be 312211, that is the previous '111221' contains three '1', two '2' and one '1'.
Answer: E
Question: A family consists of two grandparents, two parents and six grandchildren. The average age of the grandparents is 65 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of family?
Options:
A)10/6years
B)B)31
C)C)30
D)D)33
E)E)35
Rationale: Required average
= (65 x 2 + 35 x 2 + 6 x 6 )/(2 + 2 + 6)
= (134 + 70 + 18)/10
= 236/10
= 23 10/6years.
Answer is A
Answer: A
Question: The guidelines at a certain college specify that for the introductory English class, the professor may choose one of five specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: 5C1*5C2 = 5*10 = 50
The answer is A.
Answer: A
Question: Difference between the length &breadth of a rectangle is 26 m. If its perimeter is 208 m, then its area is?? We have: (l - b) = 26 and 2(l + b) = 208 or (l + b) = 104?
Options:
A)2525 m^2
B)2625 m^2
C)2535 m^2
D)2553 m^2
E)2635 m^2
Rationale: Solving the two equations, we get: l = 65 and b = 39.
Area = (l x b) = (65 x 39) m2 = 2535 m^2
C
Answer: C
Question: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the following must be true of N?
Options:
A)5/6 < N < 10/11
B)21/10 < N < 9/2
C)5 < N < 5 1/11
D)5 < N < 5 5/11
E)30 < N < 60
Rationale: Each fraction is close to 1 so we know that the sum will be less than 6.
Lets just say they're each 1 so N=6.
But now we have to subtract the difference
1/6+1/7+1/8+1/9+1/10+1/11.
We can estimate these each as 1/10-->5/10 which is 1/2.
D is the closest representation
Answer: D
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 W 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 W , t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Answer: D
Question: How many 3-digit numbers are completely divisible 6 ?
Options:
A)100
B)150
C)200
D)250
E)300
Rationale: 3-digit number divisible by 6 are: 102, 108, 114,... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then tn = 996.
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150
Number of terms = 150.
B)
Answer: B
Question: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. Find the diameter of each sphere.
Options:
A)4 cm
B)6 cm
C)8 cm
D)10 cm
E)12 cm
Rationale: Explanation:
In this type of question, just equate the two volumes to get the answer as,
Volume of cylinder =πr2h
Volume of sphere =43πr3
=>12∗4/3πr3=πr2h
=>12∗4/3πr3=π∗8∗8∗2
=>r3=8∗8∗2∗3/12∗4
=>r3=8
=>r=2cm
=>Diameter =2∗2=4cm
Option A
Answer: A
Question: A school’s annual budget for the purchase of student computers increased by 20% this year over last year. If the price of student computers increased by 10% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
Options:
A)9%
B)9.09%
C)10%
D)10.09%
E)11.09%
Rationale: Pick numbers.
Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $120, price = $1.1 --> the number of computers purchased = 120/1.1 = ~109.09
Increase in the number of computers purchased = 9.09%
Answer: B.
Answer: B