divelab/Sys2Bench huggingface dataset:
Question: Find the least number of vans needed to transport a group of 98 sports fans who are travelling for a sporting event, given that each van can carry 7 persons only?
Options:
A)9
B)17
C)14
D)13
E)15
Rationale: To find the number of vans, we divide 98 by 7.
98/7 = 14 and no remainder
So 14 vans are needed to transport 98 fans
correct answer C
Answer: C
Question: From a pack of 52 cards, 1 card is drawn at random. What is the probability that a heart is drawn?
Options:
A)1/2
B)1/3
C)1/4
D)1/13
E)3/26
Rationale: The total number of cards is 52.
The number of hearts is 13.
P(heart) = 13/52 = 1/4
The answer is C.
Answer: C
Question: x is a positive integer less than 100. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
Options:
A)14
B)22
C)23
D)24
E)25
Rationale: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=100
n=14.42
or n= 14
Answer:- A
Answer: A
Question: A boat running up stram takes 5 hours to cover a certain distance, while it takes 8 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
Options:
A)2 : 3
B)5 : 6
C)4 : 5
D)7 : 1
E)13 : 3
Rationale: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
5(x+y) = 8(x-y)
5x+5y = 8x-8y
13y = 3x
x/y = 13/3
13 : 3
Answer: Option E
Answer: E
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings?
Options:
A)Rs.3600
B)Rs.3629
C)Rs.3279
D)Rs.3629
E)Rs.3283
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 18000
=> x = 3600
Savings = Income - expenditure
= 5x - 4x = x
So, savings =Rs.3600.
Answer: A
Answer: A
Question: A can do a job in 12 days and B can do it in 20 days. A and B working together will finish twice the amount of work in days?
Options:
A)22 1/6
B)22 1/2
C)22 1/0
D)15
E)22 1/1
Rationale: 1/12 + 1/20 = 8/60 = 2/15
15/2 = 15/2 *2 = 15 days
Answer: D
Answer: D
Question: When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3l
II. 4l+10
III. 5l
IV. 2l
V .6l
Options:
A)I
B)III
C)IV
D)V
E)II
Rationale: 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)300 kmph
B)360 kmph
C)600 kmph
D)720 kmph
E)None
Rationale: Explanation: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = 1200 x 3/5 km/hr = 720 km/hr.
Answer: Option D
Answer: D
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.77
B)5.7
C)5.76
D)5.78
E)5.71
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer: C
Answer: C
Question: A train 330 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options:
A)30 sec
B)32 sec
C)36 sec
D)38 sec
E)44 sec
Rationale: Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(330×2/15) sec=44 sec
ANSWER :E
Answer: E
Question: The average weight of 26boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
Options:
A)49.05
B)42.25
C)50
D)51.25
E)52.25
Rationale: Explanation:
Average weight of 26 boys = 50.25
Total weight of 26 boys = 50.25 × 26
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 26)+ (45.15 × 8)
Total boys = 26 + 8 = 34
Average weight of all the boys = (50.25×26)+(45.15×8)/34
=49.05
Answer: Option A
Answer: A
Question: If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?
Options:
A)a/2
B)b/2
C)(a+b)/2
D)(a+2)/2
E)(b+2)/2
Rationale: a−ba−b even --> either both even or both odd
abab even --> either both even or aa is even and bb is odd.
As both statements are true --> aa and bb must be even.
As abab is an even integer --> aa must be multiple of 4.
Options A is always even.
Options B can be even or odd.
Options C can be even or odd.
Options D: a+22=a2+1a+22=a2+1, as aa is multiple of 44, a2a2 is even integer --> even+1=odd. Hence option D is always odd.
Options E can be even, odd.
Answer: D.
Answer: D
Question: In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Don are not seated next to each other?
Options:
A)24
B)48
C)56
D)74
E)72
Rationale: When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....
These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
Answer :E
Answer: E
Question: Katherine invested a certain sum of money in a bank that paid simple interest. The amount grew to $350 at the end of 2 years. She waited for another 3 years and got a final amount of $425. What was the principal amount that she invested at the beginning?
Options:
A)$360
B)$380
C)$300
D)$280
E)$275
Rationale: What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $350
At the end of 5 years, Amount = $425
This means she earned an interest of $75 in 3 years. Or $25 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $50 in 2 years.
Hence Principal Amount = $350 - $50 = $300 Option C
Answer: C
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)138
B)100
C)999
D)928
E)982
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5
= 999
C
Answer: C
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87
Options:
A)80
B)82
C)92
D)98
E)91.25
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96
The median quiz score was 91.25. (Four quiz scores were higher than 91.25 and four were lower.)
E
Answer: E
Question: Find the least number of vans needed to transport a group of 189 people who are travelling for an event, given that each van can carry 13 persons only?
Options:
A)18
B)19
C)12
D)15
E)13
Rationale: To find the number of vans, we divide 189 by 13.
189/13 = 14 and remainder = 7
So 14 vans are needed to transport 189 persons, and 1 van is needed to transport the 7 remaining persons. A total of 15 vans are needed.
correct answer D
Answer: D
Question: A monkey ascends a greased pole 12 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
Options:
A)21st
B)22nd
C)23rd
D)24th
E)None of these
Rationale: In 2 minutes, he ascends = 1 metre
∴ 10 metres, he ascends in 20 minutes.
∴ He reaches the top in 21st minute.
Answer B
Answer: B
Question: Basmati rice costs $(a−b) per kilogram in standard 7 kilogram packages, where a>b>0, and $(a) per kilogram in non-standard packages. In terms of a and b, what is the lowest possible price of exactly 24 kilograms of Basmati rice, in dollars?
Options:
A)24a−3b
B)21a−3b
C)24a−21b
D)21a−21b
E)21a−24b
Rationale: $(a-b) per kg in standard 7kg packs and $a per kg in non std packs.
For 24 kg we can use 3 packs of 7 kg and 3 non std packs of 1 kg each.
Leading to 3*7*(a-b)+3a= 21a- 21b+3a=
24a-21b.
ANSWER:C
Answer: C
Question: Two coins are tossed. Find the probability of at most 2 tails ?
Options:
A)1/2
B)1/4
C)1/3
D)1
E)3/4
Rationale: n(s) = 2^2 = 4 ....(2 coins are tossed)
let E is the event of getting at most 2 tails
n(E) = HH, TT , HT, TH = 4
P(E) = n(E) / n(s)
= 4/4
= 1
Ans- D
Answer: D
Question: Patrick has a lock that contains a 3 digit password. He forgets the combination, but knows that he only used prime numbers for each digit in the combination and he did not repeat any numbers. How many different passwords could he possibly try before opening the briefcase?
Options:
A)6
B)12
C)15
D)18
E)24
Rationale: Permutation calc is: n P r = n! / (n-r)! 4 P 3 = 4!/(4-3)! = 4x3x2x1/1!=24/1=24 Correct answer is E (24)
Answer: E
Question: If a = 105 and a^3 = 21 × 25 × 45 × e, what is the value of e?
Options:
A)35
B)42
C)45
D)49
E)54
Rationale: a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × e
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x e
=> a^3 = 3^3 * 5^3 * 7 x e
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x e
e = 7^2 = 49
Answer D
Answer: D
Question: A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone will be :
Options:
A)8 cm
B)9 cm
C)10 cm
D)11 cm
E)None
Rationale: Sol.
Let the radius of the cone be r cm.
Then, 1/3 ∏ * r² * 6 = ∏ * 8 * 8 * 2
⇔ r² = [8 * 8 * 2 * 3 / 6] = 64
⇔ r = 8 cm.
Answer A
Answer: A
Question: The following sets each have a mean of 16 and the standard deviations are given in variable form.
Set I = {11, 13, 15, 17, 19, 21}, standard deviation = P
Set II = {16, 16, 16, 16, 16, 16}, standard deviation = Q
Set III = {10, 10, 10, 22, 22, 22}, standard deviation = R
Rank these three standard deviations from greatest to least.
Options:
A)P, Q, R
B)Q, R, P
C)R, P, Q
D)P, R, Q
E)R, Q, P
Rationale: The answer should be C as the mean is most deviated in Set III followed by Set I and then Set II.
Answer: C
Question: Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/4 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?
Options:
A)1/2
B)2/3
C)3/4
D)4/5
E)5/12
Rationale: Because we see H willbring 1/3 of his booksto the new home --> try to pick a number that isdivisible by 3.
Before:
Assume H = 30 books
H = 1/2 M --> M = 60 books
After:
H' = 1/3H = 10 books
M' = 1/4M = 15 books
Total = 25 books
M' = 25 =5/12*60
Ratio: 5/12
Ans: E
Answer: E
Question: If x is a sum of all even integers on the interval 23...65 and y is their number, what is the GCD (x, y)?
Options:
A) 1
B) 21
C) 26
D) 52
E) 1014
Rationale: x = 24 + 16 + ... + 64 = (largest + smallest)/2 *(# of terms) = (24 + 64)/2*21= 44*16.
GCD of 21 and 44*21 is 21.
Answer: B.
Answer: B
Question: To reach her destination, Jeanette must drive 90 miles. If she drives 7 miles every 7 minutes, how much time will it take her to reach her destination?
Options:
A)2 hours and 2 minutes
B)1 hours and 30 minutes
C)2 hours and 10 minutes
D)2 hours and 12 minutes
E)2 hours and 15 minutes
Rationale: 7 minute for 7 miles how much for 90? minutes for 1(7/7) mile multiplied by 90 miles.
7*90/7= 90> 1 hours 30 min answer is B
Answer: B
Question: In the diagram below, the points P and Q are the midpoints of opposite sides
of a regular hexagon. What fraction of the hexagon is shaded?
Options:
A)2/3
B)3/4
C)5/6
D)7/8
E)11/12
Rationale: Assume the hexagon has side length b. The total area of the hexagon is then 6 times
the area of a equilateral triangle side-length b; this is, 6bh=2 = 3b2
p
3. The area of the shaded
quadrilateral can be seen as the addition of the area of two isosceles triangles with base 2b
and height
p
3b=2. The requested fraction is then 2=3.
correct answer A
Answer: A
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
Options:
A)14
B)27
C)32
D)22
E)17
Rationale: D
22
This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.
Answer: D
Question: A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price p. The store sold the first 150 copies in the first week at 80% more than p, and then over the next month, sold a 100 more at 20% more than p. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than p. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
Options:
A) 30% loss
B) 10% loss
C) 10% profit
D) 20% profit
E) 60% profit
Rationale: [[p(150)(1.8)+p(100)(1.2)+p(150)(0.6)]/400p] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D
Answer: D
Question: Fresh grapes contain 80% water by weight, whereas dried grapes contain
15% water by weight. How many pounds of dried grapes can be obtained
from 34 pounds of fresh grapes?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Suppose we call what’s left from a grape after removing all water “waterless
content”. Then 34 pounds of fresh grapes contain 6.8 pounds “waterless content”. Also,
x pounds dried grapes contain x−0.15x = 0.85x pounds “waterless” content”. Solving
the equation 0.85x = 6.8 we get x = 8.
correct answer A
Answer: A
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
A)7 1/8
B)7 1/6
C)7 1/5
D)7 1/2
E)7 1/1
Rationale: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 1/2 sec
Answer: D
Answer: D
Question: How many cases do you need if you have to pack 112 pairs of shoes into cases that each hold 28 shoes?
Options:
A)4
B)9
C)8
D)4
E)5
Rationale: C
8
112 pairs of shoes = 224 shoes.
224 ÷ 28 = 8.
Answer: C
Question: The concentration of spirit in three different vessels A, B and C are 45%, 30% and 16% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
Options:
A)32.10%
B)33.60%
C)34%
D)28.40%
E)36%
Rationale: Quantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*16/100)=1.8+1.5+1.5=4.26 liters
So % concentration of spirit=100*4.26/(4+5+6)=28.40%
ANSWER:D
Answer: D
Question: In a BCCI meeting there are 13 people. All shake hands with each other once. How many handshakes will be there altogether?
Options:
A)28
B)12
C)13
D)19
E)18
Rationale: There will be n-1 handshakes as A person will shake hands with all the other members.
=13-1=12
Answer:B
Answer: B
Question: Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 5 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
Options:
A)15/23
B)25/33
C)35/43
D)45/53
E)55/63
Rationale: P(no pairs) = 10/11*8/10*6/9*4/8 = 8/33
P(at least one pair) = 1 - 8/33 = 25/33
The answer is B.
Answer: B
Question: If MELT is coded as 54 and WATER is coded as 42, then PRESSED is coded as
Options:
A)39
B)44
C)48
D)56
E)None
Rationale: MELTS = 13+5+12+20+19=69 i.e 6*9=54
WATER= 23+1+20+5+18=67 i.e 6*7=42
PRESSED= 16+18+5+19+19+5+4=86 8*6=48
ANSWER:C
Answer: C
Question: A guy was asked to specify his age in years. He said, “Take my age 7 years hence, multiply it by seven and subtract seven times of my age 7 years ago and get the half of the result , you will know my age.” What was the age of that guy?
Options:
A)18
B)25
C)33
D)49
E)60
Rationale: Current age of the guy = A years.
Then, 7 (A + 7) – 7 (A – 7) = A
(7A + 49) – (7A – 49) = A
A = 98/2=49
D
Answer: D
Question: There are two bridges running parallel over river Kauvery, and they are 1 KM apart. A man started rowing the boat upstream under first bridge, his hat fell into river while he was exactly under second bridge. He realized that after 15 mts, and started rowing in opposite direction, he eventually caught his hat under First Bridge. What is the speed of river Kauvery?
Options:
A)5km/h
B)4km/h
C)3km/h
D)1km/h
E)2km/h
Rationale: Let the upstream velocity=xkm/h
so he goes first 1 km then 15 min with this velocity
so total goes=x*15/60+1 km=x+4/4 km
and now he in downstream cover this distance in 15 min
so his downstream velocity=x+4/4*15=x+4/60
now speed of river=1/2[downstream speed-upstream speed]
=1/2[x+4/60-x/60]km/min
=2km/h
ANSWER:E
Answer: E
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Options:
A)180
B)190
C)120
D)130
E)140
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: Option B
Answer: B
Question: Profit earned by an organization is distributed among officers and clerks in the ratio of 5:3 respectively. If the number of officers is 45 and the number of clerks is 80 and the amount received by each officer is Rs.25,000/-, what was the total amount of profit earned?
Options:
A)Rs.22 lakhs
B)Rs.18.25 lakhs
C)Rs.18 lakhs
D)Rs.23.25 lakhs
E)None ot these
Rationale: Explanation:
The total amount distributed among 45 officers = Rs.45x25000 = Rs.1125000.
Let the amount distributed to 80 clerks be ‘x’.
Then 1125000/x = 5/3, therefore, x = Rs.675000.
Therfore, the Total profit = Rs.1125000 + 675000 = Rs.18 lakhs
Answer: Option C
Answer: C
Question: The traffic lights at 3 different roads change after every 12 sec, 15 sec, 21 sec respectively. If they all change simultaneously at 8 AM then at what time will they again change simultaneously.
Options:
A)8:15
B)8:42
C)8:07
D)9:01
E)9:15
Rationale: LCM of 12,15,21 = 420 = 7mnts
The lines will change every 7m
The light will change again after 8 AM is = 9:00+0:07 = 8:07
Answer is C
Answer: C
Question: A sum of Rs. 2500 amounts to Rs. 3875 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)12.25%
B)12%
C)6%
D)13.75%
E)13.95%
Rationale: Explanation :
Simple Interest, SI = (3875 - 2500) = Rs.1375
Principal, P = Rs. 2500
Time, T = 4 years
R = ?
R=100×SI/PT
=100×1375/2500×4
100×1375/10000
=13.75%
Answer: D
Question: If Rs. 782 is divided into three parts, proportional to
1/2:2/3:3/4
Options:
A)190
B)204
C)220
D)230
E)250
Rationale: Explanation:
1/2:2/3:3/4
=6:8:9
First part =782∗6/23
=204
ANSWER IS B
Answer: B
Question: Share Rs.6600 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
Options:
A)2200
B)980
C)1200
D)1240
E)1400
Rationale: Amount received by sanjay.
4 / 12 X 6600 = 2200= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 2200.
A
Answer: A
Question: John earned 40% more per month than Oscar. If john salary is decreased 10% and Oscar’s salary is increased by 10%, then john would be earning what percent more than Oscar?
Options:
A)10%
B)9.09%
C)15.54%
D)14.54%
E)It cannot be determined from the information given.
Rationale: This Q is all about taking the correct BASE for taking %s..
the very first step requires taking some numbers for each..
ONE should be 100...
it is easy to take 60 and 100 here..
but the BASE is 100 here, so the salary can be 100 and 140..
100 increases 10% =110..
140 decreases 10%=126..
so the increase is 16..
again the BASE is 110, so answer 16/110 * 100= 14.54% C
without calculations,
answer cannot be equal to or greater than 16, as 16 is on 110..
so D is the only one left
Answer: D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 216 km/hr?
Options:
A)2.5 sec
B)2.9 sec
C)1.7 sec
D)7.5 sec
E)2.4 sec
Rationale: Speed = 215 * 5/18 = 60 m/sec
Time taken = 100/60
= 1.7 sec.
Answer: C
Answer: C
Question: There is a 30% chance Sandy will visit China this year, while there is a 60% chance that she will visit Malaysia this year. What is the probability that Sandy will visit either China or Malaysia this year, but NOT both?
Options:
A)42%
B)48%
C)54%
D)60%
E)66%
Rationale: P(China and not Malaysia) = 0.3*0.4 = 0.12
P(Malaysia and not China) = 0.6*0.7 = 0.42
Total probability = 0.12 + 0.42 = 0.54 = 54%
The answer is C.
Answer: C
Question: The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 88, and last 6numbers is 65 then find 6th number?
Options:
A)A)258
B)B)65
C)C)58
D)D)62
E)E)48
Rationale: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*88+6*65-11*60 = 258
Answer is A
Answer: A
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)7
B)4
C)9
D)3
E)1
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer:B
Answer: B
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Options:
A)2400
B)2880
C)2787
D)3087
E)0728
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: A
Question: If x^3 is divisible by 240 what is the least possible value of integer x?
Options:
A)12
B)30
C)60
D)90
E)120
Rationale: 240 can be written as (2^4)*3*5.
For k^3 to be divisible by 240 it should contain atleast 2^4 and 3 and 5 in its factors. We can leave out option A because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^3 will have 3 as the maximum power of 2, so we can leave out this option too.
Option C is the right answer if we follow the same method as we followed for other two previous options.
60 = (2^2)*3*5; 60^3 = (2^6)*(3^3)*(5^3). So it shows that 60^3 is divisible by 240 and hence the answer.
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 5 muffins remained. How many guests did Monica plan on?
Options:
A)9.
B)4.
C)3.
D)6.
E)7.
Rationale: 5N +2 = 5 + 6(N-1)
Solving N= 3
Hence C
Answer: C
Question: What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
Options:
A)Rs.2592
B)Rs.2492
C)Rs.2352
D)Rs.2382
E)Rs.2362
Rationale: The usual way to find the compound interest is given by the formula A = .p(1+r/100)^n
In this formula,
A is the amount at the end of the period of investment
P is the principal that is invested
r is the rate of interest in % p.a
And n is the number of years for which the principal has been invested.
In this case, it would turn out to be A =1500(1+20/100)3
= 2592. Answer: A
Answer: A
Question: If xy ≠ 0 and x^2y^2 − xy = 30, which of the following could be y in terms of x?
I. 6/x
II. -5/x
III. 3/x
Options:
A)I only
B)II only
C)I and II only
D)I and III
E)II and III
Rationale: (x^2)(y^2) – xy - 30 = 0
(xy – 6)(xy + 5) = 0
xy – 6 = 0 or xy + 5 = 0
xy = 6 or xy = -5
Since we need y in terms of x, we can isolate y in both of our equations.
y = 6/x or y = -5/x
Answer: C
Answer: C