divelab/Sys2Bench huggingface dataset:
Question: The ratio of the present ages of a man and his wife is 8 : 7. Which of the following can't be a possible ratio of their ages 45 years ago?
Options:
A)6: 8
B)7: 8
C)8:8
D)9: 8
E)10: 8
Rationale: 8x-45/7x-45 = 9/8
Therefore x=-45
Age cannot be negative.
Answer: D
Answer: D
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)189m
B)180m
C)100m
D)480m
E)1860m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m .Answer: B
Answer: B
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)18
B)99
C)77
D)26
E)12
Rationale: 9 * 2 = 18 years
Answer: A
Answer: A
Question: In how many ways can three boys can be seated on five chairs?
Options:
A)10
B)20
C)60
D)40
E)55
Rationale: There are three boys.
The first boy can sit in any of the five chairs (5 ways).
5
Now there are 4 chairs remaining. The second boy can sit in any of the four chairs (4 ways).
5	4
Now there are 3 chairs remaining. The third boy can sit in any of the three chairs (3 ways).
5	4	3
Hence, total number of ways in which 3 boys can be seated on 5 chairs
=5×4×3=60
Ans: C
Answer: C
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
Options:
A)0.07
B)0.049
C)0.7
D)0.49
E)4.9
Rationale: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*49*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 490/10,000 = 49/1000 = 0.049 ft
The answer is B.
Answer: B
Question: The ratio of the ages of Ragul and Vicky is 3 : 6. The total of their ages is 2.7 decades. The proportion of their ages after 0.3 decades will be
[1 Decade = 10 years]
Options:
A)4:7
B)3:4
C)4:5
D)7:9
E)3:6
Rationale: Let,Ragul’s age = 3A and Vicky’s age = 6A
Then 3A + 6A = 27
A = 3
Ragul’s age = 9 years
and Vicky’s age = 18 years
Proportion of their ages after 3 is = (9 + 3) : (18 + 3)
= 12 : 21
= 4 : 7
Answer : A
Answer: A
Question: If x is an integer, then x(x - 1)(x - l) must be evenly divisible by three when l is any of the following values EXCEPT
Options:
A)-4
B)-2
C)-1
D)2
E)5
Rationale: if we put l=-1 we get:
X(x-1)(X+1) rearrange:(x-1)X(X+1)
so it looks like a sequenc,
if we assume that X =2 and put number from the answer then we get:
(x – 1)x(x – l)
l=5 =1.2.-3
l=2 =1.2.0
l=-1 =1.2.3
l=-4 =1.2.6
but when we put
l=-2 =1.2.4 not satisfied
so,answer is B
Answer: B
Question: In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 65% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
Options:
A)a) 50%
B)b) 53%
C)c) 54%
D)d) 55%
E)e) 57%
Rationale: Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=50%
A
Answer: A
Question: If a#b = ab – b + b^2, then 3#7 =
Options:
A)2
B)63
C)15
D)21
E)35
Rationale: Solution -
Simply substitute 3 and 7 in equation in the place of a and b respectively.
3#7 = 3*7 - 7 + 7^2 = 21 - 7 + 49 = 63. ANS B
Answer: B
Question: John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
Options:
A)50
B)60
C)75
D)80
E)85
Rationale: (x+x1+...x14)/15 = 40
50
Option A
Answer: A
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 24 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)20.7
D)21.7
E)22.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 24 Paise is given as tax
=> Total tax incurred = 24 Paise = Rs.24/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 24/100
⇒ 6(25 −0.3 −x) = 24
⇒ (25 − 0.3 − x) = 4
⇒ x = 25 − 0.3 − 4 = 20.7
C)
Answer: C
Question: A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)3%
B)4%
C)5%
D)6%
E)7%
Rationale: S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate =(100 x 3000)/(12500 x 4)%	= 6%
answer :D
Answer: D
Question: If a and b are different positive integers and a + b+1 = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
Options:
A)I only
B)II only
C)III only
D)I and II
E)I and III
Rationale: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
D
Answer: D
Question: If P is a prime number greater than 5, what is the remainder when P^2 is divided by 6.
Options:
A)4
B)Cannot be determined
C)2
D)6
E)1
Rationale: take square of any prime number
remainder will be 1
Ans E
Answer: E
Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1. Find the sum
Options:
A)Rs 600
B)Rs 625
C)Rs 650
D)Rs 675
E)None of these
Rationale: Explanation:
Let the Sum be P
S.I.=P∗4∗2 /100=2P/25
C.I.=P(1+4/100)2−P
=676P/625−P
=51P/625
As, C.I. - S.I = 1
=>51P/625−2P/25=1
=>51P−50P/625=1
P=625
Option B
Answer: B
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12 m
B)111.72 m
C)111.15 m
D)116.12 m
E)111.32 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: A
Question: 850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
Options:
A)17
B)138
C)60
D)38
E)12
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 850 = 17
Answer: A
Answer: A
Question: X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days how long will they work together take to complete the work?
Options:
A)13 1/3
B)15
C)20
D)56
E)57
Rationale: Explanation:
Work done by x in 8 days= 8/40 = 1/5
remaining work= 4/5
4/5 work is done by Y in 16 days
whole work is done by Y in 16*5/4 = 20 days
X’s 1 day work =1/40
Y’s 1 day work =1/20
(X+Y)’s 1 day work=1/40 +1/20 = 3/40 = 13 1/3
Answer: Option A
Answer: A
Question: A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after one year service. He served only for 9 months and received uniform and Rs.650, find the price of the uniform?
Options:
A)377
B)197
C)187
D)100
E)822
Rationale: Explanation:
9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
Answer: D
Answer: D
Question: A man can row his boat with the stream at 16 km/h and against the stream in 8 km/h. The man's rate is?
Options:
A)4 kmph
B)2 kmph
C)7 kmph
D)8 kmph
E)3 kmph
Rationale: DS = 16
US = 8
S = ?
S = (16 - 8)/2 = 4 kmph
Answer:A
Answer: A
Question: A man’s speed with the current is 18 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
Options:
A)8.5 km/hr
B)9.5 km/hr
C)13 km/hr
D)12.5 km/hr
E)None of these
Rationale: Solution
Man's rate in still water = (18-2.5) km/hr = 15.5 km/hr.
Man's rate against the current = (15.5-2.5) km/hr = 13 km/hr Answer C
Answer: C
Question: 130kg of an alloy A is mixed with 160 kg of alloy B. If alloy A has lead and tin in the ratio 2:3 and alloy B has tin and copper in the ratio 3:4, then the amount of tin in the new alloy is?
Options:
A)140.6kg
B)145.3kg
C)146.5kg
D)110.8kg
E)114kg
Rationale: Quantity of tin in 130kg of A = 130*3/5 = 78kg
Quantity of tin in 160kg of B = 160*3/7 = 68.5kg
Quantity of tin in the new alloy = 78+68.5 = 146.5kg
Answer is C
Answer: C
Question: A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
Options:
A)45 kmph
B)50 kmph
C)85 kmph
D)60 kmph
E)70 kmph
Rationale: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 150/((x+5)×5/18)=6 <=> 30 (x + 5) = 2700 <=> x = 85
Speed of the train is 85 kmph.
Answer: Option C
Answer: C
Question: A natural number has exactly 10 divisors including 1 and itself.how many distint prime factors this natural number will have?
Options:
A)37
B)29
C)27
D)99
E)11
Rationale: Answer:D
Answer: D
Question: If there are 86 workers in a factory, and on a certain day, 72 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
Options:
A)82.7%
B)81.7%
C)83.7%
D)89.7%
E)88.7%
Rationale: 72/86*100=83.72
83.7%
correct answer C
Answer: C
Question: Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 7 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?
Options:
A)2y
B)3y
C)5y
D)6y
E)10y
Rationale: Anthony performed for 14 days meansw Cindy performed for(14-7)=7 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/7
Solving we get, x=3y
Now Anthony's Advance is x=3y .So answer should be B.
Answer: B
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 52 unique alphanumeric case sensitive characters.
Options:
A)63^4
B)62^5
C)62(62^4)
D)53(52^4)
E)63(62^6)
Rationale: Total number of passwords = number of 4 character password +number of 5 character password
= 52^4 + 52^5 (Since there is no limitation on repetition , each character can be chosen in 52 ways )
=52^4(1+ 52)
=52^4 * 53
Answer D
Answer: D
Question: A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 12 minutes. Then the speed of the current is :
Options:
A)1 kmph
B)2 kmph
C)3 kmph
D)2.5 kmph
E)3.5 kmph
Rationale: Rate upstream = (1/20 *60) = 3 kmph
Rate dowm stream = 1/12 * 60 = 5 kmph
Rate of the current = ½ (5-3) = 1 kmph
ANSWER:A
Answer: A
Question: What decimal of an hour is a second
Options:
A).0028
B).0027
C).0026
D).0025
E)None of these
Rationale: Explanation:
1/(60*60) = 1/3600 = .0027
Option B
Answer: B
Question: In a tea factory,one half of the workers are above 50 years,quarter are between 50 to 45 years,one-fifth are between 45 to 35 years and other 30 workers are below 20 years. How many workers total are there in the factory?
Options:
A)250
B)366
C)400
D)500
E)600
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 30
x= 30*20= 600
E is the answer.
Answer: E
Question: Find the odd man out
253, 136, 352, 323, 631, 244
Options:
A)323
B)136
C)352
D)631
E)531
Rationale: The sum all three digits comes to 10 except 323
ANSWER:A
Answer: A
Question: 6x − 12 = 6y
5y + 5x = 10
Which of the following is the number of solutions to the system of equations shown above?
Options:
A)More than three
B)Exactly three
C)Exactly two
D)Exactly one
E)None
Rationale: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
5y + 5x = 10
=>x + y = 2 -- 2
From equation 1 and 2 , we get
2x = 4
=> x=2
y=0
Therefore , the given system will have Exactly one solution
D
Answer: D
Question: Andy has grades of 84, 65, and 76 on three math tests. What grade must he obtain on the next test to have an average of exactly 80 for the four tests?
Options:
A)80
B)85
C)90
D)95
E)98
Rationale: (84 + 65 + 76+ x) 4 = 80
(4)(80) = 225 + x
320 = 225 + x
( 320-225) (225-225)
95 = x
ANSWER :D
Answer: D
Question: 81,162,49,98,25,50,66
Options:
A)126
B)127
C)129
D)128
E)132
Rationale: 81*2=162
49*2=98
25*2=50
66*2=132
ANSWER:E
Answer: E
Question: A rectangular table seats 5 people on each of two sides, with every person directly facing another person across the table. If ten people choose their seats at random, what is probability that any two of them directly face other?
Options:
A)1/56
B)1/8
C)1/7
D)1/9
E)4/7
Rationale: A B C D E
------------
| TABLE |
------------
F G H I J
A to J are 10 people.
Prob to select any 1 person = 1
Prob to select the person opposite to the chosen person = 1/9
For ex. If we select A as the person than prob of choosing F is 1/9.
Hence, answer will be D.
Answer: D
Question: A box contains 4 red balls and 4 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
Options:
A)1/4
B)1/2
C)1/2
D)5/8
E)2
Rationale: My complicated version of your simple approach
Let the 4 black balls be BBBBand 4 Red Balls be RRRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (8!)/ (4!x4!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 7 slots and 3 Black (BBB) and 4 Red (RRRR)
They can be arranged in (7!)/ (4!x3!)
Hence required probability = [(8!)/ (4!x4!)]/[(7!)/ (4!x3!)]
=2
E
Answer: E
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)Rs. 2(1/9)
B)Rs. 2(2/9)
C)Rs. 2(1/3)
D)Rs. 3(2/5)
E)Rs. 3(1/7)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: B
Question: In 1990 the budgets for projects Q and V were $620,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?
Options:
A) 1992
B) 1993
C) 1994
D) 1995
E) 1996
Rationale: Let the no of years it takes is x.
620+30x = 780-10x --> 40x = 160 and x=4.
Thus, it happens in 1994.
C.
Answer: C
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 17000, then find his savings?
Options:
A)3600
B)3400
C)3608
D)3602
E)3603
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 17000 => x = 3400
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3400.
Answer:B
Answer: B
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)4 min
B)2 min
C)8 min
D)9 min
E)3 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min.Answer: A
Answer: A
Question: Convert the 13/36 m/s into kilometers per hour?
Options:
A)2.9
B)2.2
C)1.3
D)1.2
E)1.8
Rationale: 13/36 m/s = 13/36 * 18/5 = 13/10 = 1.3 kmph.
Answer: C
Answer: C
Question: There are 8 boxes numbered from 1 to 8. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
Options:
A)32
B)34
C)36
D)38
E)40
Rationale: 1 green ball: 8 ways
2 green balls: 7 ways
3 green balls: 6 ways
4 green balls: 5 ways
5 green balls: 4 ways
6 green balls: 3 ways
7 green balls: 2 ways
8 green balls: 1 way
The total number of ways is 8*9/2=36
The answer is C.
Answer: C
Question: If 7^t is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of t?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: So the question just means that we have to find all the multiples t of 7 between 1 to 100
So there are 14 multiples of 7 ( 7 - 98)
But 49 and 98 contain two 7's as factors
so we have to add 14 + 2 = 16
E
Answer: E
Question: Difference between the length & breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Options:
A)2500 m^2
B)2510 m^2
C)2520 metre sq
D)2540 m^2
E)2590 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: The number of ways in which one or more balls can be selected out of 10 white, 9 green and 7 blue balls is
Options:
A)892
B)881
C)891
D)879
E)None of these
Rationale: The required number of ways
= (10 + 1)(9 + 1)(7 + 1) - 1 = 879.
Answer D
Answer: D
Question: A necklace is made by stringing N individual beads together in the repeating pattern green bead, white bead, yellow bead, red bead, and blue bead. If the necklace design begins with a green bead and ends with a yellow bead, then N could equal
Options:
A)55
B)65
C)75
D)68
E)85
Rationale: Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.
Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on yellow, which is 3 into the pattern.
I just went through all the answer choices, and only E fits. 5x13 = 65, and 65+3=68
Answer : D
Answer: D
Question: the sides of a triangle are in the ratio 3:5:7.if the pereimeter is 60 cms,the longest side is
Options:
A)7
B)30
C)28
D)25
E)16
Rationale: 3x+5x+7x=60
15x=60
x=4
longest side=7*4=28
ANSWER:C
Answer: C
Question: There are 6 equally spaced points A,B,C,D,E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
Options:
A)6P5
B)1
C)5
D)None of these
E)Cannot be determined
Rationale: Solution:
Since, all the points are equally spaced; hence the area of all the convex pentagons will be same.
Answer: Option D
Answer: D
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'4" tall, which of the following is the median height of the children?
Options:
A)2'2"
B)2'4"
C)3'3"
D)3'4"
E)4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'4"+2'4")/2 = 2'4"
Ans:Option B
Answer: B
Question: Find the odd man out
2, 7, 32, 157, 782, 3907, 17251
Options:
A)7
B)32
C)157
D)3907
E)17251
Rationale: 1*5-3 = 2
2*5-3 = 7
7*5-3 = 32
32*5-3 = 157
157*5-3 = 782
782*5-3 = 3907
3907*5-3= 19532
ANSWER:E
Answer: E
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
Options:
A)4:3
B)3:4
C)3:2
D)5:2
E)4:6
Rationale: 4 Ï€r2 : 3 Ï€r2 => 4:3
ANSWER A
Answer: A
Question: At a meeting of the 5 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 5 Chiefs of Staff be seated around a circular table?
Options:
A)120
B)480
C)960
D)2520
E)5040
Rationale: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer D (2520), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?D
Answer: D
Question: How much time will it take for an amount of 600 to yield 81 as interest at 4.5% per annum of simple interest?
Options:
A)3 years
B)4 years
C)6 years
D)5 years
E)7 years
Rationale: Time = (100 x 81)/(600 x 4.5) years = 3 years.
answer A
Answer: A
Question: In Kaya's teacher's desk there are 9 pink highlighters, 8 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all?
Options:
A)11
B)22
C)77
D)33
E)88
Rationale: Add the numbers of highlighters.
9 + 8 + 5 =22.
Answer is B.
Answer: B
Question: Calculate 469138 x 9999 = ?
Options:
A)4586970843
B)4686970743
C)4690910862
D)4586870843
E)NONE
Rationale: Answer
469138 x 9999 = 469138 x (10000-1)
= 4691380000 - 469138
= 4690910862.
Option: C
Answer: C
Question: A rectangular box measures internally 1.6m long, 1m broad and 60cm deep. The number of cubical box each of edge 20cm that can be packed inside the box is:
Options:
A)30
B)60
C)90
D)120
E)140
Rationale: Explanation:
Number of blocks =(160x100x60/20x20x20)=120
Answer: D
Answer: D
Question: Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
Options:
A)256
B)512
C)432
D)352
E)640
Rationale: Let total number of children be x.
Then, x *(1/8)x =(x/2)x 16
x = 64.
Number of notebooks =(1/8)x^2 =(1/8)x 64 x 64= 512.
Answer is B.
Answer: B
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
Options:
A)10 litres
B)20 litres
C)30 litres
D)5 litres
E)14 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5)=4/5 20x=4(3x+5)8x=20 x=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
ANSWER A 10 litres
Answer: A
Question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 25?
Options:
A)19
B)20
C)32
D)41
E)53
Rationale: (1056 / 25) gives remainder 6
19 + 6 = 23, So we need to add 19
A
Answer: A
Question: If a : b = 2 : 3, find the value of (3a + 5b) : (3a – b)
Options:
A)2 : 7
B)7 : 1
C)2 : 5
D)4 : 9
E)None of these
Rationale: Explanation:
Given: a/b = 2/3
(3a + 5b) / (3a – b)
= [3(a/b) +5] / [3(a/b) – 1]
= [3(2/3) +5] / [3(2/3) – 1]
= 7/1
ANSWER: B
Answer: B
Question: The size of a flat-screen tablet is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 6-inch flat-screen tablet than a square 5 -inch flat-screen tablet?
Options:
A)5.0
B)6.0
C)6.8
D)5.8
E)5.5
Rationale: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 6-inch flat-screen television
The diagonal (hypotenuse) = 6
So, we can apply the Pythagorean Theorem to get x² + x² = 6²
Simplify: 2x² = 6²
Divide both sides by 2 to get: x² = 6²/2
Since the area of the square = x², we can see that the area of this square is 6²/2
square 5-inch flat-screen television
The diagonal (hypotenuse) = 5
So, we can apply the Pythagorean Theorem to get x² + x² = 5²
Simplify: 2x² = 5²
Divide both sides by 2 to get: x² = 5²/2
Since the area of the square = x², we can see that the area of this square is 5²/2
DIFFERENCE IN AREAS =6²/2-5²/2
= (6²- 5²)/2 = (36-25)/2 =11/2=5.5
E
Answer: E