divelab/Sys2Bench huggingface dataset:
Question: If x and y are positive integers, then xy + x is
Options:
A)Always even
B)Always odd
C)Even whenever x is even
D)Even whenever x + y is odd
E)It cannot be determined from the information given
Rationale: xy + x can be factorized as x(y + 1) by taking out x common.
Now, anything multiplied by even is always even.
Answer (C).
Answer: C
Question: What is the product of all the possible values of x if x^2+4x+7=|x+2|+3
Options:
A)-6
B)–12
C)12
D)29
E)168
Rationale: x^2+4x+4=|x+2|
(X+2)^2 = |x+2|
Only 3 values possible,
x = -3, x = -2, x =-1
So multiplication = -6
answer option -6
ANSWER:A
Answer: A
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Options:
A)Rs. 1900
B)Rs. 2660
C)Rs. 2800
D)Rs. 2840
E)Rs. 2478
Rationale: For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
B's share = Rs. (7030 x	14/37) = Rs. 2660.
Answer: B
Question: If x = (y)(y + 1) and y is a prime number less than 10, which of the following could not be the product of 2 consecutive integers?
Options:
A)a) 5x
B)b) 11x
C)c) 16x
D)d) 30x
E)e) 57x
Rationale: Given y is a prime number less than 11
possible values of y are 2 3 5 7
given, x=y*(y+1)
if y = 2 x=2*3=6
if y = 3 x=3*4=12
if y = 5 x=5*6=30
if y = 7 x=7*8=56
so possible values of x are 6,12,30,56
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 16x can be (16*17)
D. 30x can be (30*31)
E. 57x can be (56*57)
So answer option C
Answer: C
Question: he 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)28
C)15
D)199
E)21
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: A statue is being carved by a sculptor. The original piece of marble weighed 140 kg. In the first week 60 percent is cut away. In the second week 40 percent of the remainder is cut away. In the third week the statue is completed when 30 percent of the remainder is cut away. What is the weight of the final statue?
Options:
A)24 kg
B)23 kg
C)28 kg
D)25 kg
E)27 kg
Rationale: A
24 kg
140 Ã— 0.4 Ã— 0.6 Ã— 0.7 = 24 kg.
Answer: A
Question: A library has an average of 510 visitors on sundays and 240 on other days . The avearge number of visitors per day in a month of 30 days beginning with a sunday is?
Options:
A)150
B)225
C)285
D)315
E)374
Rationale: Since the month begin with sunday, so there will be five sundays in the month
Required average = (510*5 + 240*25)/30 = 8550/30 = 285
Answer is C
Answer: C
Question: a number divided by 24 leaves remainder 56 what is the remainder when same number divided by 7
Options:
A)9
B)7
C)5
D)3
E)1
Rationale: add 24+56=80
now 80 divided by 7 so we get 3 as reaminder
ANSWER:D
Answer: D
Question: If three sides of the triangle are 8 , 15 and A respectively then the how many values can A ?
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 A take
Concept: Sum of any two sides of a triangle is greater then the third side.
Case 1: 8+5 > A => A<13
Case 2: 5+A > 8 => A >3
Case 3: 8+A > 5 => A > -3 (Always true since A is one side of a Triangle)
Finally, 3 < A < 13. So, we can have infinite number of sides between 3 and 13.
Answer = E
PS: If question said A can take only integer value, the A = 9. Answer choice D.
Answer: D
Question: In a paper factory 150 samples of sheets of paper were taken from a machine and checked for quality. Of these 150 samples, it was found that 3 sheets of paper were defective. If 500 bundles (10,000 sheets of paper per bundle) were produced by this machine, what is the approximate number of sheets of paper defective?
Options:
A)150,000
B)10,000
C)1,250
D)1,500
E)100,000
Rationale: Let D = sheets of paper made by the machine = 5,000,000,
B = sample number of sheets of paper = 150,
A = defective sample sheets of paper = 3, and
C = defective sheets of paper from machine, then:
Proportion: A/B = C/D
Proportion: 3/150 = C/5,000,000
C = 100,000. There are approximately 100,000 healthy fish in the pond.
Answer is E
Answer: E
Question: Three circles of radius 3.5cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is
Options:
A)1.967
B)1.963
C)2.388
D)3.388
E)2.382
Rationale: Explanation:
required area = (area of an equilateral triangle of side 7 cm)- (3 * area of sector with Ã = 60 degrees and r = 3.5cm)
\inline {\color{Black}(\frac{\sqrt{3}}{4}\times 7\times 7 )-(3\times \frac{22}{7}\times 3.5\times 3.5\times \frac{60}{360})} sq cm
=\inline {\color{Black}(\frac{\sqrt{3}}{4}\times 49 )-(11\times 0.5\times 3.5)} sq cm
= 1.967 sq cm
Answer: A) 1.967
Answer: A
Question: Total of the ages of A, B ahd C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2:
3. What is the age of B at present
Options:
A)25
B)30
C)45
D)60
E)65
Rationale: Explanation:
Let their ages 10 years ago is x, 2x and 3x years.
10 + 2x + 10 + 3x + 10 = 90 hence x= 10
B�s present age = (2x + 10) =30 years
Answer: Option B
Answer: B
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 40% profit?
Options:
A)277
B)960
C)896
D)266
E)121
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 14% of Rs. 640 = 140/100 * 640 = Rs. 896.
Answer: C
Answer: C
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options:
A)18 cm
B)20 cm
C)22 cm
D)24 cm
E)26 cm
Rationale: 2(l + b)	=	5
b	1
2l + 2b = 5b
3b = 2l
b =	2	l
3
Then, Area = 216 cm2
l x b = 216
l x	2	l	= 216
3
l2 = 324
l = 18 cm.
A)
Answer: A
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
A)32
B)55
C)6
D)78
E)81
Rationale: S = (100 + 300)/45 = 400/45 * 18/5
= 32
Answer: A
Answer: A
Question: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n61?
Options:
A)100~1,000
B)1,000~10,000
C)10,000~100,000
D)100,000~1,000,000
E)1,000,000,000,000,000,000~
Rationale: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n61?
A. 100~1,000
B. 1,000~10,000
C. 10,000~100,000
D. 100,000~1,000,000
E. 1,000,000~
-> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n61=2^60=(2^10)^6>(10^3)^6=10^18
Thus, the answer is E.
Answer: E
Question: Forks, Spoons, and Knives in drawer are in the ratio of 4: 4 : 3. If there are 16 Forks, the number of Knives in the drawer is:
Options:
A)8
B)4
C)12
D)16
E)14
Rationale: Explanation :
Let Forks = 4x, Spoons = 4x & Knives = 3x. Now, 4x = 16 hence x = 4.
Number of Knives = 3x = 12.
Answer : C
Answer: C
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
Options:
A)8
B)2
C)4
D)6
E)5
Rationale: 33 + 43 + 53
= a3
=> a = 6
Answer: D
Answer: D
Question: Bobby bought 2 shares, and which he sold for $124 each. If he had a profit of 40% on the sale of one of the shares but a loss of 17% on the sale of the other share, then on the sale of both shares Bobby had...
Options:
A)a profit of 10
B)a profit of 8
C)a loss of 8
D)a loss of 10
E)neither a profit nor a loss
Rationale: Cost of the first stock: 124/1.4=88.57, so profit from it 124-88.57=35.43
Cost of the second stock: 124/0.83=149.39, so loss from it 124-149.39=-25.39
Overall profit 35.43-25.39=10
Answer: A.
Answer: A
Question: Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 42 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?
Options:
A)70
B)80
C)100
D)140
E)150
Rationale: let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =42
or 3y =42 y =14 ;x =28 , total notes they carry = 4x+2y = 112+28 =140
D
Answer: D
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 30% goods during theft. His loss percent is:
Options:
A)23%
B)42%
C)32%
D)12%
E)22%
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 70.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 70 = Rs. 77
Hence, loss % = 23/100 * 100 = 23%
Answer:A
Answer: A
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)1887
B)9977
C)4312
D)2976
E)26612
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer: C
Answer: C
Question: If 2|2 –s| = 5, what is the sum of all the possible values for s ?
Options:
A)1/2
B)2
C)5/2
D)4
E)5
Rationale: if s<2, then 2-s=5/2; s=-1/2
if s>2 , then s-2=5/2; s=9/2
9/2-1/2=8/2=4=D
Answer: D
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Options:
A)54 sec
B)65 sec
C)25 sec
D)45 sec
E)24 sec
Rationale: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer:C
Answer: C
Question: If x is a number such that x^2 + 4x - 5 = 0 and x^2 + x - 20 = 0, then x =
Options:
A)1
B)-4
C)4
D)-5
E)5
Rationale: x^2 + 4x - 5 = (x+5)(x-1) = 0
Then x=-5 or x=1.
x^2 + x - 20 = (x-4)(x+5) = 0
Then x=4 or x=-5.
Thus x=-5.
The answer is 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. How far is the place?
Options:
A)2.91 km
B)2.88 km
C)2.78 km
D)2.98 km
E)2.87 km
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: B
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 18m/h. what is the speed of the person while he was going to his office?
Options:
A)8km/h
B)9km/h
C)10km/h
D)11km/h
E)12km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=18
\inline \Rightarrow 1.5k = 18
\inline \Rightarrow k=12km/h
E
Answer: E
Question: In the Hillside summer camp there are 50 kids. 90% of the kids are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of kids in the camp. How many more boys must she bring to make that happen?
Options:
A)50.
B)45.
C)40.
D)30.
E)25.
Rationale: Given there are 50 kids , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.
Now boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).
IMO option A is correct.
Answer: A
Question: A dealer purchased toys at 1/2 of their list price and sold them for 10% more than the list price. What is his percent gain?
Options:
A)10
B)50
C)110
D)120
E)220
Rationale: Cost = 1/2 List Price = .5*LSale = 1.10 List Price = 1.10*LGain Ratio = (Sale - Cost) / Cost = (1.10*L - .5*L) / .5*L = .6*L / .5*L = 1.20Gain Percent = 100 * Gain Ratio = 100 * 1.20 = 120% = Answer D
Answer: D
Question: A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.
Options:
A)62 kmph
B)58 kmph
C)52 kmph
D)50 kmph
E)None of these
Rationale: Relative speed = (280⁄9) m/sec = (280⁄9 × 18⁄5) kmph
= 112 kmph.
∴ Speed of goods train = (112 – 50) kmph = 62 kmph.
Answer A
Answer: A
Question: A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 550 dollars, and, in a third, loses 120. In the end he finds he has gained 300 dollars, by the three together. How much did he gain or lose bv the first ?
Options:
A)-130
B)120
C)130
D)-80
E)None
Rationale: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 550 - 120 = 300
And x = -130.
Answer A
Answer: A
Question: The ratio between x and y is 7/9; x is increased by 4 and y is decreased by 4, what is the ratio between the new values of x and y?
Options:
A)7/9
B)14/9
C)7/18
D)11/13
E)It Cannot Be Determined
Rationale: Ratio = 7k/9k = 7/9, 14/18, etc.
x is increased by 4 and y is decreased by 4--> (7k + 4)/(9k - 4)
New ratio can be 11/15, 18/14, etc.
Answer: E
Answer: E
Question: There is rain all over the city at a rate of 7 centimeters per hour. If a person is waiting in his house for the rain to stop how long did he wait to go out. The rain water filled a bucket of 28 centimeters depth and 200 square meters area?
Options:
A)5 hours 14 minutes
B)6 hours
C)4 hours
D)8 hours
E)12 hours
Rationale: Answer is : C, 4 hours
The volume of the bucket is irrelevant and only height matters since rain fell all over the city.
Thus, it takes only 28 / 7 = 4 hours of rain to fill the bucket
Answer: C
Question: 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
Options:
A)23
B)27
C)20
D)27
E)11
Rationale: 16 * 25 = 20 * x => x = 20 days
Answer:C
Answer: C
Question: in a soap company a soap is manufactured with 11 parts.for making one soap you will get 1 part as scrap.at the end of the day you have 251 such scraps.from that how many soaps can be manufactured?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: Using 251 scraps we make = 22 soaps. (i.e., 11*22 = 242)Remaining scraps = 9.
Again, 22 soaps produce = 22 scraps.
So, now we have 22+9=31 scraps remaining.
Using 31 scraps we make 2 soaps and 2scraps remaining.(i.e., 2*11 =22)
Again, that 2 soaps produce = 2 scraps. And already we have 9 scraps. Total 9+2 =11sscraps.
By using 11 scraps, we make 1 soap.
So, total = 22+2+1 = 25 soaps we produce.
ANSWER:B
Answer: B
Question: The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 82, and the average of the female students’ grades was 92, how many female students took the test?
Options:
A)8
B)9
C)10
D)21
E)32
Rationale: Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f
Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 82 Thus M = 656 ---------2
Also, F/f = 92 thus F = 92 F - --------3
Put 2 and 3 in 1: we get
(656+92f)/(8+f) = 90
solving this we get f = 32
Ans: E
Answer: E
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Options:
A)3.5
B)4.5
C)5.6
D)6.5
E)None
Rationale: Solution
C.P of 1 toy	= Rs.(375/12)
= Rs.31.25
S.P of 1 toy	= Rs.33.
Therefore,Profit	= (1.75/31.25×100)%
=(28/5)%
=5.6%.
Answer C
Answer: C
Question: If the function f(x) is defined for all real numbers x as the maximum value of 2x + 2 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 2 ?
Options:
A)–4
B)–8
C)–11
D)–13
E)–19
Rationale: Since f(x) defines maximum of 2x + 2 and 12 + 3x,
to find those x when 2x+2 has greater value,
2x + 2 > 12 + 3x
or x < -10
Only value that satisfy this is -11.
Answer is (C),
Answer: C
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)45 km/hr
B)50 km/hr
C)54 km/hr
D)55 km/hr
E)58 km/hr
Rationale: Speed of the train relative to man = 125/10	m/sec
= 25/2	m/sec.
2
= 25/2	x	18/5	km/hr
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 x = 50 km/hr.
Option B
Answer: B
Question: The average (arithmetic mean) of eight numbers is 48.1. If the sum of half of these numbers is 158.4, what is the average of the other half?
Options:
A)12.8
B)24.2
C)56.6
D)72.1
E)96.8
Rationale: arithmetic mean = sum / total numbers
sum = 48.1 * 8 = 384.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 384.8-158.4 = 226.4
Arithmetic mean of the 4 nos = 226.4/4 = 56.6
Hence, C is the answer.
Answer: C
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
Options:
A)9%loss
B)7%loss
C)8%loss
D)5%loss
E)1%loss
Rationale: (30*30)/100
= 9%loss
Answer: A
Answer: A
Question: How many possible ways can 2 girls (Rebecca, Kate, Ashley) go on a date with 3 boys (Peter, Kyle, Sam)?
Options:
A) 3
B) 4
C) 5
D) 6
E) 8
Rationale: Any one girl can go with 3 boys.
2nd girl can go with remaining 2 boys
3*2 i.e 6 (D) is the answer
Answer: D
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
Options:
A)4400
B)3000
C)4200
D)5000
E)5500
Rationale: X * (95/100) * (85/100) = 3553
X = 4400
ANSWER A
Answer: A
Question: If a - b = 3, a^2 + b^2 = 29 ,find the value of ab.
Options:
A)10
B)12
C)15
D)18
E)19
Rationale: Explanation:
2ab = (a^2 + b^2) - (a - b)^2 = 29 - 9 = 20 => ab = 10..
Answer: A
Answer: A
Question: On a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is
Options:
A)23
B)11
C)378
D)36
E)29
Rationale: Explanation:
Difference in C.I and S.I for 2 years
= Rs(696.30-660)
=Rs. 36.30.
S.I for one years = Rs330.
S.I on Rs.330 for 1 year =Rs. 36.30
Rate
= (100x36.30/330x1)%
= 11%
Answer: B) 11%
Answer: B
Question: Walking at 6/7th of his usual speed, a man is 25 mins too late. His usual time is
Options:
A)7.5 hrs
B)1.5 hrs
C)2.5 hrs
D)1.67 hrs
E)2.67 hrs
Rationale: As the distance is same s*t=6/7s*(t+25)
solving this we get t=150 sec
150/60=2.5 hrs
ANSWER:C
Answer: C
Question: A shop purchased a pair of shoes for $150 and was selling it at a price that equaled the purchase price of the shoes plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
Options:
A)$0
B)$2
C)$10
D)$6
E)$8
Rationale: Sale Price(SP) = 150 + Markup(MP)
--> Mp = SP-150
and given MP=SP/4 ( 25% is 1/4th)
so SP/4= SP-150
3SP/4= 150
SP=200
Now a discount of 20% is given so NEW SP is .8 *200 =160
Profit=160-150 =$10
Answer is C
Answer: C
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
Options:
A)31/111
B)36/145
C)21/115
D)11/154
E)None of these
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: B
Question: What is the sum of all the odd numbers between 24 and 50, inclusive?
Options:
A)592
B)481
C)330
D)475
E)483
Rationale: To solve this problem, all you have to do is take every even number between 24 and 50 and add them together. So we have 25+27+29+31+33+35+37+39+41+43+45+47+49, which is 481.
Final Answer:
B
Answer: B
Question: A shipment of 8 TV sets contains 5 black and white sets and 3 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
Options:
A)1/7
B)1/4
C)5/14
D)25/28
E)13/28
Rationale: 3/8 * 2/7 = 6/56
1-(6/56) = 50/56 = 25/28
Answer D
Answer: D
Question: What approximate value should come in place of the question mark (?) in the following equation?
1.542 × 2408.69 + 5134.632 = ?
Options:
A)4600
B)4800
C)5200
D)6400
E)8800
Rationale: Explanation 3700 + 5100 = 8800
Answer E
Answer: E
Question: In a contest, a bowl contains 9 keys, one of which will open a treasure chest and eight of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Ram is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that he wins the prize?
Options:
A)2/9
B)13/2
C)15/4
D)16/15
E)None
Rationale: The total possibilities existing while withdrawing two keys are: 9C2 = 36
For Ram to win, 8 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,8)
P = 8/36 = 2/9
Option A
Answer: A
Question: Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 5. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
Options:
A)(4m+15)/[m(m-5)]
B)(8m-15)/[m(m-5)]
C)(10m-15)/[m(m-5)]
D)(4m-15)/[m(m-5)]
E)(12m-15)/[m(m-5)]
Rationale: Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m
Amount of 4th Sandwich with remaining (m-5) students = 1/(m-5)
The amount of Sandwich that carol ate = 3/m + 1/(m-5) = (3m-15+m)/[m(m-5)] = (4m-15)/[m(m-5)]
Answer: D
Answer: D
Question: The average of five numbers is 20. If one number is excluded, the average becomes 18. The excluded number is?
Options:
A)25
B)28
C)32
D)40
E)16
Rationale: Excluded number = 20*5-18*4 = 100-72 = 28
Answer is B
Answer: B
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
Options:
A)Rs.24029
B)Rs.24000
C)Rs.24038
D)Rs.24082
E)Rs.24026
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer: B
Answer: B
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
Options:
A)160
B)150
C)100
D)80
E)50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 30 gallons then 0.12A+0.16(200-A)=30 --> A=50.
Answer: E.
Answer: E