divelab/Sys2Bench huggingface dataset:
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets W did Irwin score?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored W=2 11-point baskets in my opinion.
Answer C
Answer: C
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
Options:
A)3/9
B)2/4
C)1/3
D)4/6
E)4/7
Rationale: . Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Ans: C
Answer: C
Question: Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done
Options:
A)2 x 12C6 x (6!)2
B)2 x 6! x 6!
C)2 x 12C6 x 6!
D)2 x 6! x 8!
E)none of these
Rationale: First select 6 people out of 12 for the first row.
The other six automatically get selected for the second row.
Arrange the two rows of people amongst themselves. Besides, the papers can be given a pattern of 121212 or 212121.
Hence the answer is 2 x 12C6 x (6!)2
ANSWER:A
Answer: A
Question: A train crosses a platform of 90 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)A)150m
B)B)170m
C)C)180m
D)D)158m
E)E)390m
Rationale: Length of the train be ‘X’
X + 90/15 = X + 250/20
4X + 360 = 3X + 750
X = 390m
Answer: E
Answer: E
Question: The total age of A and B is 16 years more than the total age of B and C. C is how many year younger than
Options:
A)14 years
B)12 years
C)56 years
D)16 years
E)55 years
Rationale: Given that A+B = 16 + B + C
=> A â€“ C = 16 + B â€“ B = 16
=> C is younger than A by 16 years
Answer:D
Answer: D
Question: Calculate the share of X , if Rs. 1628 is divided among X, Y and Z in the ratio 2 : 3 : 5?
Options:
A)321.6
B)325.6
C)305.6
D)125.6
E)225.6
Rationale: 2 + 3 + 5 =10
1628/10=162.8
so X's share=2*162.8
=325.6
ANSWER:B
Answer: B
Question: Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 38 miles per hour. How many miles from the station was train A overtaken by train B?
Options:
A)205
B)245
C)285
D)325
E)365
Rationale: After two hours, Train A is ahead by 60 miles.
Train B can catch up at a rate of 8 miles per hour.
The time to catch up is 60/8 = 7.5 hours.
In 7.5 hours, train A travels another 30*7.5 = 225 miles for a total of 285 miles.
The answer is C.
Answer: C
Question: If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ?
Options:
A)9
B)11
C)12
D)13
E)10
Rationale: E
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1
Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)
Answer: E
Question: The entire contents of a full sack of flour can be used to make 15 cupcakes and 8 pizzas. The same full sack of flour can be used to make 3 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?
Options:
A)18 1/4
B)15 1/2
C)18 3/4
D)19
E)19 1/4
Rationale: 15x+8y=3x+14y
x=1/2y. Answer B
Answer: B
Question: How many integerskgreater than 100 and less than 800 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Numbers will be like 102 => 201 = 102 + 99
203 => 302 = 103 + 99
so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit.
There will be six pairs of such numbers
for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.
Total = 6 *10 = 60 hence B.
Answer: B
Question: A table is bought for Rs.600/- and sold at Rs.700/- find gain or loss percentage
Options:
A)25% loss
B)30% gian
C)25% gian
D)30% loss
E)45% gain
Rationale: Explanation:
Formula = (Selling price ~ Cost price)/Cost price * 100
= (700 - 600)/400 = 25% gain
Answer: Option C
Answer: C
Question: A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is
Options:
A)100m
B)120m
C)140m
D)160m
E)170cm
Rationale: Explanation:
Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.
Length of the train = (Speed x Time) = (20 x 6) m = 120 m
Answer: Option B
Answer: B
Question: Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
Options:
A)4000
B)5000
C)6000
D)7000
E)8000
Rationale: 10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90 = 15 * 2 * x => x = 6000
ANSWER:C
Answer: C
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)25 cm2
B)42 cm2
C)49 cm2
D)70 cm2
E)None of these
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
ANSWER:E
Answer: E
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
Options:
A)34
B)28
C)12
D)17
E)15
Rationale: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
ANSWER:B
Answer: B
Question: A train covers a distance of 280 km in 4 hrs. What is its speed?
Options:
A)70 km/hr
B)60 km/hr
C)50 km/hr
D)40 km/hr
E)80 km/hr
Rationale: Distance covered =280 km. Time taken =4 hrs. Speed =Distance/time =280/4 km=70 km/hr. Answer : A
Answer: A
Question: The perimeter of a square circumscribed about a circle of radius r is:
Options:
A)2r
B)4r
C)6r
D)9r
E)8r
Rationale: Each side of the square = 2r
Perimeter of the square = (4×2r) = 8r
Answer is E.
Answer: E
Question: A certain quantity of 65% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
Options:
A)1:3
B)1:2
C)2:3
D)2:1
E)3:1
Rationale: 25% - - - - - - - - - 35% - - - - - - 65%
From 25 to 35 =10
From 35 to 65 = 30
So the ratio is 10/30 = 1 to 3
E it is
Answer: E
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 6 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 2 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
Options:
A)16:00.
B)18:00
C)20:00
D)22:00.
E)24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 6 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 2 hours
Time taken by both buses to meet again in St. Louis will be LCM of 6 and 2 = 6
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Answer: B
Question: In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Options:
A)5 km/h
B)8 km/h
C)10 km/h
D)15 km/h
E)20 km/h
Rationale: Let A's speed be X km/hr.
Then, 30/x - 30/2x = 3
6x = 30
x = 5 km/hr.
Answer : A
Answer: A
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)6.5
B)6.25
C)6.75
D)6.0
E)7.25
Rationale: Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 40
Run rate needed = 25040=6.25
Answer is B.
Answer: B
Question: If three sides of the triangle are 8 , 15 and D respectively then the how many values can D ?
Options:
A)[A] 6
B)[B] 7
C)[C] 8
D)[D]9
E)[E] infinite number of values
Rationale: Needed: How many Values can D take
Concept: Sum of any two sides of a triangle is greater then the third side.
Case 1: 8+5 > D => D<13
Case 2: 5+D > 8 => D >3
Case 3: 8+D > 5 => D > -3 (Always true since D is one side of a Triangle)
Finally, 3 < D < 13. So, we can have infinite number of sides between 3 and 13.
Answer = E
PS: If question said D can take only integer value, the D = 9. Answer choice D.
Answer: D
Question: Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 6%. What is the approximate interest he pays annually?
Options:
A)$1200
B)$2000
C)$2150
D)$2500
E)$12000
Rationale: An easy way too attempt this is by approximation:
For the first quarter, he pays 6% of 10,000 which is $600.
So for the four quarters in the year, he will approximately play 600*4=2400 over the entire year.
The compound interest will be more than 2400. All other options are not right except D.
Answer : D
Answer: D
Question: A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 3:2:4, respectively, but he wanted to make more money, so he shifted the ratio to 2:2:5, respectively. How many more acres of land were planted with tobacco under the new system?
Options:
A)90
B)150
C)270
D)300
E)450
Rationale: Originally (4/9)*1350 = 600 acres were planted with tobacco.
In the new system (5/9)*1350 = 750 acres were planted with tobacco.
Thus 750-600 = 150 more acres were planted with tobacco.
The answer is B.
Answer: B
Question: What is the sum of all possible solutions to |x - 2|^2 + |x - 2| = 20 ?
Options:
A)-1
B)6
C)7
D)8
E)14
Rationale: Denote |x - 2| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 2|, so it's an absolute value and thus cannot be negative.
y = |x - 2| = 4 --> x = 6 or x = -2. The sum = 8
Answer: D.
Answer: D
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
Options:
A)15
B)16
C)22
D)18
E)25
Rationale: Work done by Sakshi in 1 day = 1/20
Since Tanya is 25% efficient than Sakshi, she completes 25% more work in a day than Sakshi.
=> Tanya's 1 day work = 1/20 + 1/20 * 25/100 = 1/16
So time taken by Tanya to finish the work = 16 days answer : B
Answer: B
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Options:
A)228
B)150
C)88
D)17
E)113
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Answer: B
Question: Find the odd man out. 1050, 510, 242, 105, 46, 16, 3
Options:
A)46
B)106
C)105
D)1050
E)None of these
Rationale: Explanation :
1050
(1050 - 30)/2 = 510
(510 - 26)/2 = 242
(242 - 22)/2 = 110
(110 - 18)/2 = 46
(46- 14)/2 = 16
(16- 10)/2 = 3
Hence, 110 should have come in place of 105. Answer : Option C
Answer: C
Question: A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 270 metres long in 20 seconds. The length of the train (in metres) is:
Options:
A)180
B)176
C)175
D)96
E)None of these
Rationale: Explanation:
Let the length of train be L m.
Acc. to question
(270+L)/20 = L/8
2160+8L=20L
L= 2160/12 = 180 m
Answer A
Answer: A
Question: A company that ships goods in boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)
Options:
A)9
B)8
C)7
D)6
E)5
Rationale: Back-solving is the best way to solve this problem.
You basically need 12 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - E
Answer: E
Question: If there are 30 numbers and the average of the first 10 numbers is equal to the average of last 20 number what is the sum of last 20 numbers
Options:
A)same as the sum of first 10 numbers
B)2 times the sum of first 10 numbers
C)average of first 10 numbers
D)3 times the sum of first 10 numbers
E)none of the above
Rationale: avg of first 10 no.s= sum of 10 no./10
avg of last 20 no.s= sum of 20 no./20
as gven in question,
sum of first 10 no./10= sum of last 20 no./20
so asnwr comes b)
2 times sum of first 10 no.s
ANSWER:B
Answer: B
Question: A man walk at 5 kmph uphill and 10 kmph downhill. He takes 6 hours to walk uphill from lower point A to upper point B and back to A. What is the total distance traveled by him in 6 hours?
Options:
A)20
B)22
C)24
D)30
E)40
Rationale: Uphill distance traveled per hour - 5 km,
distance traveled after 4 hours = 20 km.
He remained with 2 hours travel downhill, i.e. distance traveled in remaining 2 hours downhill = 20 km
so total distance traveled from A to B and Back to point A = 20 km uphill + 20 km downhill = 40 km
(Answer : E)
Answer: E
Question: If x#y is defined to equal x/y for all x and y, then (-1#2)#3 =
Options:
A)4/3
B)-1/6
C)1/12
D)-1/12
E)-4/3
Rationale: (-1)/ 2 = -1/2
(-1/2) / 3 = -1/6
so B is my answer
Answer: B
Question: In a St.Johns college students, 50 percent are third year students and 80 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?
Options:
A) 3/4
B) 2/5
C) 4/7
D) 1/2
E) 3/7
Rationale: = 20/50. = 2/5
my answer is B too
Answer: B
Question: The mass of the sun is approximately 2 × 10^30 kg and the mass of the moon is approximately 4 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?
Options:
A)4.0 × 10^(−18)
B)2.5 × 10^17
C)4.0 × 10^18
D)5 × 10^17
E)4.0 × 10^42
Rationale: Mass of sun = x * Mass of moon
x = Mass of sun / Mass of moon = (2 × 10^30) / (4 × 10^12) = 2*2^-2*10^18 = 10^18/2 = 5*10^17
Ans. D) 5 × 10^17
Answer: D
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Options:
A)159 m
B)167 m
C)156 m
D)100 m
E)197 m
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer: D
Answer: D
Question: In a certain group of 10 developers, 2 developers code only in C++ and the rest program in either Q-basic or Java - but not both. If a developer organization is to choose a 4-member team, which must have at least 1 developer who codes in C++, how many different programming teams can be chosen?
Options:
A)100
B)40
C)70
D)150
E)140
Rationale: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 10
r = 4
So, total teams is 10C4 = 10!/(4!(10 - 4)!) = 210, and
n = 10 - 2 = 8
r = 4
for teams without C++ is 8C4 = 8!/(4!(8 - 4)!) = 70,
so, teams with at least 1 C++ = 210 - 70 = 140
Answer: E
Answer: E
Question: While playing a certain dice game, Chris wins if the sum of the two dice is 8, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
Options:
A)1/2
B)17/36
C)137/379
D)11/36
E)25/216
Rationale: Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 8 = (2,6)(3,5)(4,4)(5,3)(6,2)= 5 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 8 in any attempt =5/36
Probability of NOT getting sum as 8 in any attempt = 1-(5/6)= 31/36
Probability of losing game =(31/36)*(31/36)*(31/36)=242/379
I.e. Probability of wining game = 1-(242/379) = 137/379
Answer : Option C
Answer: C
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year?
Options:
A)12300
B)12350
C)12000
D)12500
E)12600
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 Ã— 120/100 = 12000
C
Answer: C
Question: The value of x + x(x^x) when x = 10 is
Options:
A)100000000010
B)10000000010
C)10000000000
D)1200000000
E)12000000010
Rationale: Solution:
x + x(x^x)
Put the value of x = 10 in the above expression we get,
10 + 10(10^10)
= 10 + 10(10 Ã— 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10)
= 10 + 10(10000000000)
= 10 + 100000000000
= 100000000010
Answer: (a)
Answer: A
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
Options:
A)4/3
B)21/8
C)18/7
D)8/21
E)7/18
Rationale: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
Ans: E
Answer: E
Question: If x is 30 percent more than y and y is 40 percent less than z, then x is what percent of z?
Options:
A)78%
B)250%
C)500/3%
D)125%
E)60%
Rationale: Z = 100 ; Y = 60 so X = 78
X as % of Z = 78/100 * 100 => 78%
Answer will be (A)
Answer: A
Question: Alcohol cost 3.50 per litre and kerosene oil cost 2.50 per litre. In what proportion these should be mixed so that the resulting mixture may be 2.75 per litre?
Options:
A)2 : 5
B)1 : 3
C)4 : 7
D)2 : 3
E)None of these
Rationale: ∴ Required ratio = 0.25⁄0.75 = 1⁄3 i.e, 1 : 3
Answer B
Answer: B
Question: A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?
Options:
A)34
B)36
C)32
D)30
E)38
Rationale: Distance to be covered = 240+ 120 = 360 m
Relative speed = 36 km/hr = 36×10/36 = 10 m/s
Time = distance/speed = 360/10 = 36 seconds
Answer is B.
Answer: B
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options:
A)200
B)250
C)400
D)500
E)600
Rationale: C's 1 day's work =	1	- 1	+	1 =	1	-	7	=	1	.
3	6	8	3	24	24
A's wages : B's wages : C's wages =	1	:	1	:	1	= 4 : 3 : 1.
6	8	24
C's share (for 3 days) = Rs. 3 x	1	x 3200 = Rs. 400.
24
Answer is C
Answer: C
Question: A car covers a distance of 930 km in 6 hours. Find its speed?
Options:
A)104 kmph
B)289 kmph
C)288 kmph
D)155 kmph
E)177 kmph
Rationale: 930/6
= 155 kmph
Answer: D
Answer: D
Question: For how many different positive integers n is a divisor of n^3 + 8?
.
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: n^3 + 8 = (n+2)(n^2-2n+4)
--> 2 divisors possible, plus 1 and n
we have 4 divisors. ANSWER:E
Answer: E
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Options:
A)22
B)89
C)77
D)66
E)21
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer:B
Answer: B
Question: A man sells an article at 7% loss. Had he sold it for Rs. 105/- more he could have gained 8%. what is the cost price of the article
Options:
A)Rs. 522/-
B)Rs. 622/-
C)Rs. 700/-
D)Rs. 600/-
E)Rs. 750
Rationale: Explanation:
Short cut method:
Loss =====> 7 %
Profit ====> 8 %
~
----------------
15 % ---------> 105
100 % --------> Rs.700/-
Answer: Option C
Answer: C
Question: If each edge of cube increased by 10%, the percentage increase in surface area is:
Options:
A)33.1
B)33.5
C)33.7
D)33.2
E)33.9
Rationale: 100 × (110)/100 × (110)/100 × (110)/100 => 1331/100 = 33.1%
Answer is A.
Answer: A
Question: The arithmetic mean of set A is zero. If B = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of A consisting of all those elements in A which are more than two but less than three standard deviations away from the arithmetic mean of A, what could be equal to the standard deviation of A?
Options:
A)0.54
B)0.77
C)0.82
D)0.97
E)1.62
Rationale: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and B = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of A
B consists of all those elements in A that are more than 2 but less than 3 ADs away from the arithmetic mean of A
If an element is 1 AD away from the mean, we can write it as either m + AD or m - AD
Similarly, if an element is 2 ADs away from the mean, we can write it as either m + 2*AD or m - 2*AD
So, if these elements lie within 2 and 3 ADs of mean, m=0
we can find which one of these values of AD satisfies each value within B
Only AD = 0.77 does
Answer : B
Answer: B
Question: A horse chases a pony 3 hours after the pony runs. Horse takes 4 hours to reach the pony. If the average speed of the horse is 35 kmph, what s the average speed of the pony?
Options:
A)20kmph
B)22kmph
C)24kmph
D)26kmph
E)28kmph
Rationale: pony take 7 hours and horse take 4 hours...then Distance chased by them is 35*4.so speed of pony is (35*4)/7=20kmph.
ANSWER:A
Answer: A
Question: The number of arrangements that can be made with the letters of the word SAMEES so that the vowels occupy the even places?
Options:
A)14
B)28
C)777
D)992
E)36
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 6 * 6 = 36.
Answer:E
Answer: E
Question: A sum is divided among A, B and C in such a way that for each rupee A gets, B gets 60 paisa and C gets 40 paisa. If the share of Z is RS. 20, what is the total amount?
Options:
A)60
B)70
C)80
D)90
E)100
Rationale: a:b:c = 100:60:40
20:12:8
8 --- 20
40 --- ? => 100
Answer:E
Answer: E
Question: A and B go around a circular track of length 300 m on a cycle at speeds of 34 kmph and 50 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)120 sec
B)60 sec
C)186 sec
D)167 sec
E)168 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 300/ (36 * 5/18) , 300/ (54 * 5 /18) }
= LCM (30, 20)
=60 sec.
Answer:B
Answer: B
Question: If n is a natural numbe, then(n3 - n)is always divisible by
Options:
A)8
B)6
C)12
D)9
E)4
Rationale: Explanation:
Clearly, 223 is a prime number.
441 is divisible by 9.
357 is divisible by 3.
153 is divisible by 17.
Answer: Option B
Answer: B
Question: Hardy and Robert start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Robert. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
Options:
A)50
B)45
C)35
D)30
E)60
Rationale: let x=length of pool
at first meeting, combined distance=x
at second meeting, combined distance=3x
if andy swims 18.5 m of x, then he will swim 3*18.5=55.5 m of 3x
andy's total distance to second meeting=x+10.5 m
x+10.5=55.5 m
x=45 m
B
Answer: B