divelab/Sys2Bench huggingface dataset:
Question: Peter has $642,986 in his savings account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among his nine children?
Options:
A)$642,986
B)$642,987
C)$642,988
D)$642,989
E)$642,990
Rationale: To find the least amount the man should add to his saving account to split the money evenly among his 9 children, he needs to make the total divisible by 9
Simply add the individual digits of the total = 6+4+2+9+8+6= 35
If you add 1 , the number is divisible by 9 (35+ 1)
Correct Option : B
Answer: B
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
Options:
A)24
B)26
C)28
D)30
E)32
Rationale: Area of first rectangle is 12*15=180 hence area of second would be 6x=180x
x=30
answer is D
Answer: D
Question: The ratio of two natural numbers is 5:6. If a certain number is added to both the numbers, the ratio becomes 7:8. If the larger number exceeds the smaller number by 10, find the number added?
Options:
A)27
B)298
C)20
D)28
E)12
Rationale: Let the two numbers be 5x and 6x.
Let the number added to both so that their ratio becomes 7:8 be k.
(5x + k)/(6x + k) = 7/8
42x = 7k => k = 2x.
6x - 5x = 10 => x = 10
k = 2x = 20.
Answer: C
Answer: C
Question: What is the area of square field whose side of length 15 m?
Options:
A)225
B)2878
C)277
D)266
E)279
Rationale: 15 * 15
= 225 sq m
Answer: A
Answer: A
Question: The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
Options:
A)40 years
B)42 years
C)50 years
D)52 years
E)None
Rationale: Solution
Age of the mother	= (12 x 7 - 7 x 6)
= 42 years.
Answer B
Answer: B
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
Options:
A)300km/hour
B)360 km/hour
C)600km/hour
D)720km/hour
E)None of these
Rationale: Distance=(240*5)km=1200km.
Required speed=(1200*3/5)km/hr=720kilometer/hour.
Correct Option: D
Answer: D
Question: Carina has 85 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Lets say 5 and 10 ounce packages be x and y respectively.
Given that, 5x+10y=85 and x=y+2. What is the value of y.
Substituting the x in first equation, 5y+10+10y=85 ->y=75/15.=5
A
Answer: A
Question: Sundar invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income
Options:
A)600
B)648
C)500
D)700
E)750
Rationale: no of shares = 4455/8.25 = 540
face value = 540*10 = 5400
income = 12/100 * 5400 = 648
ANSWER B
Answer: B
Question: We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value W of the ratio A/B?
Options:
A)1/2
B)1/3
C)2/3
D)1/4
E)1/5
Rationale: W-> A/B=20*21*……*39/21*22*….*39*40=20/40=1/2.
Therefore, the answer is A.
Answer: A
Question: In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family ?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Explanation:
Let d and s represent the number of daughters and sons respectively.
Then, we have :
d - 1 = s and 2 (s - 1) = d.
Solving these two equations, we get: d = 4, s = 3.
Answer: B
Answer: B
Question: If x and y are perfect squares, then which four of the following is not necessarily a perfect square?
Options:
A)x^2
B)xy
C)4x
D)x+y
E)x^5
Rationale: If x=y=1^2=1, then each option but E is a perfect square, therefore E is NOT necessarily a perfect square.
Answer: E.
Answer: E
Question: There are 70 doors marked with numbers 1 to 70. And there are 70 individuals marked 1 to 70.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15 ...70.
If every individual in the group get one turn then how many doors are open at the end?
Options:
A)0
B)1
C)2
D)7
E)8
Rationale: Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59, 61,67 will be closed when people with respective numbers perform operations on them.
From the other numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9 ...64.
So our numbers are 1,4,9, 16,25,36,49 and 64.
Answer:-E
Answer: E
Question: [(11/2 ÷ 1/2 × 11/2)]/[(11/2 × 1/2 ÷ 11/2)] = ?
Options:
A)111
B)101
C)91
D)81
E)121
Rationale: Explanation:
[(11/2 ÷ 1/2 × 11/2)]/[(11/2 × 1/2 ÷ 11/2)]
= [11/2 × 2/1 × 11/2]/[11/2 × 1/2 × 2/11]
= 121/2 / 1/2 = 121/2 x 2/1 = 121
Answer: Option E
Answer: E
Question: A and B together have $ 1210. If of A's amount is equal to of B's amount, how much amount does B have?
Options:
A)400
B)489
C)484
D)365
E)342
Rationale: 4	A	=	2	B
15 5
A = 2	x	15 B
5 4
A =	3	B
2
A	=	3
B 2
A : B = 3 : 2.
B's share = Rs. 1210 x	2 = $ 484.
ANSWER C
Answer: C
Question: The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above condition is
Options:
A)4
B)6
C)8
D)12
E)14
Rationale: Explanation:
Let the required numbers be 33a and 33b.
Then 33a +33b= 528 inline fn_jvn Rightarrow a+b = 16.
Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
inline fn_jvn therefore Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4. Answer: A
Answer: A
Question: A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 25 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
Options:
A)40
B)45
C)108
D)55
E)60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 25 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
25 = 180/4t
t = 108
B-C = 108mph
Answer C
Answer: C
Question: B completes a work in 8 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?
Options:
A)3.75 days
B)4.44 days
C)5 days
D)6.44 days
E)7 days
Rationale: 1/8 + 1/10 = 9/40
40/9 = 4.44 days
ANSWER:B
Answer: B
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
Options:
A)monday
B)Tuesday
C)sunday
D)friday
E)wednesday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
Answer:B) Tuesday
Answer: B
Question: The height of a triangle is decreased by 5% and its base increased by 10%. Its area will
Options:
A)decrease by 12.5%
B)increase by 12.5%
C)increase by 4.5%
D)Increase by 25%
E)None of these
Rationale: Explanation :
Let the initial height be 100 and the base be 200 units.
âˆ´ Area = 1/2 x 100 x 200 = 10000sq units
Now, height = 95 units and base = 220 units
âˆ´ New area = 1/2 x 95 x 220= 10450
âˆ´ Area is increased by (10450 - 10000)/10000 x 10
= 4.5%
Answer : Option C
Answer: C
Question: The sum of ages of 4 children born 2 years different each is 40 yrs. What is the age of the Elder child?
Options:
A)13
B)9
C)16
D)17
E)18
Rationale: Let the ages of children be x, (x + 2), (x + 4), (x + 6) years.
Then, x + (x + 2) + (x + 4) + (x + 6) = 40
4x+12 = 40 => 4x= 28
x = 7
x+6= 7+6= 13
Answer : A
Answer: A
Question: A city in the US has a basketball league with three basketball teams, the Aziecs, the Braves and the Celtics. A sports writer notices that the tallest player of the Aziecs is shorter than the shortest player of the Braves. The shortest of the Celtics is shorter than the shortest of the Aziecs, while the tallest of the Braves is shorter than the tallest of the Celtics. The tallest of the Braves is taller than the tallest of the Aziecs.
Which of the following can be judged with certainty ?
Options:
A)X,U only
B)X only
C)Y only
D)8 onlY
E)T only
Rationale: Ans: B
Sol: We solve this problem by taking numbers. Let the shortest of Braves is 4 feet. Then tallest of Aziecs is less than 4. So let it be 3 feet.
A -> 2 - 3
B -> 4 - 6
C -> 1 - 7
From the above we can safely conclude X is correct. but Y cannot be determined.
Answer:C
Answer: C
Question: Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 28 more photos than Claire. How many photos has Claire taken?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: L = R
L = 3C
R = C + 28
3C = C + 28
C = 14
The answer is E.
Answer: E
Question: If the wheel is 42 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)18
B)4
C)6
D)8
E)19
Rationale: 2 * 22/7 * 42 * x = 1056
=> x = 4
Answer: B
Answer: B
Question: The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is :
Options:
A)Rs. 1325
B)Rs. 1300
C)Rs. 1350
D)Rs. 1500
E)Rs. 1800
Rationale: Solution
Required sum = P.W. of Rs.702 due 6 months hence + P.W. of Rs. 702 due 1 year hence
= Rs. [( 100x 702/100 + 8 x1/2 ) + ( 100x 702/100 + 8x 1) ] = Rs. (675 + 650) = Rs. 1325.
Answer A
Answer: A
Question: Solution X is 20% chemical A and 80% chemical B by volume; Solution Y is 30% chemical A and 70% chemical B. If a mixture of X and Y is 22% chemical A, what percent of the mixture is Solution X?
Options:
A)20%
B)44%
C)50%
D)80%
E)90%
Rationale: 22% of chemical A in X+Y grams of solution comes from 20% chemical A in solution X and 30% chemical A in solution Y, thus:
0.22(X + Y) = 0.2X + 0.3Y --> X = 4Y --> X/(X+Y)=4/5=0.8.
Answer: D.
Answer: D
Question: If a : b = 2 : 3 and b : c = 5 : 7, then find a : b : c.
Options:
A)10 : 15 : 27
B)10 : 15 : 21
C)10 : 15 : 22
D)10 : 15 : 12
E)10 : 15 : 28
Rationale: a : b : c = (2 x 5) : ( 3 x 5) : (3 x 7) = (10) : (15) : (21)
Answer:	A
Answer: A
Question: Jaydeep purchased 25 kg of rice at the rate of 16.50 per kg and 35 kg of rice at the rate of 24.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make 25 per cent profit?
Options:
A)26.5
B)27.5
C)28.5
D)30.0
E)29.0
Rationale: CP = 25 × 16.50 + 35 × 24.50 = 1270
SP = 1270 × 125⁄100 = 1587.50
Price per kg = 1587.50⁄60 ≈ 26.50
Answer A
Answer: A
Question: Jim takes a seconds to swim t meters at a constant rate from point M to point N in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point M the same time that Roger leaves point N, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?
Options:
A)c(b-a)/ a+b
B)c(a-b)/a+b
C)c(a+b)/a-b
D)t(a-b)/a+b
E)ab(b-a)/a+b
Rationale: Both JimRoger are travelling at constant speedin opposite direction:
So, speed of Jim =t /a speed of Roger = t/b
Let say Jim travelled distance x from M where it met Roger, it means that Roger travelled (t-x) from point N
[x would be less than (t-x) as Jim is travelling slow]
From above, time taken by Jim to travel x = xa/t....................... (1)
Also, time taken by Roger to travel (t-x) = (t-x)b/t.....................(2)
Time taken by both JimRoger is same, so (1) = (2)
xa/t = (t-x)b/t,
Solving further, x = bt/(a+b).................... (3)
We require to find how many fewer meters will Jim have swum i.e
additional distance travelled by Roger = (t - x) - x
= t-2x
Substituting value of x from (3)solving the equation further, we get Answer = t(a-b)/a+b
Answer = (D)
Answer: D
Question: A committee of 5 is to be selected from among 4 boys and 6 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?
Options:
A)105
B)194
C)230
D)350
E)455
Rationale: I'm sure there is some problem with the question.
R U sure its atleast one boy and not atleast 1 boy and 1 girl?
if its 1 boy and 1 girl
6C1*4C3 + 6C2*4C2 + 6C3*4C1
6*4 + 15*6 + 20*4
24 + 90 + 80
194
B
Answer: B
Question: If a+5/b is a prime integer, which of the following must be true?
1.b=5a
2. b is a prime integer
3. a+5/b is ODD.
Options:
A)None
B)1 only
C)2 only
D)1 and 2 only
E)2 and 3 only.
Rationale: I would pick up numbers and do .
i hope the question is (a+5)/b....
let a = 3 , b = 4
3+5/4 = 2 = Prime
1. b is not equal to 5a
2.b is not a prime number
3. (a+5)/b is not odd.
hence A
Answer: A
Question: A car covers a distance of 624 km in 2 2/5 hours. Find its speed?
Options:
A)104 kmph
B)194 kmph
C)109 kmph
D)260 kmph
E)271 kmph
Rationale: 624/2 2/5
=260 kmph
Answer:D
Answer: D
Question: A man traveled a total distance of 900 km. He traveled one-third of the whole trip by plane and the distance traveled by train is two-thirds of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?
Options:
A)240
B)280
C)320
D)360
E)400
Rationale: total distance traveled = 900 km.
distance traveled by plane = 300 km.
distance traveled by bus = x
distance traveled by train = 2x/3
x + 2x/3 + 300 = 900
5x/3 = 600
x = 360 km
The answer is D.
Answer: D
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options:
A)4
B)8
C)10
D)9
E)11
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B
Answer: B
Question: If w is divisible by 10 and 4, w must be a multiple of which of the following?
Options:
A)8
B)12
C)20
D)24
E)36
Rationale: If w is divisible by 2*2 and 2*5, then w is divisible by 2*2*5 = 20.
The answer is C.
Answer: C
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value V?
Options:
A)2r
B)2s
C)r +s
D)2r-s
E)2s-r
Rationale: You can answer this question by using Number Properties and logic or by TESTing VALUES.
We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.
IF....
R = 8
S = 2
Answer A: 2R = 2(8) = 16
Answer B: 2S = 2(2) = 4
Answer C: R+S = 8+2 = 10
Answer D: 2R-S = 2(8) - 2 = 14
Answer E: 2S-R = 2(2) - 8 = -4
Final Answer:
A
Answer: A
Question: The present ages of three persons in proportions 2 : 7 : 9. Eight years ago, the sum of their ages was 30. Find their present ages (in years).
Options:
A)17,20, 28
B)22,28, 36
C)21,35, 45
D)33,42,43
E)6,21,27
Rationale: Let their present ages be 2x, 7x and 9x years respectively.
Then, (2x - 8) + (7x - 8) + (9x - 8) = 30
18x = 54
x = 3.
Their present ages are 2x = 6 years, 7x = 21 years and 9x = 27 years respectively.
ANSWER:E
Answer: E
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
Options:
A)3888
B)26989
C)26700
D)28800
E)2879
Rationale: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
Answer: D
Answer: D
Question: What is the probability of getting exactly 4 heads in a single throw of five fair coins?
Options:
A)1/4
B)3/8
C)3/16
D)5/32
E)7/32
Rationale: One possible case is HHHHT.
P(HHHHT) = 1/2*1/2*1/2*1/2*1/2 = 1/32
There are 5C4 = 5 possible cases.
P(4 heads) = 5*1/32 = 5/32
The answer is D.
Answer: D
Question: Carmelo and LeBron participate in a four-person footrace on the basketball court during All-Star Weekend. If all four contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
Options:
A)5040
B)2520
C)720
D)12
E)42
Rationale: 4! = 24
24/2=12half the time carmelo is in front, vice versa
Answer:
(D) 12
Answer: D
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 3 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Options:
A)360
B)487
C)481
D)729
E)268
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 3 = 360
Answer:A
Answer: A
Question: A parking garage rents parking spaces for $10 per week or $24 per month. How much does a person save in a year by renting by the month rather than by the week?
Options:
A) $140
B) $160
C) $220
D) $232
E) $260
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 24= 288$
520 - 288 = 232
Ans D
Answer: D
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150m
B)120m
C)186m
D)167m
E)189m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 25seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minuntes ?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: a must be an integer as it is the number shoots at a rate of 25sec/shoot
3*60 + 25a = 10*60
25a = 420
a = 16
The total number of shoots -->1 +16 = 17 and
18th shoot will be taken at 605seconds which is above 10 minutes
ANSWER: E
Answer: E
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 2 m high?
Options:
A)7
B)12.8
C)11
D)13
E)None
Rationale: Explanation:
d2 = 122 + 42 + 22 = 12.8
B)
Answer: B
Question: How many three letter words are formed using the letters of the word TIME?
Options:
A)20
B)55
C)76
D)24
E)42
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer: D
Answer: D
Question: A car travels first 160 km at 75 km/hr and the next 160 km at 70 km/hr. What is the average speed for the first 320 km of the tour?
Options:
A)71.11
B)71.12
C)72.4
D)71.17
E)71.13
Rationale: Car travels first 160 km at 75 km/hr
Time taken to travel first 160 km = distancespeed=160/75
Car travels next160 km at 70 km/hr
Time taken to travel next 160 km = distancespeed=160/70
Total distance traveled = 160+160=2×160
Total time taken = 160/75+160/70
Average speed = Total distance traveled/Total time taken=320/(160/75+160/70)=72.4 km/hr
Answer:C
Answer: C
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)12 days
C)14 days
D)16 days
E)18 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days
A)
Answer: A
Question: raghu, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
Options:
A)4/9
B)1/6
C)1/3
D)7/18
E)1/9
Rationale: Let's use smart numbers here -->Work=18
Rate * Time = Work
Tom: 3 x 6 = 18
Peter: 6 x 3 = 18
John: 9 x 2 = 18
Before John joined Tom and Peter: Tom worked 2 Hours -> 2*3=6 and Peter 1*6=6 gives us 12. So we are left with 18-12=6 for all three of them --> (3+6+9)*t=6, thus t=1/3 this means that Peter worked 2+1/3 Hours = 6+2=8 --> 8/18=4/9
At least this approach helps me... Don't like dealind with fractions when you're tired.
Answer:a
Answer: A
Question: Divide $ 1162 among A, B, C in the ratio 35 : 28 : 20.
Options:
A)490,490,490
B)360,392,460
C)490,382,280
D)260,160,60
E)492,390,280
Rationale: Sum of ratio terms = (35 + 28 + 20) = 83.
A's share = $ (1162 x (35/83))= $ 490; B's share = $ (1162 x(28/83))= $. 392;
C's share = $ (1162 x (20/83))= $ 280.
Option C
Answer: C
Question: What is the measure of the radius of the circle inscribed in a triangle whose sides measure 4, 11 and 12 units?
Options:
A)1.6 units
B)6 units
C)3 units
D)5 units
E)12 units
Rationale: Sides are 4, 11 and 12...thus it is right angle triangle Since 12^2 = 4^2 + 11^2
therefore, area = 1/2 * 11 * 4 = 22
We have to find in-radius
Therefore, area of triangle = S*r ....where S=semi-perimeter and r= in-radius
Now S=semi-perimeter = 12+11+4 /2 =13,5
Thus , 22 =13,5*r
and hence r=in-radius= 1.6
Option A
Answer: A
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Options:
A)23.56
B)23.54
C)23.51
D)23.52
E)23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer: E
Answer: E
Question: A garrison of 2000 men has provisions for 54 days. At the end of 21 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
Options:
A)1977
B)1893
C)1979
D)1900
E)1300
Rationale: 2000 ---- 54
2000 ---- 33
x ----- 20
x*20 = 2000*33
x = 3300
2000
-------
1300
Answer: E
Answer: E
Question: Carol is three times Alice’s age but only twice as old as Betty. Alice is twenty years younger than Carol. How old is Betty?
Options:
A)26
B)29
C)32
D)28
E)15
Rationale: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.
We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 3 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 20 years older than Alice
We're asked for BETTY'S age.
From the answer choices and the information provided, Carol can't be that old (The difference of 20 years = 3 times; that relationship can only occur when the numbers are relatively small). Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.
IF....
Betty = 15
Then Carol = 2(15) = 30
Then Alice = 30 - 20= 10 AND 30/3 = 10
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 15
E
Answer: E
Question: A pharmaceutical company received $3 million in royalties on the first $20 million in sales of and then $9 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
Options:
A)8%
B)15%
C)45%
D)52%
E)56%
Rationale: First ratio= 3/20=15%
second ratio = (3+12)/(9+108)=15/117= 12,8%
decrease = 2,2%
2,2%/15%=15% approximately.
ANSWER:B
Answer: B