divelab/Sys2Bench huggingface dataset:
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Options:
A)69%
B)79%
C)60%
D)64%
E)24%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Answer: D
Question: If a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a > c
(III) a^2 < b^2 < c^2
Options:
A)II only
B)I only
C)None
D)III only
E)II and III
Rationale: (I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) b − a < c. Not necessarily true: try a=-1/2, b=-1/3, and c=-1/4.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: C.
Answer: C
Question: According to a survey, at least 50% 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)5%
B)10%
C)15%
D)20%
E)25%
Rationale: To minimize the percentage who like all three, let's maximize the percentage who like 2 out of 3.
80% like cherries and 20% don't like cherries.
Let's combine this with the people who like bananas.
20% don't like cherries but do like bananas.
55% like cherries and bananas.
25% like cherries but not bananas.
Now let's distribute the people who like apples.
20% like bananas and apples, but not cherries.
25% like cherries and apples, but not bananas.
5% like all three.
50% like cherries and bananas, but not apples.
The answer is A.
Answer: A
Question: A pen factory stores its toys in either a big box or a small box. The big box can store 27 pens while the small box can store 18 pens. If the factory is to store 112 newly manufactured pens, what is the least number of pens that will be left unboxed?
Options:
A)6
B)2
C)4
D)3
E)1
Rationale: Total pens to be stored 112
The big box can store 27
small box can store 18
storing 112 pens in big box 112/27 =4 r 4
least number of pens that will be left unboxed=4
Answer: C
Answer: C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)278
B)240
C)88
D)21
E)192
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m Answer:B
Answer: B
Question: If the price of petrol increases by 44, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
Options:
A)25%
B)20%
C)16.67%
D)33.33%
E)None of these
Rationale: Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+44) i.e 144.
Now, his consumption should be reduced to :-
=(144−100)/144 ∗ 100.
Hence, the consumption should be reduced to 30.6%.
Answer : E
Answer: E
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,6), (12,0) and (12,6). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Options:
A)1/2
B)2/3
C)1/4
D)2/5
E)5/12
Rationale: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (6,3).
The slope of line passing through points (1,1) and (6,3) = (3-1)/(6-1) = 2/5
The answer is D.
Answer: D
Question: A envelop weight 8.5 gm,if 800 of these envelop are sent with an advertisement mail. How much wieght?
Options:
A)6.6kg
B)6.8kg
C)6.7kg
D)6.9kg
E)7.8kg
Rationale: 800*8.5
6800.0gm
6.8kg
ANSWER:B
Answer: B
Question: If XY denotes X is raised to the power Y, Find the last two digits of 19413843+ 19614181
Options:
A)12
B)22
C)42
D)82
E)92
Rationale: 1941^3843
unit digit= 1^3=1
10th digit=4*3=12=2 means last two digit =21
and 1961^4181
unit digit=1
10th digit=6*1=6 mean last two digit= 61
hence,
21+61= 82
ANSWER:D
Answer: D
Question: Ravi can do a piece of work in 20 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
A)13 1/3 days
B)15 1/3 days
C)17 1/3 days
D)17 7/3 days
E)18 1/3 days
Rationale: 1/20 + 1/40 =3/40
40/3
= 13 1/13 days
Answer: A
Answer: A
Question: In a camp, there is a meal for 180 men or 200 children. If 150 children have taken the meal, how many men will be catered to with the remaining meal ?
Options:
A)38 men
B)32 men
C)34 men
D)45 men
E)None of these
Rationale: Explanation:
There is meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 180 men
So, 50 Children = 180/200 * 50 = 45 men
Answer: D
Answer: D
Question: A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 1
II. -3
III. 5
Options:
A)I only
B)II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
Answer: C
Question: In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score B that Lindsey could have received on her midterm exam?
Options:
A)52%
B)64%
C)72%
D)76%
E)80%
Rationale: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: A
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 40 km apart both 3 and 6 hours after start, then find the distance between the two stations.
Options:
A)120km
B)150km
C)220km
D)180km
E)200km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+40+ 40
2(R+S ) = R+S +80
R+S = 180
Hence distance between XY is R+S+ 40 = 40 +80 =120
Answer : A
Answer: A
Question: The measures of the 2 acute angles of a triangle are in the ratio of 2:7. What are the measures of the 2 angles?
Options:
A)50°
B)70°
C)80°
D)90°
E)100°
Rationale: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
2x + 7x = 90
9x = 90
x = 10
Measures of the two acute angles are
2x = 2 × 10 = 20°
7x = 7 × 10 = 70°
B
Answer: B
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)10
B)16
C)20
D)22
E)29
Rationale: C
20%
900 ---- 180
100 ---- ? => 20%
Answer: C
Question: In a kilometer race, A beats B by 50 meters or 5 seconds. What time does A take to complete the race?
Options:
A)199 sec
B)190 sec
C)726 sec
D)90 sec
E)128 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 5)/50 = 100 sec.
Time taken by A = 100 - 10
= 90 sec.
Answer: D
Answer: D
Question: In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg?
Options:
A)3 : 1
B)3 : 2
C)4 : 3
D)5 : 3
E)None
Rationale: Required ratio = 750 : 250 = 3 : 1
Answer A
Answer: A
Question: The perimeter of a semi circle is 180 cm then the radius is?
Options:
A)22
B)28
C)35
D)37
E)13
Rationale: 36/7 r = 180
=> r
= 35
Answer: C
Answer: C
Question: A train 250 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform?
Options:
A)150m
B)200m
C)250m
D)270m
E)300 m
Rationale: D = 72 * 5/18 = 20 = 400 â€“ 250 = 150m
ANSWER:A
Answer: A
Question: A certain university will select 1 of 9 candidates eligible to fill a position in the mathematics department and 2 of 15 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)351
B)425
C)748
D)854
E)945
Rationale: 1C9*2C15 = 9*105 = 945
the answer is (E)
Answer: E
Question: In current of a stream runs at 2 km/hr. A motor boat goes 30 km upstream and back again to the starting point in 20 hours. The speed of the moter boat in still water is:
Options:
A)5 km/hr
B)8 km/hr
C)2 km/hr
D)4 km/hr
E)8 km/hr
Rationale: Explanation:
Let the speed ofboat in still water be x km/hr.
Speed down stream = (x + 2) km/hr
Speed up stream = (x - 2) km/hr
30/(x+2) + 30/(x-2) = 20 hours
(30x-60+30x+60)/(x2-4) = 20
60x = 20x2 - 80
3x = x2 - 4
x2-3x-4=0
x2-4x+x-4=0
x(x-4)+1(x-4)=0
x=4, x=-1
Speed of moter boat is 4 km/hr
Answer: Option D
Answer: D
Question: A fair coin is tossed 15 times. What is the probability of getting more heads than tails in 15 tosses?
Options:
A)1/2
B)63/128
C)4/7
D)61/256
E)63/64
Rationale: On each toss, the probability of getting a head is 1/2 and the probability of getting a tail is 1/2.
There is no way to get the same number of heads and tails on an odd number of tosses.
There will either be more heads or more tails.
Then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes.
P(more heads) = 1/2
The answer is A.
Answer: A
Question: A total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?
Options:
A)22
B)60
C)77
D)26
E)23
Rationale: Let the number of boys be x.
Number of girls is 120 - x.
Total number of chocolates received by boys and girls = 2x + 3(120 - x) = 300
=> 360 - x = 300 => x = 60.
So, the number of boys or girls is 60.
Answer: B
Answer: B
Question: From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:
Options:
A)149 m
B)156 m
C)173 m
D)200 m
E)none
Rationale: Solution
Let AB be the tower.
Then, <APB =30° and AB= 100 m
AB/AP= tan30°
= 1 / √3
AB = (AB x √3)= 100√3 m.
= (100 x 1.73) m = 173 m.
Answer C
Answer: C
Question: In a shower, 8 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
Options:
A)75 cu. m
B)1200 cu. m
C)7500 cu. m
D)75000 cu. m
E)7.50 cu. m
Rationale: 1 hectare = 10000 sq mtr
The volume of water that falls on 1.5 hectares of ground = 0.08*1.5*10000 = 1200 cub mtr .
ANSWER:B
Answer: B
Question: In what time will a railway train 90 m long moving at the rate of 44 kmph pass a telegraph post on its way?
Options:
A)3
B)5
C)4.3
D)6.5
E)7.4
Rationale: T = 90/44* 18/5 = 7.4 sec
Answer:E
Answer: E
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
Options:
A)3/2
B)1/2
C)4/3
D)3/4
E)1/5
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
=> (27x + 17 y)/(x+y) = 23
=> (27x + 17 y)/ = 23(x+y)
=> 4x = 6y
=> x/y = 6/4 = 3/2
Answer is A.
Answer: A
Question: Let the polynomials be:
P1(x)=3x2−7x+8,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
Options:
A)2x2 + 11x - 7
B)-2x2 - 11x + 10
C)-2x2 - 11x + 6
D)2x2 - 9x + 7
E)None of these
Rationale: Solution:
P1(x)+P2(x)=(3x2−7x+8)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+8)+(−5x2−4x+2)=
3x2−7x+8−5x2−4x+2=3x2−7x+8−5x2−4x+2=
−2x2−11x+10
Answer B
Answer: B
Question: Two trains of lengths 150m and 180m respectively are running in opposite directions with a speed of 30 km/hr and 24 km/hr respectively. How much time will they take to cross each ther?
Options:
A)21 secs.
B)23 secs.
C)24 secs.
D)22 secs.
E)28 secs.
Rationale: Relative speed = (30+24) km/hr =15m/s. Time taken by the trains to cross each other =sum of lengths of two trains /Relative speed. (150+180)/15sec. =330/15 = sec22s. Answer : D
Answer: D
Question: 3x^2-6x+3 = 0
Find the above equation find the value of x
Options:
A)0
B)X=1
C)2
D)4
E)5
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √ ( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: B
Question: A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 30% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
Options:
A)1:20
B)1:10
C)1:120
D)23:4
E)23:120
Rationale: First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.
This $36 should be a 30% increase over cost. Here, we need to think about percentage increases as multipliers.
Using multipliers
(cost)*1.30 = $36
cost = 36/1.3 = 360/12 = $27.69
If he wants a 30% increase over cost on the sale of one liter of his milk-water, the cost has to be $27.69.
Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 27.69/33 = 120/143 of a liter. If milk is 120/143 of the liter, then water is 23/143 of the liter, and the ratio of water to milk is 23:120. Answer choice(E)
Answer: E
Question: Sarah's seafood restaurant gets a delivery of fresh seafood every day, 6 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?
Options:
A)6cdx/100
B)d + 6cx/100
C)6d + xc/100
D)6d + 6xc/100
E)6cdx
Rationale: Answer will be D. Straightforward question.
Answer: D
Question: A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true?
Options:
A)a must be 2
B)c must be 2
C)b must be 0
D)None
E)Cannot be determined
Rationale: Sol:
Given (abc)5=(cba)7(abc)5=(cba)7
or 25a + 5b + c = 49c + 7b + a
or 24a = 2b + 48c
or 12a = b + 24c
as abc is a 3 digit number in base 5, the possible values for a, b and c are 0, 1, 2, 3, 4 only
The possible solutions of the above equation are:
(a, b, c) = (2, 0, 1) and (4, 0, 2) only
a can take value = 2 or 4
b can take value = 0 only
c can take value = 1 or 2 only.
So correct option c.
Answer C
Answer: C
Question: A photo-mat shop charges $0.6 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $36 if each film contains 36 photos?
Options:
A)2 films and 26 photos
B)5 films and 6 photos
C)5 films and 14 photos
D)6 films and 4 photos
E)6 films and 28 photos
Rationale: 1st photo = 0.60
Subsequent = 0.60*0.6=0.36
Price of 1 full film=0.6+0.36*35=13.2
Price of 4 full film = 13.2*2=26.4
36-26.4=9.6
9.6=0.6+0.36x
x=25
36--->2 full films and 1+25=26 photos
Answer: A
Answer: A
Question: In how many ways can a four-letter password be chosen, using the letters A, B, C, D, and/or E, such that at least one letter is repeated within the password?
Options:
A)505
B)864
C)900
D)936
E)1,296
Rationale: Total number of four letter passwords = 5*5*5*5= 625 ------(1)
Total number of passwords in which no letter repeats = 5C4*4!= 5*24=120------(2)
therefore required value = (1)-(2)= 625-120=505
A
Answer: A
Question: The two lines y = x and x = -5 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
Options:
A)16
B)5/√2
C)8
D)2√2
E)(√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-5, -5) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 25/2; so z = 25/2.
The next step requires us to find the length of a side of a cube that has a face area equal to 25/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 25/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 25/2. Clearly s = √25/2 = 5/√2 , oranswer choice (B).
Answer: B
Question: In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and seven different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?
Options:
A)719/720
B)1/120
C)2/233
D)3/543
E)1/5040
Rationale: 7 ties and 7 shirts...
red tie can take any of 7 shirts..
orange can take any of the remaining 6 shirts
yellow any of remaining 5..
and so on till last indigo chooses the 1 remaining..
Total ways= 7*6*5*4*3*2*1= 5040
out of this 5040, ONLY 1 way will have same colour tie and shirt..
prob = 1/5040
E
Answer: E
Question: During a certain two-week period, 80 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 4 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
Options:
A)5 A
B)15 A
C)20 A
D)1/25 A
E)30 A
Rationale: Movies: 80 % comedies. 20 % remaining genre.
Now in this 20 %, there are only 2 categories. Action movies and Drama Movies.
If Action = x; Drama movies = 4x. Total 5x.
5x = 20; x = 4
Action movies: 4 %
Drama movies: 16 %
we can say that out of 100z,:
comedies: 80z
action: 4z
drama: 16 z
Now action movies wereA
This means:
A = 4z.
z = (A/4)
Comedies: 80z = 80 * (A/4)
20 A
C is the answer.
Answer: C
Question: What percent of selling price would be 34% of cost price if gross profit is 26% of the selling price?
Options:
A)17.16
B)74.0
C)25.16
D)88.4
E)None of these
Rationale: Let the selling price of the article be 100.
∴ Profit = 26
∴ Cost price of the article = 100 – 26 = 74
∴ Reqd.% = 34×74/100=25.16%
Answer C
Answer: C
Question: Two horses begin running on an oval course at the same time. One runs each lap in 9 minutes; the other takes 12 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
Options:
A)36
B)12
C)9
D)4
E)3
Rationale: The rate of the faster horse is 1/9 lap/minute;
The rate of the slower horse is 1/12 lap/minute;
Their relative rate is 1/9-1/12=1/36 lap/minute;
The faster horse to gain one full lap will need time=distance/rate=1/(1/36)=36 minutes.
Answer: A.
Answer: A
Question: If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
Options:
A)2
B)5
C)6
D)8
E)None Of These
Rationale: Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
P = 1.
Answer :E
Answer: E
Question: the probability that I will sit next to Ann is 1/12.
the probability that I won't sit next to Alice is 11/12.
What is the probability that I will sit next to Ann and Alice?
Options:
A)1/6
B)11/12
C)11/144
D)1/12
E)1/144
Rationale: the probability that I will sit next to Ann is 1/12.
the probability that I will sit next to Alice is 1-11/12 = 1/12.
Therefore the probability that I will sit next to Ann and Alice is 1/12*1/12=1/144
Answer:E
Answer: E
Question: What is 2 2/3 - 1 1/4 divided by 1/2 - 1/4 ?
Options:
A)17/36
B)36/17
C)17/6
D)17/3
E)51/4
Rationale: 2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/2 - 1/4 = (2-1)/4 = 1/4
So 17/12/1/4 = 17/12 *4 = 17/3
Answer - D
Answer: D
Question: A car travelling with 5/7 of its actual speed covers 42km in 1hr 40 min 48 sec find the actual speedof the car?
Options:
A)52km/hr
B)25km/min
C)35km/hr
D)125km/hr
E)63km/hr
Rationale: Time taken=1hr 40 min 48sec
=1hr 404/5 min=1 51/75hrs =126/75hrs.
let the actual speed be xkm/hr.
then x 5/7*126/75=42
x=(42*7*75/5*126)=35km/hr
Answer(C)
Answer: C
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
Options:
A)20
B)24
C)23
D)22
E)None of these
Rationale: Explanation:
Let the pipe B be closed after x minutes.
30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24 = 21.
ANSWER IS E
Answer: E
Question: A chemical supply company has 60 liters of a 20% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
Options:
A)12
B)15
C)20
D)24
E)36
Rationale: 60 liters of a 20% HNO3 solution means HNO3 = 12 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
12 + x = 50% of (60 + x)
or x =36. Hence, E
Answer: E
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
Options:
A)4
B)5
C)2
D)1
E)3
Rationale: 150 = (750*5*R)/100
R = 4%
ANSWER A
Answer: A
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 3294, how much was it in the beginning?
Options:
A)2988
B)2776
C)4079
D)2871
E)881
Rationale: X * (95/100) * (85/100) = 3294
X = 4079
Answer:C
Answer: C
Question: A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 6 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
Options:
A)11/30
B)29/60
C)17/30
D)19/30
E)11/15
Rationale: I think E - 11/15 is the correct answer.
Here goes:
Lets assume originally the number of beds = x
After the new tower, the total combined no of beds = 6x
So old = x, New = 5x
Now 1/3 of x are occupied and 1/5 of 5x are occupied which simplifies to (5/5)x
We are shifting 1/3 of x to the new ward so there will now be:
1/3 of x plus 5/5 of x occupied in the new ward. Add them up to get 4/3 of x
There are 5x beds in New Tower so ratio is:
(4/3)x / 5x = 4/15 of x
Subtract that from 15/15 of x and you get the number of un-occupied beds to total capacity of New Tower =11/15.
E
Answer: E
Question: The total of the ages of Jai, Prajan and Sarath is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Sarath?
Options:
A)24 years
B)32 years
C)38 years
D)42 years
E)None
Rationale: Sol.
Let the ages of Jai, Prajan and Sarath 10 years ago be 2x, 3x and 4x years respectively.
Then, (2x + 10) + (3x + 10) + (4x + 10) = 93
⇔ 9x = 63
⇔ x = 7.
∴ Sarath's present age = (4x +10) = 38 years.
Answer C
Answer: C