divelab/Sys2Bench huggingface dataset:
Question: According to a survey, at least 80% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
Options:
A)15%
B)20%
C)25%
D)0%
E)35%
Rationale: It seems that something is wrong with your answer options.
1) minimum applesbananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum ab = 80 - (100-75) = 55%
2) minimum (applesbananas)cherries:
[XXXXXXXXX-----------] - applesbananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum ab = 55 - (100-80) =35%
E
Answer: E
Question: What is the volume of an tetrahedron with edge length of 1?
Options:
A)sqr(2)/12 = 0.11785113
B)sqr(2)/14=0.13571785
C)sqr(2)/12=0.15798562
D)sqr(2)/13=0.21254478
E)sqr(2)/12=0.12457896
Rationale: The following can be derived using the Pythagorean theorem:
The height of a face is 3.5/2.
The area of any face is 3.5/4.
The distance from any corner to the center of a joining face is 1/3.5.
The height of the tetrahedron is (2/3).5
The area is 1/3*base*height =
(1/3) * 3.5/4 * (2/3).5 = 21/2/12.
Answer: A
Question: Solve the given two equations and find the inequality of X and Y. (a) 225X^2-4 = 0 and (b) (225y)^(1/2) +2 = 0
Options:
A)If x>y
B)If x>=y
C)If x<y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X= +2/15 and -2/15
Y= 4/225
Comparing we get X>Y and X<Y
Hence, no relationship can be established
E
Answer: E
Question: A sum of Rs. 1800 amounts to Rs. 9000 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)50%
B)75%
C)100%
D)60%
E)25%
Rationale: S.I. = (9000 - 1800) = Rs. 7200\
Rate = (100 * 7200) / (1800* 4)
= 100%
Answer: C
Answer: C
Question: Look at this series: 14, 7, (7/2), (7/4), ... What number should come next?
Options:
A)1/8
B)3/8
C)7/8
D)5/8
E)6/8
Rationale: Explanation:
28/2 = 14
14/2 = 7
7/2 = 7/2
(7/2)/2 = 7/4
(7/4)/2 = 7/8 and so on.
Answer: Option C
Answer: C
Question: A pharmacist has 4 quarts of a 15% solution of iodine. How much alcohol must be added to
reduce it to a 10% solution of iodine?
Options:
A)1 quart
B)2 quarts
C)3 quarts
D)4 quarts
E)5 quarts
Rationale: What’s being added? Hopefully, you said alcohol. Therefore our equation will look like this:
ALCOHOL + ALCOHOL = ALCOHOL
4 qts + x qts = (4 + x) qts
We start off with 4 quarts, add x quarts, then end up with (4 + x) quarts.
+ =
4 x (4 + x)
Notice that you started with 4 quarts and added x quarts on the left side of the equation and you
ended up with (4 + x) on the other side. The parentheses indicate that it’s one container, Neato!
Of the original 4 quarts, 15% is iodine. Since we are doing the problem in terms of what we are
adding – alcohol, we must change 15% iodine solution to an 85% solution of alcohol. Let’s write
the equation.
.85(4) + x = .90(4x)
Where’d the .90 come from? Well, since I wanted to end up with a 10% solution of iodine, that
meant it must be a 90% solution of alcohol.
Multiplying both sides of the equation by the common denominator – 100, we have
85(4) + 100x = 90(4 + x)
340 + 100x = 360 + 90x
10x = 20
x = 2
You would have to add 2 quarts of alcohol to reduce the mixture to 10% iodine.
correct answer B
Answer: B
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √2 ¤ √2 =
Options:
A)0
B)8
C)10
D)15
E)20
Rationale: X = √2 and Y also =√2
Applying the function (√2+√2)^2 - (√2-√2)^2 = (2√2)^2 - 0 = 4 x 2 = 8.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√2 and y = √2 you get the answer 8.
Answer B
Answer: B
Question: The first Republic Day of India was celebrated on 26th January, 1950. It was :
Options:
A)Tuesday
B)Wednesday
C)Thursday
D)Friday
E)None of these
Rationale: 26th Jan., 1950 = (1949 years + Period from 1st Jan.,1950 to 26th Jan., 1950)
1600 years have 0 odd day. 300 years have 1 odd day.
49 years = (12 leap years + 37 ordinary years)
= [(12 × 2) + (37 × 1)] odd days = 61 odd days
= 5 odd days.
Number of days from 1st Jan. to 26th Jan. = 26
= 5 odd days
Total number of odd days = (0 + 1 + 5 + 5) = 11
= 4 odd days
∴ The required days was ‘Thursday’
Answer C
Answer: C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)247 m
B)256 m
C)245 m
D)527 m
E)725 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x)
= 750 => x = 245 m.
Answer:C
Answer: C
Question: What is the reciprocal of (AB)/(A+B)^2?
Options:
A)(AB)/(A^2+2AB+B^2)
B)A/B+B/A+AB
C)B/A+A/B+2
D)(A+B)^2/AB
E)A/B+2AB
Rationale: Answer:
Reciprocal = (A+B)^2/AB
= (A^2+B^2+2AB)/AB = B/A + A/B +2
ANSWER:C
Answer: C
Question: 8 couples attend a dance show in a TV channel. A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is at least 1 couple will be selected is :
Options:
A)1/41
B)11/23
C)15/39
D)15/18
E)21/31
Rationale: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)
= 15/39
C
Answer: C
Question: A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.75?
Options:
A)1280
B)1145
C)1040
D)950
E)260
Rationale: The charge is 65 cents for the first 250 grams.
This leaves a charge of $1.75 - $0.65 = $1.10
The charge for the next 1000 grams is $1.00 which leaves a charge of $0.10
The weight is somewhere between 1250 and 1350.
The answer is A.
Answer: A
Question: 40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6?
Options:
A)5
B)8
C)10
D)12
E)15
Rationale: Let x be the amount of liquid Q to be added.
(3/8)*40 + x = (6/11)*(40+x)
1320 + 88x = 1920 + 48x
40x = 600
x = 15
The answer is E.
Answer: E
Question: In a store 6 different CDs are there. If John can buy 2 CDs, how many cases that he can buy are there?
Options:
A)12
B)15
C)18
D)21
E)24
Rationale: Let CDs are A, B, C, D, E, F
He may choose any pair as mentioned below
AB, AC, AD, AE, AF = 5 cases
BC, BD, BE, BF = 4 cases
CD, CE, CF = 3 cases
DE, DF = 2 cases
EF = 1 case
Total cases = 5+4+3+2+1 = 15
Answer: Option B
Answer: B
Question: What percent of a day is 15 hours?
Options:
A)37Ã—1/2%
B)16Ã—1/2%
C)18Ã—2/3%
D)22Ã—1/2%
E)None
Rationale: Solution
Required percentage	= (15/24Ã—100)%
= (75 / 2)%.
= 37Ã—1/2%.
Answer A
Answer: A
Question: If P * Q implies (P2 + Q2), 8 * (3 * 2) = ?
Options:
A)239
B)278
C)233
D)2697
E)771
Rationale: Explanation:
We have, P * Q = (P2 + Q2) ......... Given
8 * (3 * 2) = ?
8 * 13 = (64 +169) = 233
ANSWER: C
Answer: C
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 100 pages?
Options:
A)8 hours 30 mins
B)8 hours
C)9 hours
D)7 hours
E)6 hours
Rationale: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 100 pages when Anil and Suresh work together = 100 × 3 /40 = 75/10
= 7 1/2 hours = 7 hour 30 minutes
Answer is A.
Answer: A
Question: Country X taxes each of its citizens an amount equal to 10 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
Options:
A)$40,000
B)$56,000
C)$60,000
D)$66,667
E)$80,000
Rationale: Equation is correct, so math must be a problem.
0.10*40,000+0.2*(x-40,000)=8,000 --> 4,000+0.2x-8,000=8,000 --> 0.2x=12,000 --> x=60,000.
Answer: C.
Answer: C
Question: The total weight of eight nougat nuggets is 3 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
Options:
A)0.18 oz.
B)0.375 oz.
C)1.8 oz.
D)5 oz.
E)18 oz
Rationale: Average = Total/Number of items
= 3/8 = 0.375.
Hence, B
Answer: B
Question: Last year a certain bond price with a face value of 5000 yielded 6% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
Options:
A)4615
B)5325
C)5351
D)6000
E)6154
Rationale: Interest = 0.06*5000 = 0.065*selling price --> selling price = 0.06*5000/0.065 --> selling price = ~4,615
Answer: A.
Answer: A
Question: On a map, 1 inch represents 28 miles. How many Z inches would be necessary to represent a distance of 383.6 miles?
Options:
A)5.2
B)7.4
C)13.7
D)21.2
E)28.7
Rationale: Z inches necessary to represent a distance of 383.6 miles = 383.6/28
= 13.7
Answer C
Answer: C
Question: Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share thrice, no apples were left.How many apples were there?
Options:
A)500
B)510
C)511
D)501
E)504
Rationale: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 9 times. So answer is (2^9)-1=511.
ANSWER:C
Answer: C
Question: 4 years ago, Paula was 4 times as old as Karl. In 12 years, Paula will be twice as old as Karl. What is the sum of their ages now?
Options:
A)36
B)40
C)44
D)48
E)52
Rationale: P-4 = 4(K-4) and so P = 4K-12
P+12 = 2(K+12)
(4K-12)+12 = 2K+24
K = 12
P = 36
P+K = 48
The answer is D.
Answer: D
Question: Find the average of the series : 220, 180, 328, 147 and 160?
Options:
A)230
B)200
C)250
D)201
E)207
Rationale: Average = (220 + 180 + 328 + 147 + 160)/5
= 1035/5
= 207
Answer: E
Answer: E
Question: If 20% of a number = 1000, then 120% of that number will be?
Options:
A)20
B)120
C)360
D)6000
E)820
Rationale: Let the number x. Then,
20% of x = 1000
x = (1000 * 100)/20 = 5000
120% of x = (120/100 * 5000) = 6000.
ANSWER:D
Answer: D
Question: In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 300 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 40% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
Options:
A)40 ml
B)100/3 ml
C)140 ml
D)20/3 ml
E)10 ml
Rationale: There are 0.4*100=40 ml of element X in the initial solution.
We need X to be 1/3rd of 300 ml in the resulting solution, so 100 ml. Thus out of 200 ml of solution added, 60 must be X (in order it to become 100 ml) ans the remaining 140 must be Y.
Answer: C
Answer: C
Question: What is the probability that the position in which the consonants appear remain unchanged when the letters of the word "Math" are re-arranged?
Options:
A)1/4
B)1/6
C)1/3
D)1/24
E)1/12
Rationale: Explanatory Answer
Step 1: Compute denominator
In any probability question, the denominator represents the total number of outcomes for an event. The numerator represents the number of favorable outcomes.
The total number of ways in which the word MATH can be re-arranged = 4! = 4*3*2*1 = 24 ways.
Step 2: Compute numerator and the probability
If the positions in which the consonants appear do not change, the first, third and the fourth positions are reserved for consonants and the vowel A remains at the second position.
The consonants M, T and H can be re-arranged in the first, third and fourth positions in 3! = 6 ways so that the positions in which the positions in which the consonants appear remain unchanged.
Therefore, the required probability 6/24=/14
Choice A
Answer: A
Question: Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
Options:
A) 25%
B) 28.1%
C) 20%
D) 12.5%
E) 11.1%
Rationale: Welcome, just post the question and the choices
Let's see, the way I did it was
1/3 are clerical out of 3600 so 1200 are clerical
1200 reduced by 1/4 is 1200*1/4
so it reduced 300 people , so there is 900 clerical people left
but since 300 people left, it also reduced from the total of 3600 so there are 3300 people total
since 900 clerical left / 3200 people total
Answer : B
Answer: B
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different W ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
Options:
A)5
B)6
C)9
D)12
E)18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible W is 2*6=12.
Answer: D.
Answer: D
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)(2x-5) = 0?
Options:
A)1/12
B)1/6
C)1/4
D)1/3
E)1/2
Rationale: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5, x=-10 and x=5/2=2.5. So, two solutions present in our set of 12 distinct numbers, therefore P=2/12=1/6.
Answer: B.
Answer: B
Question: At a certain high school, the senior class is twice the size of the junior class. If 7/8 of the seniors and 1/2 of the juniors study Japanese, what fraction of the students in both classes study Japanese?
Options:
A)3/4
B)1/2
C)1/4
D)3/8
E)5/16
Rationale: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 200 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (7/8)*200=175 and (1/2)*100=50. 175+50=225. There are a total of 300 students in the junior class and senior class combined (100+200=300), and there are 225 total students in Japanese, so 225 students in Japanese / 300 total students equals 3/4 of the students in both classes that study Japanese.
Answer: A
Answer: A
Question: A bat is bought for Rs.400 and sold at a gain of 20% find its selling price?
Options:
A)Rs.430/-
B)Rs.440/-
C)Rs.480/-
D)Rs.490/-
E)Rs.500/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
C
Answer: C
Question: The ratio of two quantities is 5 : 8. If each of the quantities is increased by 10, what is the ratio of the new quantities?
Options:
A)5:8
B)50:78
C)2:3
D)It cannot be determined from the information given.
E)6:7
Rationale: Since the ratio is 5:8 we can put the quantities as 5K and 8K.
Moreover increasing quantities implies that the quantities become 5K+10 and 8K+10. So the ratio is (5K+10):(8K+10). The ratio value depend on the value of K. So It cannot be determined from the information given.
The answer is D
Answer: D
Question: $364 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share?
Options:
A)$200
B)$204
C)$208
D)$212
E)$216
Rationale: Let the shares for A, B, and C be x, 2x, and 4x respectively.
7x = 364
x = 52
4x = 208
The answer is C.
Answer: C
Question: If the tens digit of positive integers q, y are 6, how many values of the tens digit of 2(q+y) can be there?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: If the tens digit of positive integers q, y are 6, how many values of the tens digit of 2(q+y) can be there?
A. 2
B. 3
C. 4
D. 5
E. 6
-> If q=y=60, 2(q+y)=240 is derived. If q=y=69, 2(q+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
Answer: C
Question: The difference between a number and its three-fifth is 50. What is the number ?
Options:
A)75
B)100
C)125
D)none of these
E)95
Rationale: Let the number be x. Then, x-(3/5)x=50
=>(2/5)*x=50
=>x=(50*5)/2=125
Answer :C
Answer: C
Question: In the equation 2x â€“ cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 2 ?
Options:
A)âˆ’9/2
B)-4
C)-3
D)6
E)9/2
Rationale: 2x - cy = 18
x=6, y=2;
12-2c=18
c=-3
2x-cy=18
when y=3, c=-3, x=
x=6
ANSWER:D
Answer: D
Question: A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 25 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
Options:
A)2
B)5
C)1
D)6
E)7
Rationale: Explanation:
He covered 5 km in 1 hour , so he might cover 25 km in 5 hours.
But he took 10 hours.
He would have saved 10 â€“ 5 = 5 hours.
Answer: B
Answer: B
Question: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 35 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
Options:
A) 3
B) 5
C) 7
D) 16
E) 24
Rationale: Total work = 4*35 machine hrs
Time taken = 4* 35 /5 => 28 hours...
Thus all five machines, operating simultaneously will take ( 35 - 28 ) 7 hours..
Answer will be (C) 7
Answer: C
Question: What least number must be added to 9879, so that the sum is completely divisible by 10 ?
Options:
A)3
B)4
C)1
D)2
E)6
Rationale: If we divide 9879 by 10 remainder is 9
10-9 =1
Answer : C
Answer: C
Question: IN Common Wealth Games an athlete runs 200 meters in 24 seconds. Hisspeed is ?
Options:
A)25 km/hr
B)27 km/hr
C)30 km/hr
D)32 km/hr
E)None of these
Rationale: Explanation :
(200/1000)/(24/3600)=30 km/hr
Answer : C
Answer: C
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options:
A)20
B)30
C)40
D)50
E)10
Rationale: A
20
Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: A
Question: Anand and Deepak started a business investing Rs. 6,000 and Rs. 7,000 respectively. Out of a total profit of Rs. 1,300. Deepak's share is?
Options:
A)s. 650
B)s. 780
C)s. 800
D)s. 760
E)s. 700
Rationale: Ratio of their shares = 6000 : 7000 = 7 : 13
Deepak's share = Rs. (1300 * 7/13) = Rs. 700 ANSWER "E
Answer: E
Question: An art gallery owner is hanging paintings for a new show. Of the seven paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
Options:
A)18
B)30
C)64
D)120
E)210
Rationale: Arrangment means permutations questions..
7P3 = 7!/3! = 210.
IMO option E is correct answer..
Answer: E
Question: If a2 - b2 = 10 and a*b = 5, find a4 + b4.
Options:
A)50
B)100
C)150
D)92
E)25
Rationale: a2 - b2 = 10 : given
a4 + b4 - 2a2b2 = 102 : square both sides and expand.
a*b = 5 : given
a2b2 = 52 : square both sides.
a4 + b4 - 2(25) = 100 : substitute
a4 + b4 = 150
correct answer C
Answer: C
Question: A numberais squared and then multiplied by negative 3. The result of this operation T is equal to three times the sum of three timesaand two. What is one possible value ofa?
Options:
A)-3
B)-2
C)1
D)2
E)3
Rationale: T=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: B
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
Options:
A)22 min
B)30 min
C)87 min
D)26 min
E)11 min
Rationale: Explanation:
Distance travelled by Ramu = 45 x 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively.
Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer: B
Answer: B
Question: If 9a - b = 10b + 50 = -12b - 2a, what is the value of 11a + 11b?
Options:
A)-4
B)-2
C)0
D)2
E)4
Rationale: This implies 9a - b = 10b + 50, 9a -b = -12b -2a, 10b + 50 = -12b -2a
Manipulating the second equation gives us 9a - b = -12b - 2a ==> 11a + 11b = 0
Answer is C
Answer: C
Question: If 40 percent of the members of a certain organization are women and 4/8 of the members of the organization are married men, which of the following statements concerning the membership must be true?
I. The number of women in the organization is greater than the number of married men in the organization.
II. The number of women in the organization is greater than the number of unmarried men in the organization.
III. The number of married men in the organization is greater than the number of unmarried men in the organization.
Options:
A)I,II
B)III
C)II,III
D)II
E)I
Rationale: 4/10 (40%) of the members are women and 4/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:
4/10*80 = 32 women;
80 - 32 = 48 men;
4/8*48 = 24 married men;
48 - 24 = 24 unmarried men.
So, option I,II is true.
Answer: A
Answer: A
Question: What is the remainder when (71)(73) is divided by 9?
Options:
A)1
B)2
C)4
D)6
E)8
Rationale: (71)(73) = (72-1)(72+1) = 72^2 - 1 which is 1 less than a multiple of 9.
Then the remainder will be 8.
The answer is E.
Answer: E
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Options:
A)40 kg
B)42kg
C)50kg
D)58kg
E)60 kg
Rationale: Volume of water displaced	= (3 x 2 x 0.01) m3
= 0.06 m3.
Mass of man
= Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
answer : E
Answer: E
Question: Look at this series: 70, 71, 76, 70, 81, __, 70, 91, ... What number should fill the blank?
Options:
A)70
B)86
C)82
D)77
E)52
Rationale: B
86
In this series, 5 is added to the previous number; the number 70 is inserted as every third number.
Answer: B
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
Options:
A)2:7
B)2:3
C)2:1
D)2:9
E)2:2
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
Answer: Option B
Explanation:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
Answer: B
Answer: B
Question: What is the smallest positive integer X such that (X+1)^2 is divisible by 28, 98, 242, and 308?
Options:
A)153
B)308
C)121
D)96
E)511
Rationale: 28 = 2 * 2 * 7
98 = 2 * 7 * 7
242 = 2 * 11 * 11
308 = 2 * 2 * 7 * 11
So (X+1)^2 = 2 * 2 * 7 * 7 * 11 * 11, which means (X+1) = 2 * 7 * 11 = 154, which means X = 153, which is option A
Answer: A
Question: The area of a right-angled triangle is two-thirds of the area of a rectangle. The base of the triangle is 80 percent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
Options:
A)20 cm
B)30 cm
C)15 cm
D)Data inadequate
E)None of these
Rationale: Let the base and height of triangle, and length and breadth of rectangle be L and h, and L1 and b1 respectively.
Then 1⁄2 × L × h = 2⁄3 × L1 × b1 .....(i)
L = 4⁄5b1 .....(ii)
and L1 + b1 = 100 .....(iii)
In the above we have three equations and four unknowns. Hence the value of ‘h’ can’t be determined.
Answer D
Answer: D