divelab/Sys2Bench huggingface dataset:
Question: To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of Y dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
Options:
A)Y/T
B)Y/(T-S)
C)SY/(T-S)
D)SY/T(T-S)
E)Y(T-S)/T
Rationale: Since no absolute values are given in the question we can replace the given parameters with assumed numbers,
Let Total colleagues be 100 (T)
Let total contribution be 600 (Y) (point to note is that its total cost not per person)
Those who dont pay are S (30)
Per person cost = Y/T = 600/100 = 6
So cost for those who failed to pay = (Y/T) * S = SY/T = 30*6=180
The equation for people who would bear the total cost after S people fail = (T-S)=70
There fore the solution is (SY/T)/ (T-S) = SY/T(T-S) = 180/70
Answer D
Hope this helps !!!
Answer: D
Question: The ratio of two quantities is 2 : 3. If each of the quantities is increased by 6, what is the ratio of the new quantities?
Options:
A)2 : 3
B)6 : 7
C)8 : 9
D)8 : 3
E)It cannot be determined from the information given
Rationale: let quantities are 2x and 3x
ratio of quantities after each is increased by 6 = (2x+6)/(3x+6)
For x = 1, (2x+6)/(3x+6) = 8/9
For x = 2, (2x+6)/(3x+6) = 10/12
The value of final expression is dependent on the value of x which can't be determined as per given information. Hence, The answer can not be determined
Answer: Option E
Answer: E
Question: If $1000,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
Options:
A)10,000(x^n)
B)10,000(x/100)^n
C)10,000n(x/100)
D)1,000,000n(x/100)
E)10,000n(1+x/100)
Rationale: I think answer D is for compound interest (which i assumed)
and answer D is for simple interest because it is not compounding.
Answer: D
Question: How many bricks each measuring 30cm x 12cm x 10cm, will be needed to build a wall 6m x 4m x 20.5m
Options:
A)5655
B)1366
C)6444
D)7266
E)None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (600 x 400 x 20.5) / (30 x 12 x 10) = 1366
Answer: B
Answer: B
Question: A and B starts a business with Rs.8000 each, and after 5 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Options:
A)18:11
B)22:13
C)23:12
D)36:23
E)11:10
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 5 months and then withdraws Rs.4000. So, the investment of B for remaining 13 months is Rs.4000 only.
A : B
8000*18 : (8000*5) + (4000*13)
144000 : 92000
A:B = 36:23
ANSWER:D
Answer: D
Question: When 1/10 percent of 1,000 is subtracted from 1/10 of 1,000, the difference is
Options:
A)10
B)100
C)999
D)99
E)9
Rationale: (1/10)*1000 - (1/10)%*1000 =
100 - (1/1000)*1000 =
100 - 1 = 99
The answer is D.
Answer: D
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:8
B)3:4
C)3:5
D)3:2
E)3:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer:B
Answer: B
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)9 a.m.
B)10 a.m.
C)10.30 a.m.
D)11 a.m.
E)11.30 a.m
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m.
Answer: Option B
Answer: B
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)11
B)16
C)18
D)10
E)14
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer:B
Answer: B
Question: Quarters (US $ 0.25) are stacked in 18 columns. The first column has 10 quarters and each subsequent column has 3 quarters more than the previous column. Find the total number of quarters.
Options:
A)648
B)630
C)578
D)639
E)646
Rationale: Number of coins in the 18 columns forms an AP with first number 10 and last 61
Avg is 35.5 and the total number of coins is 35.5*18
Answer is D
Answer: D
Question: In a room are five chairs to accommodate 3 people, one person to a chair. How many seating arrangements are possible?
Options:
A)45
B)60
C)72
D)90
E)120
Rationale: I actually solved this problem by the following thoughts (derived from factorials):
First Person: 5 Chairs to choose
Second Person: 4 Chairs to choose
Third Person: 3 Chairs to choose
Then I simply multiplied this values and got the answer. Basically it’s 5! – 2!.=60
Answer: B.
Answer: B
Question: A can do a job in 15 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?
Options:
A)20
B)22 1/2
C)22 1/0
D)22 1/9
E)22 1/1
Rationale: 1/15 + 1/30 = 3/30 = 1/10
10= 10 *2 = 20 days
Answer: A
Answer: A
Question: A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)50%
B)40%
C)60%
D)70%
E)45.45%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50
Now, we need to calculate 50 is what percent of 110.
=> 50/110 x 100 = 45.45 %
ANSWER:E
Answer: E
Question: For integers x and y, when x is divided by y, the remainder is odd. Which of the following statement is not wrong?
Options:
A)x is odd
B)xy is odd
C)x and y share no common factors other than 1
D)either integer x or integer y is odd
E)The sum x + y is odd
Rationale: either integer x or integer y is odd
D
Answer: D
Question: A miniature roulette wheel is divided into 9 equal sectors, each bearing a distinct integer from 1 to 9, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun three times, approximately what is the probability that the product of the three winning sectors’ integers will be even?
Options:
A)50%
B)67%
C)83%
D)90%
E)96%
Rationale: The only way to have an odd product is if all 3 integers are odd.
P(odd product) = 5/9*5/9*5/9 = 125/729
P(even product) = 1 - 125/729 = 604/729 which is about 83%
The answer is C.
Answer: C
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability T that exactly two visitors will buy a pack of candy?
Options:
A)0.343
B)0.147
C)0.189
D)0.063
E)0.027
Rationale: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=T
Answer - C
Answer: C
Question: Find the average of all the numbers between 9 and 26 which are divisible by 5.
Options:
A)15
B)19
C)18
D)22
E)None
Rationale: Sol.
Average = (10 + 15 + 20 + 25 / 4) = 70 / 4 = 17.5
Answer C
Answer: C
Question: Reduce 4128/4386 to its lowest terms
Options:
A)14/13
B)13/17
C)16/17
D)13/18
E)None of these
Rationale: Explanation:
HCF of 4128 and 4386
4128)4386(1
4128
-----
258)4128(16
4128
----
0
Hence HCF of 4128 and 4386 is 258.
4128/258 = 16
4386/258 = 17
4128/4386 = 16/17
Answer: Option C
Answer: C
Question: If xy+5z = x(y+z), which of the following must be true?
Options:
A)1. x=0 and z=0
B)2. x=5 and z=0
C)3. y=1 and z=0
D)4. x=1 or y=0
E)5. x=1 or z=0
Rationale: xy+5z=x(y+z)
xy+5z=xy+xz
5z=xz
it means x=5 or z=0
Answer B
Answer: B
Question: There are 23 balls in a box: 10 balls are green, 8 are blue and 5 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?
Options:
A)7/21
B)4/13
C)3/13
D)5/13
E)6/13
Rationale: If 1 green and 1 blue ball are taken from the box, then there are 9 green, 7 blue and 5 white balls, a total of 21 balls. If one ball is selected at random, the probability that it is blue is given by 7 / 21
Answer : A
Answer: A
Question: Find the value of y from (12)^3 x 6^4÷432 = y?
Options:
A)5618
B)5232
C)5889
D)5184
E)5132
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
D
Answer: D
Question: Express Airlines has a transcontinental flight between Big City and Urbana - a distance of 1,500 km that it completes in three hours. Akatsuki is going from her home in Urbana to a convention in Big City that starts 5 hours after her plane leaves for Big City and ends 6 hours later. Akatsuki's plane suffers a mechanical failure and is forced to land at the Middlebrook airport, located 750 km away from both Big City and Urbana. What's the longest amount of time that Akatsuki can wait for repairs before she misses her convention?
Options:
A)10.5 hours
B)6 hours
C)5 hours
D)4.5 hours
E)3 hours
Rationale: Airplane's rate of speed: 1,500/3 = 500 km/h
Distance between Middlebrook and Big City: 750 km
Travel time between Middlebrook and Big City/Urbana: 750/500 = 1.5 hours
Time into flight: 1.5 hours.
Time until convention begins: 5 - 1.5 = 4.5 hours
Time until convention ends: 4.5 + 6 = 10.5 hours
IMO, the correct answer is "A."
Answer: A
Question: Compute the number of distinct line segments that can be drawn inside a square such that
the endpoints of the segment are on the square and the segment divides the square into two
congruent triangles.
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: Cutting along opposite corners are the only valid ways, so there are 2 such pairs.
correct answer D
Answer: D
Question: If v is an integer, which of the following must be an even integer?
Options:
A)v^2-v-1
B)v^2-4v+6
C)v^2-5v+5
D)v^2+3v+8
E)v^2+2v+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: v^2-v-1 = -1 { If v = 1 }
B: v^2-4v+6 = 3 { If v = 1 }
C: v^2-5v+5 = 1 { If v = 1 }
D: v^2+3v+8 = 12 { If v = 1 }v^2+3v+8 = 18 { If v = 2 }
E: v^2+2v+10 = 13 { If v = 1 }
Thus the only possible answer is (D)
Answer: D
Question: Varma can read a book in k minutes. What part of the book can he read in 12 minutes?(k>12)
Options:
A)(k - 8)/k
B)k/8
C)8 + k
D)12/k
E)8/k
Rationale: Option D
Explanation:
Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 12 minutes =12/k.
Answer: D
Answer: D
Question: Remainder of (6^17+17^6)/7= ?
Options:
A)2
B)1
C)0
D)3
E)4
Rationale: 6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7
17^6/7 = (2*7+3)^6/7 = 3^6/7 = 27^2/7 =(4*7-1)^2/7 =(-1)^2/7 = 1/7
so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0
ANSWER:C
Answer: C
Question: A certain pilot flew 400 miles to City K at an average speed of 450 miles per hour with the wind and made the trip back at an average speed of 250 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?
Options:
A)280
B)290
C)300
D)310
E)320
Rationale: Avg speed = total distance/ total time
total distance = 800
total time = 400/450 + 400/250 = 112/45
=> avg speed = (800*45)/112 = 320(approx)
ans is E
Answer: E
Question: In a bag there are 3 Snicker's bars and 2 Milky Way bars. What is the probability of choosing at least one Snickers when choosing two consecutive candy bars randomly?
Options:
A)9/10
B)16/20
C)2/5
D)3/5
E)½
Rationale: P(at least one Snicker's Bar) = 1 - P(no Snicker's Bar, so 2 Milky Way Bars) = 1- 2/5*1/4 = 9/10.
Answer: A.
Answer: A
Question: The number of permutations of the letters of the word 'MESMERISE' is?
Options:
A)9!/(2!)2 3!
B)9!/(2!)2 8!
C)9!/(8!)2 3!
D)8!/(2!)2 3!
E)9!/(2!)2 1!
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!
Answer: A
Answer: A
Question: A password for a computer is six digits from 0 and 9. The six digit number is a prime number. What is the approximate probability that the last digit is a 3?
Options:
A)1/4
B)1/6
C)1/10
D)1/20
E)1/50
Rationale: If the last digit is 0, 2, 4, 6, or 8, the number is even and therefore not prime. If the last digit is 5, the number is divisible by 5 and therefore not prime. The only possibilities are 1, 3, 7, and 9. So the probability is approximately 1/4 (answer A). We say approximately because there is a certain degree of randomness in the distribution of prime numbers.
Answer: A
Question: The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ?
Options:
A)10,12
B)10,16
C)10,18
D)10,19
E)10,91
Rationale: Explanation:
Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
let the price of one book be Rs. x
Then, the price of other book = Rs. (x + 60% of x) = Rs. = Rs.
So,
The prices of the two books are Rs. 10 and Rs. 16
Answer: B) 10,16
Answer: B
Question: A train covers a distance of 15 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
Options:
A)240m
B)150 m
C)120 m
D)200 m
E)165 m
Rationale: Speed = (15/10 * 60) km/hr
= (90 * 5/18) m/sec
= 25 m/sec.
Length of the train
= 20 * 10
= 200m.
Answer: D
Answer: D
Question: If |4x+2| = 46, what is the sum of all the possible values of x?
Options:
A)2
B)-1
C)4
D)-5
E)6
Rationale: There will be two cases
4x+2= 46 or 4x+2 = -46
=> x =11 or x= -12
sum of both the values will be -12 +11 = -1
Answer is B
Answer: B
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 5 years?
Options:
A)45 years
B)42 years
C)40 years
D)37 years
E)None of the above
Rationale: 2+3+4=9
4*(90/9)=40yrs
after 5yrs=45
ANSWER:A
Answer: A
Question: Profit of one hospital is 320 percent of the cost. If the cost increases by 25 % but the SP is same, approximately what % of the SP is the profit?
Options:
A)40%
B)45%
C)50%
D)70%
E)75%
Rationale: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage = 295	x 100	%	=	1475	% = 70% (approximately).
420	21
D
Answer: D
Question: (1000)7÷(10)20=?
Options:
A)10
B)100
C)1000
D)10000
E)None of these
Rationale: Explanation:
=(103)7/(10)20
=(10)21/(10)20=10(1)=10
Option A
Answer: A
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 8. What is the radius of circle O?
Options:
A)–2/pi
B)2
C)3
D)4
E)5
Rationale: pi*r^2 + 2r -2*pi*r = 8
Simplifying the equation: pi*r(r-2)+2r=8
Without much algebraic: We can Test the answers quickly, then 4 is the only possible answer that will eliminate pi from equation.
Answer is D
Answer: D
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
Options:
A)4/16
B)4/17
C)4/11
D)4/13
E)4/12
Rationale: P(SᴜK)
= P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK)
= 13/52 + 4/52 - 1/52
= 4/13
Answer:D
Answer: D
Question: There are 35 students in a hostel. If the no. of students increases by 5, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
Options:
A)s. 64.80
B)s. 69.80
C)s. 72.80
D)s. 78.80
E)s. 79.80
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 5) = x – 1
or, 35x + 42 = 40x – 40
or, x = 16.4
Thus the original expenditure of the mess = 35 x 16.4=574
Therefore x-1 = 15.4
hence 42 x 15.4 =646.80
646.80 - 574 = Rs. 72.80
C
Answer: C
Question: When the price of an article was reduced by 20% its sale increased by 80%. What was the net effect on the sale?
Options:
A)44% increase
B)44% decrease
C)60% increase
D)66% increase
E)66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 20%, the new price is 0.8p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.8p)(1.8n) = 1.44np, which is 1.44 times the old revenue, so is 44% greater.
ANSWER:A
Answer: A
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
Options:
A)9
B)10
C)12
D)18
E)14
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: Option C
Answer: C
Question: A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton, how many kilos did he consume on the sixth hour?
Options:
A)38
B)43
C)50
D)53
E)62
Rationale: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 360/9 = 40, so the median is also 40, and that is the amount eaten in the 5th hour. We need to add 3 to find the total eaten in the next hour, so the answer is 43.
option B
Answer: B
Question: A, B and C have Rs.350 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)A)200
B)B)190
C)C)180
D)D)170
E)E)160
Rationale: A+B+C = 350
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 350
----------------
C = 200
Answer:A
Answer: A
Question: Xavier starts from P towards Q at a speed of 90 kmph and after every 12 mins increases his speed by 10 kmph. If the distance between P and Q is 51km, then how much time does he take to cover the distance?
Options:
A)30
B)32
C)30
D)36
E)40
Rationale: first 12min = 90 *12/60 =18km
2nd 12min = 100*12/60 =20km
3rd 12 min = 110*12/60 = 22 km
TOTAL time 12 *3 = 36 min
D
Answer: D
Question: The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 4 revolutions ? (use Ï€ = 22â„7)
Options:
A)35.2 m2
B)44 m2
C)48 m2
D)36 m2
E)None of these
Rationale: Required area covered in 5 revolutions
= 4 Ã— 2Ï€rh = 4 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 2 = 35.2 m2
Answer A
Answer: A
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is?
Options:
A)1/50
B)1/13
C)1/26
D)1/52
E)1/4
Rationale: Probability of a spade = 13/52 = 1/4
Probability of a jack = 4/52 = 1/13
Probability of both = P1*P2 = 1/(4*13) = 1/52
Answer is D.
Answer: D
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)17%
B)62%
C)12%
D)19%
E)22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: C
Question: How many times are the hands of a clock at right angle in 2 days?
Options:
A)80
B)82
C)84
D)86
E)88
Rationale: In 1 day, they are at right angles 44 times.
In 2 days, they are at right angles 88 times. Answer: Option E
Answer: E
Question: The compound interest on Rs.2800 for 1 1/2years at 10% per annum is
Options:
A)Rs.441.35
B)Rs.436.75
C)Rs.434
D)Rs.420
E)None
Rationale: Explanation:
Amount = Rs.[[2800×(1+10/100)](1+5/100)]
= Rs.[2800×11/100×21/20]= Rs.3234
C.I = Rs.(3234-2800)= Rs.434
Correct Option: C
Answer: C
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)1/15
B)31/32
C)1/10
D)30/32
E)25/27
Rationale: Probability of getting least one tail at the coin tossed five times.
= There is not even a single tail.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER B
Answer: B
Question: The price of a car is marked at $11,000. If the car has successive discounts of 20%, 15% and 5%, then at what price does a customer buy the car?
Options:
A)$6702
B)$6924
C)$7106
D)$7348
E)$7580
Rationale: 0.95*0.85*0.8*11000 = $7106
The answer is C.
Answer: C
Question: Six students - 3 girls and 3 boys - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two girls and no two boys can sit next to one another?
Options:
A)A)12
B)B)36
C)C)72
D)D)240
E)E)720
Rationale: in order not to have two girlss or two boys next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B).
Total ways = 2C1*3!*3!
=2*6*6
=72
Ans - C
Answer: C
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $300, by what percent is the price to be reduced?
Options:
A)10%
B)15%
C)20%
D)60%
E)30%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $300
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (300)*100 / 500 = 60%
Answer: Option D
Answer: D
Question: What is the smallest positive integer that can be multiplied by 432 to make it a perfect square?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: 432=2^4*3^2*3
Therefore the smallest integer to multiplied to 1008 to make it a perfect square is 3.
Answer B.
Answer: B
Question: Obra drove 120π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
Options:
A)6.67%
B)12.5%
C)18.75%
D)25%
E)33.3%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 120π/480π =25%
Hence, answer is D.
Answer: D
Question: Difference of two numbers is 1650. If 7.5% of the number is 12.5% of the other number , find the number ?
Options:
A)2660, 1000
B)3660, 2000
C)3000, 4160
D)2490, 4150
E)2475, 4125
Rationale: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1650
5*y/3 –y =1650
2*y/3= 1650
y =[ (1650*3)/2] =2475.
One number = 2475, Second number =5*y/3 =4125.
Answer E.
Answer: E
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 4-letter code words?
Options:
A)20
B)30
C)35
D)40
E)45
Rationale: Method #1: Using the permutation formula
# of 6 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 6)! = 10*9*8*7*6*5
# of 4 letter code words:
nPr = 10! / (10 – 4)! = 10*9*8*7
# of 5 words / # of 4 words = (10*9*8*7*6*5)/(10*9*8*7) = 30
B
Answer: B
Question: A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 25% of the length of the race?
Options:
A)35%
B)48%
C)52%
D)42%
E)46%
Rationale: First calculate the distance, B has covered with his speed in the time, in which A reached 80% of the race.
Then Add the remaining distance as head start for B to win the race.
Its best to apply Ratios concept here.
Since A's speed is 15/13 of B, therefore, B's speed is 13/15 of A
Distance covered by B = speed x time = (13/15) x (0.75) = 0.65%
(Which means B would have covered 0.65 of the race length during the time in which A has covered 0.75 of the race length.
Therefore to win, B needs a headstart of (1 - 0.65 = ) 0.35 of the race length.
So the answer is A
Answer: A