mathewhe/aqua_rat huggingface dataset:
Question: a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find a+b+c=?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: a^2*b^2+a^2+b^2+1= (a^2+1)(b^2+1)
by using above one we can write
a^2*b^2+a^2+b^2+1=260..(1)
b^2*c^2+b^2+c^2+1=1300..(2)
c^2*a^2+c^2+a^2+1=500..(3)
by doing (1)/(2) we will get a^2+1/c^2+1 = 1/5..(4)
by doing (4)*(3) we will get (a^2+1)^2=10,
by solving a=3, b=5,c=7
so a+b+c=15
ANSWER:C
Answer: (C) 15
Question: There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairy tales, novels and plays.
(A) 17200
(B) 17250
(C) 17280
(D) 17300
(E) 17400
Rationale: There are 4 books on fairy tales and they have to be put together.
They can be arranged in 4! ways.
Similarly, there are 5 novels.
They can be arranged in 5! ways.
And there are 3 plays.
They can be arranged in 3! ways.
So, by the counting principle all of them together can be arranged in 4!×5!×3!=4!×5!×3!= 17280 ways
Option is C
Answer: (C) 17280
Question: One side of a rectangular field is 15 m and one of its diagonal is 17 m. Find the area of the field.
(A) 100
(B) 120
(C) 150
(D) 180
(E) None
Rationale: Solution
Other side = √(17)2 - (15)2
= √289 - 225
= √64
= 8 m.
∴ Area = (15 x 8)m2 = 120 m2.
Answer B
Answer: (B) 120
Question: A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm .If the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted?
(A) 408
(B) 418
(C) 428
(D) 438
(E) 448
Rationale: first the number of cubes....
the hollow cube size 5 cm.thickness 1c.m. so the total no. of unit cubes neede to build one face is 16 cubes..so total no. of cubes (5*16+9*2)=98
the total no. of faces unpainted(98*6 - 25*6)=438
ANSWER:D
Answer: (D) 438
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
(A) 5/11
(B) 4/11
(C) 3/11
(D) 6/45
(E) 7/44
Rationale: The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
Answer: C
Answer: (C) 3/11
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 3377
(B) 2899
(C) 2500
(D) 2778
(E) 1991
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
Answer: C
Answer: (C) 2500
Question: A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Solution
(1000 + N) > (1000N)
Clearly, N=1.
Answer A
Answer: (A) 1
Question: If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to
(A) 143
(B) 150
(C) 123.75
(D) 140.55
(E) None
Rationale: Solution
y = 125 + 10% of 125
= 125 + 12.50 = 137.50.
x = 137.50 - 10% of 137.50
= 137.50 - 13.75
= 123.75.
Answer C
Answer: (C) 123.75
Question: Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 75 percent carbonated water, what percent of the volume of the mixture is P?
(A) 40%
(B) 50%
(C) 60%
(D) 80%
(E) 90%
Rationale: 75% is 5%-points below 80% and 20%-points above 55%.
So the ratio of solution P to solution Q is 4:1.
Mixture P is 4/5 = 80% of the volume of mixture PQ.
The answer is D.
Answer: (D) 80%
Question: Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. The edge of the new cube formed is
(A) 10 cm
(B) 12 cm
(C) 16 cm
(D) 18 cm
(E) None
Rationale: Sol.
Volume of the new cube
= (63 + 83 + 103) cm3
= 1728cm3.
Let the edge of the new cube be a cm.
∴ a3 = 1728
⇒ a = 12.
Answer B
Answer: (B) 12 cm
Question: which of the following options is the correct value of r, given the equation 6^r +1^(-r) = 217?
(A) 5
(B) 7
(C) 3
(D) 2
(E) 0
Rationale: Plugging in the various option into the equation to find out which is correct:
6^r +1^(-r) = 217
6^3 +1^(-3) = 217 Ans. C
Answer: (C) 3
Question: Which of the following is equal to 2^k*3^(k-1)?
(A) 2*6^(k-1)
(B) 3*6^(k-1)
(C) 6^k
(D) 2*6^k
(E) 6^(2k-1)
Rationale: 2^k*3^(k-1) = 2*2^(k-1)*3^(k-1) = 2*6^(k-1)
The answer is A.
Answer: (A) 2*6^(k-1)
Question: A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?
(A) 30 days
(B) 35 days
(C) 40 days
(D) 45 days
(E) 50 days
Rationale: Explanation:
Let ‘x’ be the number of days taken by B alone to finish the whole work
Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days.
Then, working together,
3x/2 × x/3x/2 + x = 18 days
3x × x/5x = 18
3x/5 = 18
Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days.
Answer: Option A
Answer: (A) 30 days
Question: A number a is squared and then multiplied by negative 1. The result of this operation is equal to 2 times the sum of 4 times a and 8. What is one possible value of a ?
(A) 1
(B) 2
(C) 4
(D) 8
(E) 5
Rationale: -1*a^2=2(4a+8)
a= -4 or -4
a=-4=B
ANSWER:C
Answer: (C) 4
Question: 2 persons allotted to one work. John can do piece of work in 30 days while Bruce alone can do it in 40 days. In how many days can John and Bruce working together to do it?
(A) 17 2/7days
(B) 17 1/7days
(C) 17 3/5days
(D) 18 1/7days
(E) 17 1/4days
Rationale: Therefore John′s one day’s work = 130
Bruce′
s one day’s work = 140
(A+B)′
s one day’s work = 130+140
4+3120=7120
Number of days required for John
and Bruce to finish the work = 17/120=17 1/7days
B
Answer: (B) 17 1/7days
Question: A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
(A) 2/4
(B) 3/4
(C) 4/5
(D) 5/6
(E) 6/7
Rationale: consider A,B,C events and AA,BB,CC not solving the problems
now P(1)=1/2, P(B)=2/3 and P(C)=1/4
Not solving events =1/2*2/3*3/4
==>1-1/4= 3/4
ANSWER B
Answer: (B) 3/4
Question: A certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself?
(A) 24 years
(B) 14 years
(C) 65 years
(D) 17 years
(E) 15 years
Rationale: Let the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.
R = (100 * 3x)/(x * 8)
= 300/8 %
If the sum becomes ten times itself, then interest is 9x.
The required time period
= (100 * 9x)/(x * 300/8)
= (100 * 9x * 8)/(x * 300)
= 24 years.
Answer:E
Answer: (E) 15 years
Question: If in a race of 100m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
(A) 20m
(B) 16m
(C) 11m
(D) 10m
(E) 15m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (100 * 5) / 25 = 20m
Hence, A beats B by 20m.
ANSWER A
Answer: (A) 20m
Question: The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 30 terms of this sequence?
(A) 1/30-1/32
(B) 1 - (1/30 + 1/30)
(C) (1+1/2) – (1/31 +1/ 32)
(D) 1 - 1/32
(E) 1/32-1/30
Rationale: The answer would most certainly be[C]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.
The sequence is :
a1 = 1-1/3
a2 = 1/2 - 1/4
a3 = 1/3 - 1/5....
We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/32 and -1/31 from a30 and a29 term which could not be cancelled.
Hence the sum = (1+1/2) – (1/31 +1/ 32)
Answer : C
Answer: (C) (1+1/2) – (1/31 +1/ 32)
Question: Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
(A) 2 kg
(B) 2.4 kg
(C) 2.5 kg
(D) 10 kg
(E) none of these
Rationale: The weight of non-water in 20 kg of fresh grapes (which is 100-90=10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20=80% of whole weight), so 20∗0.1=x∗0.8--> x=2.5
Answer: C.
Answer: (C) 2.5 kg
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 802
(B) 800
(C) 829
(D) 389
(E) 245
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200
= 800 cm.
Answer: B
Answer: (B) 800
Question: Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 10 + 5 = ??
(A) 11
(B) 12
(C) 13
(D) 14
(E) 18
Rationale: 14
ANSWER:D
Answer: (D) 14
Question: In a group of 250 readers who read science fiction or literacy works or both, 180 read science fiction and 88 read literacy works. How many read both science fiction and literacy works?
(A) 268
(B) 180
(C) 150
(D) 18
(E) 88
Rationale: Consider total number of reader n(S U L) = 250
People who read science fiction n(S) = 180
People who read literacy works n(L) = 88
both science fiction and literacy n(S âˆ© L) = ?
n(S U L) = n(S)+ n(L) - n(S âˆ© L)
250 = 180 + 88 - n(S âˆ© L)
n(S âˆ© L) = 268 - 250
n(S âˆ© L) = 18
SO People read both science fiction and literacy works are 18
ANSWER:D
Answer: (D) 18
Question: At Veridux Corporation, there are 180 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?
(A) 95
(B) 20
(C) 85
(D) 75
(E) 35
Rationale: Well, first letâ€™s take care of the â€œtotalsâ€. The numbers in the â€œtotalsâ€ row must add up. If 90 are females, the other 180 â€“ 90 = 90 must be males. Similarly, the numbers in the â€œtotalsâ€ column must add up. If 40 are managers, then the other 180 â€“ 40 = 140 must be associates.
Now, in the â€œassociateâ€ row, 135 + E = 140, which means E = 5 â€” the other 5 associates must be female.
Now, to find B, which is what the question is asking, we need only look at the sum in the â€œfemaleâ€ column: B +5 = 90, which means B = 85. There are fifteen female managers in this company. Thus, the answer = (C).
Answer: (C) 85
Question: Two electric trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 10 sec
(B) 30 sec
(C) 40 sec
(D) 20 s
(E) 50 sec
Rationale: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 s.
Answer: (D) 20 s
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many V cubes are painted on only 2 faces?
(A) 12
(B) 8
(C) 6
(D) 10
(E) 16
Rationale: 1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. V=4 + 4 + 4 = 12. Answer A
Answer: (A) 12
Question: 2n boys are randomly divided into two sub-groups containing n boys each. Find the probability that two TOP RANK-HOLDER are in differed groups.
(A) (n-1) / 2n
(B) (n-1) / (2n-1)
(C) n / (2n-1)
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Without restriction
No. of ways to divide 2n boys into 2 equal groups having n boys each = 2nCn x nCn.
With restriction,
No. of ways to have two top ranks-holder in different group = 2n-2Cn-1 x n-1Cn-1 x 2!.
( i.e separate two top rankers and then make two groups out of (2n - 2) boys.
The required probability
= Selections with restriction / Selections without restriction .
= (2n-2Cn-1 x n-1Cn-1 x 2! ) / (2nCn x nCn ).
= { (2n-2)! / [ (n-1)! x (n-1)! ] } x 2! / (2n! / ( n! x n! ) ) .
= (n-1) / 2n - 1.
Hence, the probability is (n-1) / (2n-1).
Answer : B
Answer: (B) (n-1) / (2n-1)
Question: Two brothers took the GMAT exam, the higher score is M and the lower one is N. If the difference between the two scores is equal to their average, what is the value of N/M ?
(A) 3
(B) 2
(C) 1/2
(D) 1/3
(E) There isn't enough data to answer the question.
Rationale: M - N = (M + N)/2
Solving for N/M = 1/3
D
Answer: (D) 1/3
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5
(A) 45
(B) 20
(C) 25
(D) 27
(E) 22
Rationale: Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5 = 20.
Answer:B
Answer: (B) 20
Question: In an animal behavior experiment, 50 tagged white pigeons and 200 tagged gray pigeons were released from a laboratory. Within one week, 90 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?
(A) 80.5
(B) 82.4
(C) 82.5
(D) 85
(E) 86.5
Rationale: Weighted mix method is best here....
Ratio is 1:4 for 90:80.5...
So the answer required = 80.5+ (90-80.5)*1/5=80.5+9.5*1/5
80.5+1.9=82.4
B
Answer: (B) 82.4
Question: Price of a product is reduced by 30% . What percentage should be increased to make it 100%
(A) 22.85%
(B) 32.85%
(C) 42.85%
(D) 52.85%
(E) 62.85%
Rationale: Lets Assume 100 as Price of the Product.
After reduced by 30%, value becomes 70.
To Make it 100%, The percentage which we need to increase is
(100-70)/70 = 42.85%
we need to increase by 42.85%
ANSWER:C
Answer: (C) 42.85%
Question: Rates for having a manuscript typed at a certain typing service are $10 per page for the first time a page is typed and $6 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
(A) $430
(B) $1620
(C) $1650
(D) $1110
(E) $1770
Rationale: For 100-40-10=50 pages only cost is 10$ per page for the first time page is typed - 50*10=500$;
For 40 pages the cost is: first time 5$ + 6$ of the first revision - 40*(5+6)=440$;
For 10 pages the cost is: first time 5$ + 6$ of the first revision + 6$ of the second revision - 10(5+6+6)=170$;
Total: 500+440+170=1110$.
Answer: D.
Answer: (D) $1110
Question: Today is Saturday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?
(A) SUNDAY
(B) MONDAY
(C) TUESDAY
(D) WEDNESDAY
(E) FRIDAY
Rationale: Today is saturday
after three days--->TUESDAY
now, (tuesday)after before day--->MONDAY
then, (monday)day after tomorrow--->WEDNESDAY
ANSWER:D
Answer: (D) WEDNESDAY
Question: The population of a bacteria colony doubles every day. If it was started 7 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?
(A) 512
(B) 768
(C) 256
(D) 2048
(E) 4096
Rationale: 7 days ago- 2
6 days ago- 4
5 days ago- 8
4 days ago- 16
3 days ago- 32
2 days ago- 64
Yesterday- 128
Today- 256
Ans:C
Answer: (C) 256
Question: From the below series find the remainder? 1201×1203×1205×1207 is divided by 6?
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Answer: (A) 3
Question: A shepherd had 17 sheep. All but nine died. How many was he left with ?
(A) Nil
(B) 8
(C) 9
(D) 10
(E) 17
Rationale: all but nine died means all except nine died..
ANSWER:C
Answer: (C) 9
Question: If the probability Q of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
(A) 8/125
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4
Rationale: 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
Q= 5/16
Answer - C
Answer: (C) 5/16
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/36
(C) 31/30
(D) 31/32
(E) 31/35
Rationale: 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: A
Answer: (A) 31/32
Question: A three-character password consists of one letter of the alphabet and two different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 4,680
(B) 18,720
(C) 26,000
(D) 37,440
(E) 52,000
Rationale: 4 character password: DLD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
This gives us 10*26*9 ways
Now, the letter can also be DDLD so there will be another 10*9*26 ways
Total = 10*26*9*2 = 4,680 ways
A
Answer: (A) 4,680
Question: A man can row upstream at 4km/hr and down stream at 11km/hr find mans rate in still water ?
(A) 4.5km/hr
(B) 5.5km/hr
(C) 7.5km/hr
(D) 6.5km/hr
(E) 3.5km/hr
Rationale: given upstream(u) =4km/hr
down stream (v)= 11km/hr rate in still water =1/2(u+v)=1/2(4+11)=7.5km/hr Answer is (C):7.5
Answer: (C) 7.5km/hr
Question: For which of the following functions is f(w+b)=f(w)+f(b) for all positive numbers w and b?
(A) a) f(x)=x^2
(B) b) f(x)=x+1
(C) c) f(x)=root x
(D) d) f(x)=2/x
(E) e) f(x)= -3x
Rationale: f(w+b)=f(w)+f(b)= E
Answer: (E) e) f(x)= -3x
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 65 years, that of the parents is 45 years and that of the grandchildren is 8 years. What is the average age of family?
(A) 6/7years
(B) B)31
(C) C)30
(D) D)33
(E) E)35
Rationale: Required average
= (65 x 2 + 45 x 2 + 8 x 3 )/(2 + 2 + 3)
= (130 + 90 + 24)/7
=244/7
= 34 6/7years.
Answer is A
Answer: (A) 6/7years
Question: The present ages of three persons are in proportions 4:7:9 Eight years ago ,the sum of their ages was 56.Find their present ages (in years)
(A) 8,20,28
(B) 16,28,36
(C) 20,35,45
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let their present ages be 4x,7x and 9x years respectively.
Then,(4x-8)+(7x -8)+ (9x-8)=56 ⇔ 20x =80 ⇔ x=4.
∴ Their present ages are 16 years ,28 years and 36 year respectively. Answer B
Answer: (B) 16,28,36
Question: A certain college's enrollment at the beginning of 1992 was 40 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
(A) 63%
(B) 24%
(C) 50%
(D) 55%
(E) 61%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 140
And enrollment in 1993 will be 140*1.15=161
Increase in 1993 from 1991 = 161-100= 61
Answer : E
Answer: (E) 61%
Question: What is the remainder if 7^4 is divided by 100?
(A) 5
(B) 4
(C) 1
(D) 2
(E) 10
Rationale: 7*7*7*7/100=2401/100=24 reminder 1
Answer : C
Answer: (C) 1
Question: There are two concentric circles with radii 8 and 6. If the radius of the outer circle is increased by 25% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase?
(A) 225
(B) 250
(C) 275
(D) 300
(E) 325
Rationale: The area of a circle is piR^2, where R is the radius.
The area of the big circle is 64pi.
The area of the small circle is 36pi.
The area A1 between the circles is 28pi.
When the big circle's radius increases, the new area is 100pi.
When the small circle's radius decreases, the new area is 9pi.
The area A2 between the circles is 91pi.
The ratio of A2/A1 is 91/28 = 3.25 which is an increase of 225%.
The answer is A.
Answer: (A) 225
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) Rs.488
(B) Rs.428
(C) Rs.299
(D) Rs.480
(E) Rs.412
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer: D
Answer: (D) Rs.480
Question: A garrison has provisions for 90 soldiers for 160 days. After 100 days 45 more soldiers will join the group. For how many more days will the provisions last?
(A) 15 days
(B) 30 days
(C) 35 days
(D) none of the above
(E) Cannot be determined
Rationale: Explanation :
Actually after 100 days,
If 90 members are there, provisions come for 60 more days (since total 160 days)
But now 135 members are there.
So number of days = (90/135) X 60 = 20 days.
Answer : D
Answer: (D) none of the above
Question: Three faces of a fair die are Yellow, two faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
(A) 1/36
(B) 1/18
(C) 1/32
(D) 1/37
(E) None of these
Rationale: Probability of getting yellow color = P(Y) = 3/6 = 1/2
Probability of getting red color = P(R) = 2/6 = 1/3
Probability of getting blue color = P(B) = 1/6
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/6 = 1/36
ANSWER:A
Answer: (A) 1/36
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) Rs.2.9
(B) Rs.2.1
(C) Rs.2.5
(D) Rs.2.2
(E) Rs.2.7
Rationale: Explanation:
100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer: C
Answer: (C) Rs.2.5
Question: A certain lab experiments with white and brown mice only. In one experiment, 3/7 of the mice are white. If therare24 brown mice in the experiment, how many mice in total are in the experiment?
(A) 14
(B) 16
(C) 18
(D) 12
(E) 20
Rationale: Let total number of mice = M
Number of white mice = 3/7 M
Number of brown mice = 4/3 M = 18
=> M = 18
Answer C
Answer: (C) 18
Question: A right circular cylinder and a cone are there. Base radius of cone is equal to radius of cylinder. What is the ratio of height to slant side if their volume are the same?
(A) 1:3
(B) 3:1
(C) 1:2
(D) 2:1
(E) 1:4
Rationale: 1/3 pi r^2 h1 = pi r^2 h2
h1/h2= 3/1
height of cone : height of cylinder = 3:1
ANSWER:B
Answer: (B) 3:1
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 16000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
(A) 22
(B) 21
(C) 35
(D) 37
(E) 29
Rationale: Explanation:
Lot the total number of workers be v Then,
8OOOv = (16000 * 7) + 6000 (v - 7) <=> 2000v = 70000 <=> v = 35
Answer: C) 35
Answer: (C) 35
Question: A train 280 m long, running with a speed of 72 km/hr will pass a tree in?
(A) 17 sec
(B) 16 sec
(C) 18 sec
(D) 14 sec
(E) 12 sec
Rationale: Speed = 72 * 5/18
= 20 m/sec
Time taken = 280 * 1/20
= 14 sec
Answer: D
Answer: (D) 14 sec
Question: Abinaya invested an amount of Rs. 12,500 at the rate of 12% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
(A) 11850
(B) 18500
(C) 11180
(D) 20,000
(E) 11800
Rationale: Let the second amount be Rs. x. Then,
(12500 * 12 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100
15000+ 15x= 16800 + 14x
x = 1800
Total investment = 10000 + 1800= Rs. 11800 .Answer: E
Answer: (E) 11800