divelab/Sys2Bench huggingface dataset:
Question: In a school of 600 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
Options:
A)102
B)112
C)122
D)132
E)142
Rationale: 45 + 23 + 15 = 83%
100 – 83 = 17%
600 * 17/100 = 102
The answer is A.
Answer: A
Question: The probability of pulling a black ball out of a glass is 1/X. The probability of pulling a black ball out of a glass and breaking the glass is 1/Y. What is the probability of breaking the glass?
Options:
A)1/(XY).
B)Y/X
C)X by Y
D)1/(X+Y).
E)1/(X-Y).
Rationale: pulling a black ball out of a glass and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass = P(a) and Prob of breaking the glass= P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer should be C.
Answer: C
Question: Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 2244 sq. metres.
Options:
A)A)25.4
B)B)26.7
C)C)24.3
D)D)22.5
E)of these
Rationale: Explanation:
Clearly, the cow will graze a circular field of area 2244 sq. metres and radius
equal to the length of the rope.
Let the length of the rope be R metres.
Then, Π(R)2= 2244 => R2 = (2244 X (7/22)) = 714=> R = 26.72
Length of the rope = 26.72 m.
Answer: Option B
Answer: B
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
Options:
A)1/2
B)3/4
C)3/5
D)3/7
E)5/7
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: A
Question: {9,4,3,5,7,12,10}
What value should be inserted into the above set of 7 values to get a median value of 6?
Options:
A)5
B)4
C)3
D)7
E)6
Rationale: Median is the middle number of a sorted distribution. In case of even number of items, Median will be the average of middle two values.
The question asks fora new number that will cause the median of new set at 12.
Mentionable that given set is already sorted and number of items of new set will be 7+1 = 8.
To get median 6,the sum of 4th5th Term should be 12 and luckilyit's exactly same in the existing series i.e. 5+7.
So to keep the median 6, the new item should be >=7
Answer is D
Answer: D
Question: One-fourth of the students at a nursery school are 4 years old or older. If 15 students have not yet reached their third birthday, and a total of 40 students are not between 3 years old and 4 years old, how many children are in the nursery school?
Options:
A)80
B)90
C)100
D)110
E)120
Rationale: x/4 students are > 4 yrs
15 students are < 3 yrs
x/4+ 15 = 40
x/4 = 25
x = 100
Answer: C
Answer: C
Question: A pharmaceutical company received $3 million in royalties on the first $20 million in sales of and then $9 million in royalties on the next $102 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $102 million in sales?
Options:
A)8%
B)15%
C)40%
D)52%
E)56%
Rationale: (9/102)/(3/20) = 30/54 = 58,5% it means that 9/108 represents only 58,5%. Therefore a decrease of 45%.
Answer C
Answer: C
Question: A miniature gumball machine contains 4 blue, 4 green, and 2 red gumballs, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
Options:
A)2/15
B)4/15
C)5/30
D)7/30
E)11/60
Rationale: The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 4*4*2=32.
P(dispensing one of each color)=32/120=4/15.
The answer is B.
Answer: B
Question: Let f(x) = x^2 + bx + c. If f(5) = 0 and f(-3) = 0, then b + c =
Options:
A)18
B)-17
C)-15
D)-21
E)-24
Rationale: f(x) = x^2 + bx + c. If f(5) = 0 and f(-3) = 0, then b + c =
f(5) = 0= 25+5b+c--- Taking 25 to the other side
-> 5b+c= -25
f(-3) = 0= 9-3b+c --- taking -3b+c to the other side
-> 3b-c=9
When we add these 2 equations, we get 8b= -16---> b= -2
And while substituting b= -2 we get c= -15.
b+c= -17--- Answer B
Answer: B
Question: Three numbers are in the ratio 1:4:6 and their H.C.F is 7. The numbers are?
Options:
A)7, 28, 40
B)7, 28, 42
C)7, 28, 45
D)7, 21, 42
E)7, 28, 35
Rationale: Let the required numbers be x, 4x and 6x. Then, their H.C.F = x. So, x = 7.
The numbers are 7, 28, 42.
Answer: B
Answer: B
Question: A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 25 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Options:
A)0.5024
B)2/5
C)1/2
D)3/4
E)5/6
Rationale: It is a circle inscribed in a square.
Square side=25---> square(table) area=25^2
Circle diameter=20---> Circle area=PiR^2=100Pi (where Pi=~3.14)
covered fraction=100*3.14/25*25=~314/25*25=0.5024
A
Answer: A
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Options:
A)30%
B)33%
C)33 1/3%
D)35%
E)34%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
ANSWER:C
Answer: C
Question: The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from y to z, inclusive, where 0<y<z?
Options:
A)z(z+1)/2 - (y+1)(y+2)/2
B)z(z+1)/2 - y(y+1)/2
C)z(z+1)/2 - (y-1)y/2
D)(z-1)z/2 - (y+1)(y+2)/2
E)(z-1)z/2 - y(y+1)/2
Rationale: Or try plug-in method: let z=4 and y=3 --> then z+y=7. Let see which option yields 7.
A. z(z+1)/2 - (y+1)(y+2)/2 = 10-10=0;
B. z(z+1)/2 - y(n+1)/2 = 10-6=4;
C. z(z+1)/2 - (y-1)y/2 = 10-3=7 --> OK;
D. (z-1)z/2 - (y+1)(y+2)/2 = 6-10=-4;
E. (z-1)z/2 - y(y+1)/2 = 6-6=0.
Answer: C.
Answer: C
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)31/32
B)31/89
C)31/97
D)31/90
E)31/56
Rationale: Explanation:
Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: Option A
Answer: A
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)298 m
B)888 m
C)120 m
D)217 m
E)166 m
Rationale: Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec
= 20 m/sec.
Length of the train
= 20 * 6
= 120 m.
Answer: C
Answer: C
Question: What is the difference between the place value of 2 in the numeral 7559?
Options:
A)160
B)165
C)180
D)190
E)450
Rationale: Answer: Option 'E'
500 - 50 = 450
Answer: E
Question: If four coins are tossed, the probability of getting two heads and two tails is -.
Options:
A)3/8
B)6/11
C)2/5
D)4/5
E)5/11
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
ANSWER:A
Answer: A
Question: 3 litre of water is added to 11 litre of a solution containing 42% of alcohol in the water. The
percentage of alcohol in the new mixture is
Options:
A)25%
B)20%
C)30%
D)33%
E)None of these
Rationale: Explanation :
----------------------------------------------------------Method-1 to solve the question--------------------------------------
--------------------We have a 11 litre solution containing 42% of alcohol in the water=> Quantity of alcohol
in the solution= 11×42100Now 3 litre of water is added to the solution=> Total Quantity of the new
solution = 11+3=14Percentage of alcohol in the new solution=11×4210014×100=11×3100=33%-------------
---------------------------------------------Method-2 to solve the question---------------------------------------------------
-------%Concentration of alcohol in pure water = 0%Concentration of alcohol in mixture = 42quantity of
water : Quantity of mixture = 3 : 11Let the %Concentration of alcohol in the new mixture = x
By the rule of alligation, we have
%Concentration of alcohol : 0
in pure water %Concentration of alcohol
in mixture : 42
Mean %Concentration
x
42 - x x - 0 = x
But (42 - x) : x = 3 : 11
⇒42−xx=311⇒42−xx=311⇒42×11−11x=3x⇒14x=42×11⇒x=3×11=33=> The percentage of alcohol in the
new mixture is 33%
Answer : Option D
Answer: D
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/6 of the remaining paint. How many gallons of paint has Joe used?
Options:
A)18
B)135
C)175
D)216
E)250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/6)*270 = 45 gallons
Total paint used = 135 gallons.
Option B
Answer: B
Question: What is the total % gain or loss if a trader sold two items for Rs.1500 each, and makes a profit of 20% from the first item and a loss of 12% from the second item.
Options:
A)2.4
B)4.4
C)1.4
D)12.4
E)20.5
Rationale: (20*12)/100 = 2.4%
Answer: A
Answer: A
Question: What least number must be substracted from 427398 so that the remaining number is divisible by 15?
Options:
A)3
B)1
C)16
D)11
E)15
Rationale: On dividing 427398 by 15, we get remainder = 3.
Required number be substracted
ANSWER:A
Answer: A
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
Options:
A)1204
B)1296
C)1340
D)1754
E)1674
Rationale: Number of rectangles that can be formed by using m horizontal lines and n vertical lines
= mC2 × nC2
Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)2
=(9×82×1)2=362=1296=(9×82×1)2=362=1296
ANSWER B 1296
Answer: B
Question: Today is Monday. After 63 days, it will be:
Options:
A)Monday
B)Sunday
C)Saturday
D)Friday
E)Thursday
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
answer :A
Answer: A
Question: There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 8 other amateurs, what is the total number of chess games possible to be played in the tournament?
Options:
A)10
B)20
C)40
D)60
E)120
Rationale: Method 2:
Each person is one participant of 4 games. So there are in all 8*5 =40 instances of one participant games. But each game has 2 participants so total number of games = 40/2 = 20
B
Answer: B
Question: The food in a camp lasts for 32 men for 48 days. If eight more men join, how many days will the food last?
Options:
A)80 days
B)30 days
C)38 days
D)16 days
E)15 days
Rationale: one man can consume the same food in 32*48 = 1536 days.
8 more men join, the total number of men = 40
The number of days the food will last = 1536/40
= 38 days.
Answer:C
Answer: C
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
A)1871
B)9172
C)8797
D)8112
E)1899
Rationale: A = 7500(26/25)2 = 8112'
Answer:D
Answer: D
Question: Three grades of milk are 1 percent, 33 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Options:
A)y + 3z
B)(y +z) / 4
C)2y + 3z
D)3y + 3z
E)3y + 4.5z
Rationale: Soln:
The resulting equation is
=> (.01x + .03y + .03z)/(x+y+z) = 1.5/100
=> x + 3y + 3z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 3y + 3z
Ans is D
Answer: D
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed
Options:
A)50 km
B)52 km
C)54 km
D)56 km
E)58 km
Rationale: Explanation:
Let the length of the train be x meters,
Then, the train covers x meters in 8 seconds and (x + 180) meters in 20 sec
x/8=(x+180)/20 ⇔ 20x = 8 (x + 180) <=> x = 120
Length of the train = 120 m.
Speed of the train = (120/8)m / sec = m / sec = (15 ×18/5)kmph = 54 km
Answer: Option C
Answer: C
Question: A business finds that their ratio of spending to income is 5 to 9. Their total profit is $48,000. What is their total income?
Options:
A)$90,000
B)$108,000
C)$119,000
D)$126,000
E)$140,000
Rationale: Let x equal the amount of spending, and y equal the amount of income.
We know that x = 5/9y
We also know that x = y - 48000
Therefore we can simplify to:
y-48000 = 5/9y
We isolate y, and get:
4/9y = 48000
And to solve for y, we get:
y = 48000
Answer: B
Answer: B
Question: Points A, B, C, and D, in that order, lie on a line. If AB = 2 cm, AC = 5 cm, and BD = 6 cm, what is CD, in centimeters?
Options:
A) 1
B) 2
C) 3
D) 4
E) 5
Rationale: Putting a value to each point, lets use the following:
A - 0
B - 2 (AB = 2)
C - 5 (AC = 5)
D - 8 (BD = 6)
CD is 8-5 = 3.
Ans C
Answer: C
Question: In an examination 38% of students fail in English and 61% pass in Hindi and 23% fail in both. Find the actual failure percentage?
Options:
A)10%
B)12%
C)54%
D)28%
E)42%
Rationale: Explanation:
Fail percentage=38+61+23=54%
Answer: C
Answer: C
Question: I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 3 junior staff officers, how many possible committees are there?
Options:
A)12
B)44
C)56
D)80
E)200
Rationale: 6C3*4C3
=80=D
Answer: D
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options:
A)12:15:19
B)12:15:16
C)12:15:19
D)12:15:11
E)12:15:13
Rationale: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer:B
Answer: B
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (7.5/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
Options:
A) 3/8
B) 1/2
C) 11/16
D) 23/32
E) 3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 7.5/8*c:
(b+c)/2 = (7.5/8)*c
b = (7/8)*c
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (7/8*c)/2 = (7/16)*c
Median = (a + c)/2 = (7/16*c + c)/2 = (23/16)*c/2 = (23/32)*c (ANSWER D)
Answer: D
Question: If r = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
Options:
A)-2
B)-1
C)0
D)2
E)None of the above
Rationale: Let us transform the formula:
r = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Answer: D
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.4 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?
Options:
A)9.21
B)12.
C)12.5.
D)14.
E)15.4.
Rationale: Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.4 *5= 7 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (7^2+ 6^2)^1/2= 9.21 KM
A is the answer
Answer: A
Question: What is the highest integer that is the sum of 2 distinct prime integers, each smaller than 80 ?
Options:
A)140
B)152
C)153
D)169
E)176
Rationale: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.
Immediate two prime numbers before 80 are - 79 and 73
Sum = 79 + 73 = 152
Answer - B
Answer: B
Question: A Kloke's train rails across an open track at 250 kilometers per hour. A regular passenger train travels at 68% of the Kloke's train speed. If the two trains start moving from the same station at the same time, how much time longer will it take the passenger train than the Kloke's to travel 850 kilometers?
Options:
A)1 hour and 24 minutes.
B)1 hour and 36 minutes.
C)2 hours and 24 minutes.
D)2 hours and 36 minutes.
E)5 hours.
Rationale: Difference in time = time taken by passenger train- time taken by Kloke's train
850/(250*68) *100 - 850/250
850 (100/ 250*68 - 1/250)
850*32/ (250*68)
1.6 hrs or 1 hr and 36 mins
B is the answer
Answer: B
Question: Pipe A can fill a tank in 4 hours. Due to a leak at the bottom, it takes 6 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)12
B)67
C)95
D)36
E)66
Rationale: Let the leak can empty the full tank in x hours 1/4 - 1/x = 1/6
=> 1/x = 1/4 - 1/6 = (3 - 2)/12 = 1/12
=> x = 12.
Answer: A
Answer: A
Question: The speed at which a woman can row a boat in still water is 120 kmph. If she rows downstream, where the speed of current is 60 kmph, what time will he take to cover 500 metres?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Speed of the boat downstream = 120 + 60 = 180 kmph
= 180 * 5/18 = 50 m/s
Hence time taken to cover 500 m = 500/50 = 10 seconds.
Answer: C
Answer: C
Question: A highway is to be divided into four lanes. For this purpose, three yellow stripes are painted so that stripes divide the highway into four lanes. If 3 gallons of paint cover an area of 2P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
Options:
A)1320mx/P
B)880mx/P
C)1320P/mx
D)440P/mx
E)1980mx/P
Rationale: 1 square foot needs 3/2P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For three stripes, the total area is 1320mx square feet.
The number of gallons needed is (1320mx)*(3/2P) = 1980mx/P gallons.
The answer is E.
Answer: E
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
Options:
A)22
B)6
C)17
D)10
E)88
Rationale: 7*5: 5*x = 7:10
x = 10
Answer:D
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is?
Options:
A)178 m
B)240 m
C)120 m
D)168 m
E)178 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 12
= 240 m.
Answer: B
Answer: B
Question: Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 20% and its breadth is decreased by 5%?
Options:
A)14 percent increase
B)5 percent increase
C)24 percent increase
D)13 percent increase
E)11 percent increase
Rationale: let L and B be 100 each
100 * 100 = 10000
L increase by 20% = 120
B decrease by 5% = 95
120 * 95 = 11400
14 percent increase
ANSWER:A
Answer: A
Question: A Jar contains 18 balls. 3 blue balls are removed from the jar and not replaced.Now the probability of getting a blue ball is 1/5 then how many blue balls jar contains initially?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: x/15 = 1/5
x =3
3+3(removed 3 blue balls) = 6
ANSWER:E
Answer: E
Question: If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?
Options:
A)53
B)54
C)55
D)56
E)57
Rationale: A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 55.
The answer is C.
Answer: C
Question: In how many different ways can the letters of the word ‘POSITIVE’ be arranged ?
Options:
A)120
B)720
C)40320
D)24
E)6
Rationale: C
40320
Required number of arrangements = 8! = 40320
Answer: C
Question: (128.5 x 64) + (13.8 x 465) = ? x 25
Options:
A)524.48
B)556.02
C)574.36
D)585.64
E)595.46
Rationale: Explanation :
? = (128.5 x 64) + (13.8 x 465)/25
= 8224 + 6417/25 = 585.64
Answer : Option D
Answer: D
Question: In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 15 and 150, then the least and greatest integer on the card would be
Options:
A)3 and 15
B)3 and 20
C)4 and 12
D)4 and 14
E)5 and 14
Rationale: Given: 15<x(x+1)<170.
Now, it's better to test the answer choices here rather than to solve:
If x=4 then x(x+1)=20>15 --> so, the least value is 4. Test for the largest value: if x=12 then
x(x+1)=12*13=156>150
Answer: C.
Answer: C
Question: If a motor bike's wheel is 12 cm diameter and rotating at the rate of x cm/min and another motor bike's wheel is 6 cm diameter rotating at the rate of y cm/min and if both the bikes reach the distance at same time then what is the value of y in terms of x?
Options:
A)4x/2
B)3x/6
C)4x/2
D)1x/2
E)2x/3
Rationale: t=S1/V1=S2/V2
or 12/x=6/y
or y=6x/12=1x/2
Answer is D
Answer: D
Question: The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Options:
A)18
B)28
C)38
D)48
E)58
Rationale: Explanation:
l2 + b2 = 41
Also, lb = 20
(l + b)2 = l2 + b2 + 2lb
= 41 + 40 = 81
(l + b) = 9
Perimeter = 2(l + b) = 18 cm. Answer: A
Answer: A
Question: The ratio of the present ages of Giri and Hari is 5 : 8. 12 years hence, the ratio of their ages will be 11 : 14. Find the difference in their present ages?
Options:
A)8
B)6
C)5
D)4
E)2
Rationale: Let the present ages of Giri and Hari be 5x and 8x years respectively.
(5x + 12) / (8x + 12) = 11/14
70x + 168 = 88x + 132 => x= 2
Difference in their ages will be the same at all times.
This difference = Difference of their present ages
= 8x - 5x = 3x = 6 years.
Answer:B
Answer: B
Question: How many multiples of 5 are there between 5 to 95?
Options:
A)9
B)18
C)17
D)none of these
E)Cannot be determined
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90.
Answer : C
Answer: C
Question: The speed of a boat in still water is 60kmph and the speed of the current is 40kmph. Find the speed downstream and upstream?
Options:
A)kmph
B)kmph
C)kmph
D)kmph
E)kmph
Rationale: Speed downstream = 60 +40 = 100 kmph
Speed upstream = 60 - 40 = 20 kmph
Answer:D
Answer: D
Question: Jaclyn buys $40 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter
Options:
A)950
B)1234
C)1289
D)1345
E)None of these
Rationale: Explanation:
I=(p x r x t)/100
= 40000*9.5/100*(18/12)^1/6 = 950
Answer: A
Answer: A
Question: If S = T/P, -1 < P < 0 and 4 < T, which of the following is correct?
Options:
A)S > 4.
B)0 < S <4.
C)-4 < S < 0.
D)S < -4.
E)S < -20.
Rationale: T is +veP is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take T=4.1S=-0.9
S=4.1/-0.9
S<-4
Ans D
Answer: D