divelab/Sys2Bench huggingface dataset:
Question: What is the least value of x. So that 4x569 is divisible by 3?
Options:
A)2
B)5
C)1
D)0
E)7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
4 + x +5 + 6 + 9 =24 + x
Least value of x may be 0
Therefore 24+0 = 24 is divisible by 3.
D
Answer: D
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 20% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
Options:
A)$100
B)b $115
C)c $125
D)d $130
E)e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 20% less than the price each head sold for on the day before i.e , (80/100)*0.5 = $ 0.4
Hence selling cost for the remaining cabbage = 500 * 0.4 = $ 200
Total selling cost = 500 + 200 = $ 700
Gross profit = $ 700 - $ 600 = $ 100
Hence Answer is A.
Answer: A
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 42, what is the value of a?
Options:
A)24
B)25
C)28
D)30
E)32
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 42:
9k/3 = 42
3k = 42
k=14
Then a=28.
The answer is C.
Answer: C
Question: What is the remainder when 9^1 + 9^2 + 9^3 +...+ 9^9 is divided by 3?
Options:
A)0
B)3
C)2
D)5
E)None of the above
Rationale: Notice that in the brackets we have the sum of 8 odd multiples of 3, which yields remainder of 0 upon division by 3.
Answer : A
Answer: A
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 117. What is that number?
Options:
A)12
B)29
C)27
D)17
E)99
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 117
6x + 15 = 117
6x = 102
x = 17
ANSWER:D
Answer: D
Question: What will the value replace by x if 210x0 is divisible by 5?
Options:
A)4
B)3
C)2
D)All the Above
E)None
Rationale: Divisibility of 5 is Last of the digit is 0 or 5.
In 210x0 has 0.So the Number must divisible by 5.
That is any number can be replaced in the place of x
Answer is D
Answer: D
Question: A certain restaurant offers 7 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
Options:
A)8
B)12
C)15
D)21
E)35
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 7C2*2C2=21*1=21
B. 1 kind of cheese and 1 kind of fruit --> 7C1*2C1=7*2=14
A+B=21+14=35
Answer: E.
Answer: E
Question: A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width?
Options:
A)12 by 2
B)11 by 3
C)20 by 5
D)10 by 4
E)9 by 3
Rationale: 2x+2y=50
x+y=25
x+4x=25
5x=25
x=5
Answer C
Answer: C
Question: A motorcyclist goes from Bombay to Nagpur, a distance of 600 kms at an average of 120 kmph speed. Another man starts from Bombay by car 1 Â½ hours after the first, and reaches Nagpur Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:7
C)1:9
D)3:5
E)1:1
Rationale: T = 600/120 = 5 h
T = 5 - 2 = 3
Time Ratio = 5:3
Speed Ratio = 3:5
Answer: D
Answer: D
Question: Three picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
Options:
A)A)4^30
B)B)2^30
C)C)1^30
D)D)3^30
E)E)6^30
Rationale: Each Mango can be given to any one of the Three people or in other words..1 mango can be divided into 3 ways...so all 30 can be divided in 3^30 ways
ANS:D
Answer: D
Question: 45% of 750 - 25% of 480 = ?
Options:
A)216
B)217.5
C)236.5
D)245
E)250
Rationale: Explanation:
Given expression = (45/100 * 750) - (25/100 * 480) = (337.50 - 120) = 217.50
Answer IS B
Answer: B
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 20 minutes, how much time will she spend doing yoga? (rounded to minutes)
Options:
A)10 min.
B)33 min.
C)17 min.
D)23 min.
E)25 min.
Rationale: The ratio is 2:3 = gym:ride, so (20)(3/2) = 30 minutes at the gym, and 30 + 20 = 50 minutes exercise, so (2/3)(50) = 33 minutes yoga.
Answer: B
Answer: B
Question: 53 x 22 = 1276 then (4221)n=()10?
Options:
A)3896
B)3897
C)3898
D)3899
E)None
Rationale: Sol:
As we don't know the base system here we take the base as n. So 53 in base n can be written as 5n+3, and 22 as 2n+2 and 1276 as n3+2n2+7n+6
⇒⇒ (5n + 3)(2n + 2) = n3+2n2+7n+6
⇒⇒ 10n2+16n+6=n3+2n2+7n+6
⇒⇒ n3−8n2−9n=0
⇒⇒ n(n2−8n−9)=0
⇒⇒ (n + 1)(n - 9) = 0
So n = 9
(4221)9=4×93+2×92+2×9+1
= 3716 + 162 + 18 + 1 = 3897
Answer B
Answer: B
Question: Four friends, Thomas, Mike, Brian, and John, went on a fishing trip. If Mike caught 4 more than Brian did, John caught 12 less than Thomas did, and Thomas caught 4 more than Mike did, how many more fish did Brian catch than John did?
Options:
A)6
B)4
C)8
D)1
E)12
Rationale: In this word problem, the first key is to turn the story into equations:
Mike caught 4 more than Brian did: M = 4 + B
John caught 12 less than Thomas did: J = T - 12
Thomas caught 4 more than Mike did: T = 4 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and J (how many more fish did Brian catch than John did?). This means that your goal is to get the equations in terms of B and J so that you can solve for the expression B - J.
Taking the first equation and solving for B, you have B = M - 4.
Taking the second equation and solving for J you have J = T - 12, and then with the third equation you can replace T with 4 + M so that both B and J are in terms of M: J = (4 + M) - 12.
So if B = M - 4 and J = M - 8, then:
B - J = (M - 4) - (M - 8)
B - J = M - 4 - M + 8 (remove the parentheses by distributing the multiplication)
B - J = 4, so the answer is B.
Answer: B
Question: A group of 3 integers is to be selected one after the other, and at random and without replacement, from list L above. What is the probability that the 3 integers selected are not 3 consecutive integers?
Options:
A)3/5
B)7/10
C)3/4
D)4/5
E)14/15
Rationale: Determining that there were 120 ways to select 3 numbers from that group was the perfect first step. Next, you just have to figure out which combinations of 3 involve three consecutive integers. Thankfully, it's not that hard - and you can list them out:
123
234
345
456
567
678
789
89&10
Thus there are 8 ways (out of 120) that ARE three consecutive integers and the other 112/120 are NOT three consecutive integers.
112/120 = 14/15
Final Answer:E
Answer: E
Question: Ram's age and Shyam's age are in the ratio 3 : 4. Seven years ago the ratio of their ages was 2: 3. Find the ratio of their ages five years hence?
Options:
A)33:21
B)44:44
C)33:45
D)26:33
E)44:66
Rationale: Let ages of Ramu and Shyamu be x and y respectively.
x/y = 3/4 => x = 3/4 y
Also (x - 7) / (y - 7) = 2/3
=> 3x - 21 = 2y - 14
3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28 years
Ratio of their ages five years hence
= (21 + 5) / (28 + 5) = 26/33.
Answer:D
Answer: D
Question: Dick and Jane each saved $4,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $6,500. Approximately what percent less did Jane save in 1990 than in 1989?
Options:
A)20%
B)70%
C)50%
D)30%
E)40%
Rationale: 1990
Dick saved = $ 4400
Jane saved = $ 2100 (jane saved $2800 less than she did the prior year)
Jane saved approximately $2800/4000$ (70%) less in 1990
Answer: B
Answer: B
Question: 2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 3/4 of the red fish and 3/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?
Options:
A)2/5
B)3/10
C)7/10
D)9/20
E)11/20
Rationale: 3/4*2/5 + 3/5*1/4 = 9/20
The answer is D.
Answer: D
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1994. She ended on her
Options:
A)thumb
B)the index finger
C)the middle finger
D)the ring finger
E)the little finger
Rationale: Notice the pattern. The thumb lands up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1994 has to be the index finger
Answer is B
Answer: B
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 66 km/hr?
Options:
A)11
B)30
C)29
D)88
E)61
Rationale: Speed of train relative to man = 66 - 3 = 63 km/hr.
= 63 * 5/18 = 35/2 m/sec.
Time taken to pass the man = 500 * 2/35 = 28.57 sec.
approx. 29 sec
Answer: C
Answer: C
Question: Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 1 ?
Options:
A)2/5
B)2/7
C)33/83
D)99/250
E)98/250
Rationale: SOLUTION
The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 98/250
Answer: E
Answer: E
Question: A group of 8 students are seated in a linear arrangement. There are 2 girls who must sit together always. in how many arrangements can the students sit?
Options:
A)A.1296
B)B.1850
C)C.2880
D)D.3546
E)E.10080
Rationale: Glue two girls together: {AB}
6 units {AB}, {C},{D}, {E}, {F}, {G}, {H} can be arranged in 7! ways. Each girls within their unit can be arranged in 2! ways.
Therefore the final answer is 7!*2!=
Answer: E.
Answer: E
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)8 months
B)9 months
C)1months
D)12months
E)23months
Rationale: Let B joins for x months. Then
A:B = 85000*12 : x* 42500 = 3 : 1
=> 850*12 : 425x= 3 : 1
=> 850*12/ 425x = 3/1 = 3
=> 850*4 /425x = 1
=> 2*4/x = 1
=> x = 8
Answer is A
Answer: A
Question: Of three numbers, the third is four times the second and the second is two times the first. If their average is 165, the smallest of the three numbers is:
Options:
A)18
B)19
C)45
D)21
E)22
Rationale: Explanation:
Let first number be x.
So,2nd no. = 2x & 3rd no.=8x.
So,x+2x+8x=165 × 3 = 495
11x = 495/11
x = 495/11
Hence,smallest Number x=45
Answer: C
Answer: C
Question: Using all the letters of the word "NOOKIASS", how many words can be formed, which begin with N and end with S?
Options:
A)550
B)160
C)720
D)620
E)820
Rationale: There are five letters in the given word.
Consider 8 blanks ....
The first blank and last blank must be filled with N and S all the remaining three blanks can be filled with the remaining 6 letters in 6! ways.
The number of words = 6! = 720.
Answer: C
Answer: C
Question: A 75m long train is running at 54 km/hr. In how much time will it cross an electric pole?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: Speed of the train = ( 54 * 5 / 18) m/sec = 15 m / sec. Length of the train = (Speed x Time)
Time = (Length of the train / Speed)
=(75/ 15) = 5sec
Answer: A
Answer: A
Question: At what time between 9’o clock and 10’o clock will the hands of a clock point in the opposite directions?
Options:
A)16 4⁄11 minutes past 9
B)16 4⁄11 minutes past 8
C)55 5⁄61 minutes past 7
D)55 5⁄61 minutes past 8
E)None of these
Rationale: At 9’o clock, the Minute Hand is ahead of Hour Hand by 45 minutes. The hands will be opposite to each other when there is a space of 30 minutes between them.
This will happen when the Minute Hand gains 15 minutes space over Hour Hand.
Time taken by Minutes Hand to gain 15 minutes
= 15 × (1 + 1⁄11) = 15 + 15⁄11 = 15 + 14⁄11 + 16 4⁄11 minutes.
Hence the Hands are opposite to each other at 16 4⁄11 minutes past 9.
Answer A
Answer: A
Question: Lina works 10 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
Options:
A)m/(10d)
B)5md/6
C)10d
D)10d/m
E)10md
Rationale: Total income of Lina in a year = d*10*m dollars. Now Monthly income = Total/12 = d*10*m / 12 = 5md/6 Answer is B
Answer: B
Question: If 9x^2-16y^2=3x+4y,then what will give the answer?
Options:
A)3x-4y=0
B)3x-4y=2
C)3x-4y=1
D)3x+4y=0
E)3x+4y=1
Rationale: 9x^2-16y^2=3x+4y
(3x+4y)(3x-4y)=3x+4y
3x-4y=(3x+4y)/(3x+4y)
3x-4y=1
Answer is option C
Answer: C
Question: During one month at a particular restaurant, 1/5 of the burgers sold were veggie burgers and 1/4 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
Options:
A)x/8
B)x
C)2x/3
D)3x/4
E)4x/5
Rationale: Let y be the number of total burgers.
veggie = y/5 , non veggie = 4y/5
1/4 of the rest of the burgers sold were double-meat
=> 4y/5 * 1/4 = double meat = x
=> y/5 = x= veggie
Hence B
Answer: B
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)15 sec
B)16 sec
C)18 sec
D)20 sec
E)22 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
ANSWER:B
Answer: B
Question: Tough and Tricky questions: Work/Rate Problems.
A group of 4 junior lawyers require 3 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?
Source: Chili Hot GMAT
Options:
A)13
B)10
C)9
D)6
E)5
Rationale: # of people times the # of hours:
4*3 = 12 --> 3 lawyers do 12worksin 3 hours.
3*6/3 = 6 --> 3 assistants do 6 worksin 2 hours
So, since the amount of work the assistants do is half the work the lawyers do, the time will be double, soANS D
Answer: D
Question: A bowl contains 3 parts of which are milk and 5 parts water. How much of the mixture must be drawn off and replaced with milk sothat the mixture may be half milk and half water?
Options:
A)2/5
B)3/5
C)1/5
D)1/7
E)2/7
Rationale: Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = 3 -	3x	+ x litres
8
Quantity of syrup in new mixture = 5 -	5x litres
8
3 -	3x	+ x = 5 -	5x
8	8
5x + 24 = 40 - 5x
10x = 16
x =	8	.
5
So, part of the mixture replaced = 8	x	1 =	1/5
5	8	5
C
Answer: C
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 59.4. The difference between the unit digit and hundreds digit of that number is :
Options:
A)a) 6
B)b) 3
C)c) 2
D)d) 1
E)e) 0
Rationale: Since the average increased by 59.4 and there were a total of 10 numbers, it means the incorrect number was 594 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 594
99c - 99a = 99(c - a) = 594
594 = 99*6 = 99(c - a)
So c - a = 6
Answer (A)
Answer: A
Question: A crate of apples contains 1 bruised apple for every 30 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 15 apples not fit to sell in the crate, how many apples are there in the crate?
Options:
A)270
B)360
C)480
D)600
E)840
Rationale: as given 3 out of every 4 bruised apple is not fit to sell
or, 75% of the bruised apples are not fit to sell.
as per the question 15 are not fit to sell
or,
0.75x=15
x=1500/75=20
thus total number of bruised apples =20
total number of apples =30*20=600
Answer: D
Answer: D
Question: Find the SI on Rs 8000 for 4 yrs at 10% per annum rate of interest?
Options:
A)Rs 3000
B)Rs 3500
C)Rs 4000
D)Rs 4400
E)Rs 4800
Rationale: Simple Interest =
PTR
100
= 8000 X 5 X
10
100
= Rs 4000
C
Answer: C
Question: In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,5) and (t,-8). What is the least possible value of the slope of line L?
Options:
A)-6.5
B)2
C)-2
D)-6
E)-10
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,-8) should satisfy the equation. hence x=t and Y=-8.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-8-5)/(4-2) = -6.5
IMO option A is correct answer.
Answer: A
Question: A began a business with Rs.85,000. He wasjoined afterwards by B with Rs.42,500. For how muchperiod does B join, if the profits at the end of the yr are dividedin the ratio of 3:1?
Options:
A)5 months
B)8 months
C)9 months
D)11 months
E)21 months
Rationale: Suppose B joined for x months. Then,
Then, 85000 x 12	=	3
42500 x x	1
x = 85000 x 12 = 8.
42500 x 3
So, B joined for 8 months.
B
Answer: B
Question: A batsman makes a score of 56 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Options:
A)25
B)8
C)27
D)29
E)39
Rationale: Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 56 = Total runs scored in 17 innings
=> 16(x-3) + 56 = 17x
=> 16x - 48 + 56 = 17x
=> x = 8
Answer is B.
Answer: B
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
Options:
A)15
B)12
C)13
D)18
E)19
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
ANSWER A
Answer: A
Question: If x is real, find the maximum value of the expression -2x^2 + 9x + 11.
Options:
A)12.125
B)15.125
C)18.125
D)21.125
E)24.125
Rationale: This is an equation of a downward facing parabola.
The maximum value is the top point of the parabola.
-2x^2+9x+11 = (-2x+11)(x+1)
The roots are 11/2 and -1.
The maximum value must be when x is halfway between these two points.
x = 2.25
The maximum value is -2(2.25)^2+9(2.25)+11 = 21.125
The answer is D.
Answer: D
Question: A pump can fill a tank with water in 4 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?
Options:
A)15hr 10min
B)16hr 20min
C)9hr 20min
D)15hr
E)14hr 25min
Rationale: Work done by the leak in 1 hour = 1/4 - 1/7 = 3/28
Leak will empty the tank in 28/3 hrs = 9hr 20min
Answer is C
Answer: C
Question: A box contains five bulbs out of which 3 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Options:
A)39/10
B)29/10
C)19/10
D)9/10
E)125/128
Rationale: Required probability
= 1 - 1/10
= 9/10
Answer: D
Answer: D
Question: A certain company consists of 7 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)
Options:
A)84
B)108
C)135
D)270
E)364
Rationale: Total # of teams of 3 possible is 15C3=455
# of teams with only managers or only non-managers is: 7C3+8C3=35+56=91;
# of teams of 3 with at least one manager or at least one non-manager is: 455-91=364.
ANSWER:E
Answer: E
Question: The L.C.M. of 2 numbers is 30. The numbers are in the ratio 2:3. Find their sum?
Options:
A)36
B)25
C)48
D)32
E)56
Rationale: Let the numbers be 2x and 3x
L.C.M. = 6x
6x = 30
x = 5
The numbers are = 10 and 15
Required sum = 10+15 = 25
Answer is B
Answer: B
Question: If an average hard drive had a capacity of 0.4 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
Options:
A)256
B)512
C)4096
D)1024
E)1536
Rationale: 0.4*2^10=0.4*1024=409.6
The answer is C.
Answer: C
Question: A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
Options:
A)11/30
B)29/60
C)17/30
D)31/45
E)11/15
Rationale: I think D - 31/45 is the correct answer.
Here goes:
Lets assume originally the number of beds = x
After the new tower, the total combined no of beds = 4x
So old = x, New = 3x
Now 1/3 of x are occupied and 1/5 of 3x are occupied which simplifies to (3/5)x
We are shifting 1/3 of x to the new ward so there will now be:
1/3 of x plus 3/5 of x occupied in the new ward. Add them up to get 14/15 of x
There are 3x beds in New Tower so ratio is:
(14/15)x / 3x = 14/45 of x
Subtract that from 45/45 of x and you get the number of un-occupied beds to total capacity of New Tower =31/45
D
Answer: D
Question: A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
Options:
A)20%
B)30%
C)35%
D)40%
E)50%
Rationale: Let the side of the square(ABCD) be x metres.
Then, AB + BC = 2x metres.
AC = 2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = 0.59x x 100 % = 30% (approx.)
2x
B)
Answer: B
Question: Find the number which is nearest to 3105 and is exactly divisible by 21.
Options:
A)3104
B)3106
C)3108
D)3109
E)3103
Rationale: On dividing 3105 by 21, we get 18 as remainder.
Number to be added to 3105 = (21 - 18) - 3.
Hence, required number = 3105 + 3 = 3108.
ANSWER C 3108
Answer: C
Question: The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time E all five colored lights will all flash together at the exact same time?
Options:
A)0:03 AM
B)0:04 AM
C)0:06 AM
D)0:12 AM
E)0:24 AM
Rationale: Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Answer: D
Question: If 7% of the sale price of a watch is equivalent to 8% of its cost price and 9% of its sale price exceeds 10% of its cost price by Re 1, then what is the cost price of the watch?
Options:
A)Rs 400
B)Rs 350
C)Rs 300
D)Rs 280
E)Rs 380
Rationale: Let C.P. = X and S.P. = Y
=> 7 % of Y = 8% of X and 9% of Y =10% of X + 1
=> 7Y = 8X and 9Y = 10X + 100
=> 9 x (8X / 7) = 10 X + 100
=> X = Rs. 350
ANSWER:B
Answer: B
Question: Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?
Options:
A)150
B)125
C)140
D)180
E)200
Rationale: 3x+4x = 420
x=60== 3x=180
ANSWER D
Answer: D