divelab/Sys2Bench huggingface dataset:
Question: From a group of boys and girls,15 girls leave.There are then left 2 boys for each girl.After this,45 boys leave.There are then 5 girls for each boy.Find the number of girls in the beginning?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: 15 girls leave,B+(g-15)=0
then,B=2*(g-15)---------------------->>>1
45 boys leave,(b-45)+(g-15)=0
then,(g-15)=5(b-45)
Hence,the number of girls in the beginning are,
5(b-45)-(g-15)=0------------------->>>2
put 1 in 2, we get,
5(2*(g-15)-45)-(g-15)=0
10g-150-225-g+15=0
9g-360=0
9g=360
g=40
ANSWER:C
Answer: C
Question: If x is a positive integer, then the least value of x for which x! is divisible by 100,000 is?
Can someone please explain intuitively what the question is asking?
Options:
A)5
B)9
C)12
D)20
E)30
Rationale: In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3.
5! = 120 has 1 trailing zeros.
10! will have 2 trailing zeros.
15! will have 3 trailing zeros.
20! will have 5 trailing zeros.
Answer: D.
Answer: D
Question: Find the average of first 40 natural numbers?
Options:
A)12.6
B)20.5
C)22.9
D)30.5
E)32.1
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 40 natural numbers = 40*41/2 =820
average = 820/40 = 20.5
Answer is B
Answer: B
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)76 km/hr
B)66 km/hr
C)60 km/hr
D)67 km/hr
E)22 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer:C
Answer: C
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 7, 24 and 25?
Options:
A)2.5
B)6.5
C)12.5
D)14
E)16
Rationale: Some of pyhtagron triplets we need to keep it in mind.
Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).
So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.
The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 25 / 2 = 12.5
Ans. C
Answer: C
Question: How many plants will be there in a circular bed whose outer edge measure 35 cms, allowing 4 cm2 for each plant ?
Options:
A)18
B)750
C)24
D)19
E)None of these
Rationale: Circumference of circular bed = 35 cm
Area of circular bed = (35)2â„4Ï€
Space for each plant = 4 cm2
âˆ´ Required number of plants
= (35)2â„4Ï€ Ã· 4 = 24.36 = 24(approx)
Answer C
Answer: C
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 1.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)60
B)277
C)48
D)99
E)22
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 1.4 = 2.5 km = 2500 m.
Required time = 2500 * 3/125 = 60 sec.
Answer:A
Answer: A
Question: (0.0066)(3.6) / (0.04)(0.1)(0.006)=
Options:
A)990
B)99.0
C)9.9
D)0.99
E)0.099
Rationale: (0.0066)(3.6) / (0.04)(0.1)(0.006)=0.0060 * 360/4 * (0.1)(0.006)
= 0.066*90/1 * 0.006 = 66*90/6 = 11*90
=990
Answer : A
Answer: A
Question: Which of the following points is symmetric with y=x at (2,3)?
Options:
A)(-2,-1)
B)(-2,1)
C)(2,1)
D)(3,2)
E)(-1,2)
Rationale: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.
(2,3) would become (3,2).
Answer (D).
Answer: D
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Options:
A)10508
B)10567
C)10528
D)10512
E)10500
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7 = Rs. 10500
Answer:E
Answer: E
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
Options:
A)22
B)27
C)15
D)77
E)16
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
Answer: C
Answer: C
Question: Farm Tax is levied on the 45% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
Options:
A)15%
B)25%
C)15.125%
D)27.78%
E)none
Rationale: Only trick n this question is to ignore 45% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/45) = 27.78% and the answer is not there in the options.
The correct answer is (D).
Answer: D
Question: A patient was given four pills which he is required to take one after every forty minutes.
How long can the pills run for him?
Options:
A)1 hour and 10 minutes.
B)1 hour and 15 minutes.
C)1 hour and 20 minutes.
D)1 hour and 30 minutes.
E)1 hour and 40 minutes.
Rationale: He took the first pill at the zero minute.
He took the second pill after 20 minutes = 0+40=40
He took the third pill after 20 minutes = 40+40=80
He took the fourth pill after 20 minutes = 80+40=100
Then it will last for 100 minutes or an hour and 40 minutes.
Answer E
Answer: E
Question: A pharmaceutical company received $5 million in royalties on the first $40 million in sales of and then $9 million in royalties on the next $210million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $40 million in sales to the next $210 million in sales?
Options:
A)8%
B)15%
C)45%
D)52%
E)66%
Rationale: (9/210)/(5/40) = 12/35 = 34% it means that 9/210 represents only 34%. Therefore a decrease of 66%.
Answer E
Answer: E
Question: A restaurant meal cost $50 and there was no tax. If the tip was more than 15 percent but less than 20 percent of the cost of the meal, then the total amount paid must have been between
Options:
A) $58 and $59
B) $56 and $61
C) $58 and $60
D) $57 and $59
E) $56 and $57
Rationale: Hence it will be between 50 * (1+15/100) and 50 * (1+20/100).
i.e b/w 57.5 and 60. Hence the answer B (b/w 56 and 61).
Answer: B
Question: In a throw of dice what is the probability of getting number greater than 5
Options:
A)1/7
B)1/6
C)1/11
D)1/13
E)2/9
Rationale: Number greater than 5 is 6, so only 1 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 1/6
B)
Answer: B
Question: The function f is defined for all the positive integers d by the following rule: f(d) is the number of positive integers each of which is less than d and has no positive factor in common with d other than 1 . if p is a prime number then f(p)?
Options:
A)p-1
B)p-2
C)(p+1)/2
D)(p-1)/2
E)2
Rationale: The moment you put a prime number in the function f(d), notice that all the numbers lesser than d have no divisor clashing with divisor of d since d is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Answer: A
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the distance traveled by Maxwell when they meet in the middle?
Options:
A)16
B)18
C)20
D)24
E)30
Rationale: Distance between Maxwell's and Brad's home = 50 km
Maxwell's speed = 4 km/h
Brad's speed = 6 km/h
Relative speed of approach = 10 km/h
Time = 50/ 10 = 5 hours
Distance traveled by Maxwell when they meet in the middle = 4*5 = 20 km
Answer C
Answer: C
Question: If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 80 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?
Options:
A)60 %
B)65 %
C)70%
D)75%
E)80%
Rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 80 - {Both correctly} + 5
{Both correctly} = 70.
Answer: C.
Answer: C
Question: How many pieces of 0.85 metres can be cut from a rod 42.5 metres long?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Number of pieces = 42.5/0.85
= 42.50/0.85
= 4250/85
= 50.
ANSWER:C
Answer: C
Question: Of the 1000 inhabitants of a town, 60% are males of whom 20% are literate. If, of all the inhabitants, 25% are literate, then what percent of the females of the town are literate?
Options:
A)22.5
B)27.5
C)32.5
D)37.5
E)None
Rationale: Sol.
Number of males = 60% of 1000 = 600.
Number of females = (1000-600) = 400.
Number of literates = 25% of 1000 = 250.
Number of literate males = 20% of 600 = 120.
Number of literate females = (250 - 120) = 130.
∴ Required percentage = (130 / 400 x 100)% = 32.5%
Answer C
Answer: C
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)5
C)6
D)67
E)7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer:A
Answer: A
Question: A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill?
Options:
A)30 seconds
B)20 seconds
C)40 seconds
D)10 seconds
E)None
Rationale: 7.2 km = 7200 m. 1 h = 3600 s. The speed will be 7200 m/3600 s = 2 m/s. The necessary time to climb will be 20 seconds. When descending, if the speed is two times greater, the necessary time will be two times smaller, so 10 seconds. The total necessary time is 20 s + 10 s = 30 seconds.
Answer A
Answer: A
Question: 12,31,68,129,220,347,?
Options:
A)129
B)220
C)347
D)516
E)520
Rationale: 2*2*2 + 4 = 12
3*3*3 +4 = 31
4*4*4 + 4 = 68
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
ANSWER : D
Answer: D
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 54 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: Total Distance = 54 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1 hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 50 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 50 / 10 = 5 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 5 = 20+4 = 24 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 24 /4 = 6 hrs ... Answer D
Alternatively ...
Total Time taken by Maxwell to meet Brad = Maxwell started 1 hour earlier to Brad + total time taken to meet brad after Brad started = 1+ 5 = 6 hrs... Answer D
Answer: D
Question: ine m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ?
Options:
A)-3
B)-1
C)-1/3
D)0
E)Undefined
Rationale: y intercept of line m is -2 ; i.e. one point on the line m is (0,-2)
Line m passes through the midpoint of (2,4) & (6, -8) i.e. ((2+6)/2 , (4+-8)/2) = (4, -2)
So two point on line m are (0,-2) and (4, -2) As the y coordinates of the two points are same, this is a line parallel to X axis.
So slope is zero.
Answer D
Answer: D
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
Options:
A)23,500
B)24,500
C)25,500
D)26,500
E)27,500
Rationale: Let the weekly sales of both = x
550+(x−1000)8/100=10/100x
x = 23500
ANSWER:A
Answer: A
Question: If a: b = 11: 4, b: c = 15: 12, find a: b: c?
Options:
A)155: 50: 42
B)165: 60: 52
C)175: 70: 62
D)185: 80: 72
E)195: 90: 82
Rationale: a: b = 11: 4
b: c = 15: 13
a: b: c = 165: 60: 52
ANSWER:B
Answer: B
Question: It was intended that Rs. 585 be divided among P, Q and R in the ratio of 4 : 3 : 2, but by mistake the distribution was made in the proportion of 1/4 : 1/3 : 1/2. How much does 'R' gain by the error ?
Options:
A)Rs. 99
B)Rs. 126
C)Rs. 140
D)Rs. 152
E)None of these
Rationale: Explanation:
Total amount = Rs. 585
on dividing it in the ratio of 4 : 3 : 2
Share of P = 4/9 * 585 = Rs. 260
Share of Q = 3/9 * 585 = Rs. 195
Share of R = 2/9 * 585 = Rs. 130
But the amount has been divided in the proportion of 1/4 : 1/3 : 1/2 i.e. 3 : 4 : 6
Share of P = 3/13 * 585 = Rs. 135
Share of Q = 4/13 * 585 = Rs. 180
Share of R = 6/13 * 585 = Rs. 270
Therefore, gain for R by virtue of error = Rs. 270 – Rs. 130 = Rs. 140
ANSWER C
Answer: C
Question: Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 1 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
Options:
A)R-4
B)R/(R+4)
C)R/(R-2)
D)8/(R-8)
E)2R - 4
Rationale: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.
In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*1T=R(T-1) --> 2T=RT-R --> T=R/(R-2).
Answer: C.
Answer: C
Question: A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 3% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.
Options:
A)3.5
B)3.75
C)4
D)4.25
E)4.86
Rationale: (1000xtx3/100) + (1400xtx3/100) = 350 â†’ t =4.86 answer E
Answer: E
Question: (A% of 5B + B% of A) is equal to ?
Options:
A)A% of B
B)B% of A
C)6% of AB
D)AB% of 3
E)None
Rationale: Answer
A% of 5B + B% of A =5AB/100 + AB/100
= 6AB/100 = 6% of AB
Correct Option: C
Answer: C
Question: If A = B/C, -1 < C < 0 and 4 < B, which of the following is correct?
Options:
A)A > 4.
B)0 < A <4.
C)-4 < A < 0.
D)A < -4.
E)A < -20.
Rationale: B is +veC is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take B=4.1A=-0.9
A=4.1/-0.9
A<-4
Ans D
Answer: D
Question: On a track for remote controlled racing cars, racing car A completes the track in 56 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
Options:
A)275
B)325
C)280
D)425
E)None of these
Rationale: Time required in seconds will be LCM ( 35, 56 ) = 280
Hence, answer will be (C) 280
Answer: C
Question: On a purchase of $118, a store offered a payment plan consisting of a $18 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
Options:
A)16.7%
B)16.2%
C)16.5%
D)15.5%
E)15.3%
Rationale: 12*10 + 18 = 138
(18/118)* 100 = 15.3
Answer : E
Answer: E
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop?
Options:
A)128
B)64
C)32
D)16
E)8
Rationale: Before stop 3, there were 2 passengers on the bus.
Before stop 2, there were 4 passengers on the bus.
Before stop 1, there were 8 passengers on the bus.
The answer is E.
Answer: E
Question: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
Options:
A)6 %
B)6.3 %
C)6.2 %
D)6.1 %
E)6.4 %
Rationale: Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: E
Question: A mixture contains milk and water in the ratio 7:3. On adding 20 liters of water, the ratio of milk to water becomes 7:5. Total quantity of milk & water before adding water to it?
Options:
A)90
B)100
C)110
D)120
E)140
Rationale: milk:water = 7:3
7x : 3x + 20 = 7 : 5
5[7x] = 7[3x + 20]
35x = 21x + 140
35x - 21x = 140
14x = 140
x = 10
The quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10
10x = 100
Option 'B'
Answer: B
Question: If 4 - (3/7)x = (x-3) / 7,
then what is the value of x ?
Options:
A)8
B)31
C)4
D)31/4
E)-31/4
Rationale: 4 - (3/7)x = (x-3) / 7
=> 28 - 3x = x - 3
=> -4x = -31
=> x = 31/4
Answer: D
Answer: D
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/4 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
Options:
A)12 greater
B)17 fewer
C)28 fewer
D)36 fewer
E)52 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/4 * 480 =120
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 120-68 =52>>> therfore answer is 28 fewer
E
Answer: E
Question: If a + b > 5 and a - b < 3, which of the following must be true?
I. a > b
II. b > 1
III. a > 5
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I, II, and III
Rationale: I. Not true, example: a=3, b=4
II. True, add the equations together so that the greater parts are added. Thus, a + b + 3 > 5 + a - b. Combining like terms, we get 2b > 2. Thus, b > 1.
III. Not true, example: a = r, b = 4
Thus, II only so the answer if B.
Answer: B
Question: The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 4-hour period?
Options:
A)88
B)56
C)42
D)34
E)64
Rationale: Complete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4 = 5 minutes plus 2 minutes = 7 minutes.
4 hour = 240 minutes.
In 240 minutes operator can make 240/7=34 trips.
Answer: D.
Answer: D
Question: Of the teams competing in the world archery championships, Ten percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
Options:
A)13/20
B)16/20
C)13/15
D)17/20
E)13/17
Rationale: Half as manymeans half of EU, then
EU 10%
US 5%
AF 5%
the rest is 50%, answer B
Answer: B
Question: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/4 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
Options:
A)1/2
B)2/3
C)3/4
D)5/6
E)7/8
Rationale: (1/2)X = (1/4)Y
(1/4)Y + (1/4)Y = (1/2)Y
The answer is A.
Answer: A
Question: If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due?
Options:
A)8 months
B)11 months
C)10 months
D)9 months
E)12 months
Rationale: Explanation :
F = Rs. 498
TD = Rs. 18
PW = F - TD = 498 - 18 = Rs. 480
R = 5%
TD = (PW × TR)/100
⇒ 18 = (480 × T × 5)/100
⇒ 18 = 24 × T
⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D
Answer: D
Question: if the price of a book is first decreased by 25% and then increased by 20%, then the net change in the price will be :
Options:
A)10
B)388
C)37
D)29
E)22
Rationale: Explanation:
Let the original price be Rs. 100.
New final price = 120 % of (75 % of Rs. 100) = Rs. (120/100 * 75/100 * 100) = Rs. 90.
Decrease = 10%
Answer: A) 10
Answer: A
Question: E and F represent two distinct digits. If the number 457E89F is divisible by 36, what is the value of (E+F)?
Options:
A)a) 9
B)b) 3
C)c) 12
D)d) 6
E)e) 10
Rationale: A no. divisible by 36 means it is div by 49 .
to be div by 4 last 2 digits to be multiple of 4 So, F could be either 2 or 6 only
similarly for a number to be div by 9 its sum must be multiple of 9 first. filtering we find E could be either 1,4,7 only.
To be divisible by 9 only 1 works .(if we choose f=6 then E have to be 6 but as per condition EF are distinct) So
E=1
F=2
Ans:- 3.B
Answer: B
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters)
Options:
A)92
B)90
C)82
D)78
E)75
Rationale: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
O=12.5*6 = 75=E
Answer: E
Question: If x > 7, which of the following is equal to (x^2 + 4x + 4)/(x^2 - 4) ?
Options:
A)(x + 4)/(4(x - 4))
B)(x - 4)/(x + 4)
C)(x - 2)/(x + 4)
D)(x + 4)/(x - 4)
E)(x + 2)/(x - 2)
Rationale: (x^2 + 4x + 4)/(x^2 - 4)
= (x + 2)(x + 2) / (x + 2)(x - 2)
=(x + 2)/(x - 2)
E. (x + 2)/(x - 2)
Answer: E
Question: The C.P of 5 pens is equal to the S.P of 7 pens. Find his gain % or loss%?
Options:
A)25 4/7%
B)26 4/7%
C)28 4/7%
D)14 4/7%
E)23 4/7%
Rationale: 5CP = 7 SP
7 --- 2 CP loss
100 --- ? => 28 4/7%
Answer: C
Answer: C
Question: A homeless man wins the lottery and winds up with $200,457,543. He wishes to share it equalling with 8 other homeless friends of his. How much more money does he need to be able to distribute the money equally?
Options:
A)7
B)0
C)6
D)1
E)4
Rationale: Using the rule on the divisibility of 9, we add all the digits together. The sum of those numbers is 30 and 36 is divisible by nine. Therefore, he needs 6 dollars.(option C)
Answer: C