mathewhe/aqua_rat huggingface dataset:
Question: A salt manufacturing company produced a total of 3000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?
(A) 119
(B) 185
(C) 190
(D) 116
(E) 200
Rationale: Total production of salt by the company in that year = 3000 + 3100 + 3200 + .... + 4100 = 42600.
Average monthly production of salt for that year = 42600/365 â‰ˆ 116
ANSWER:D
Answer: (D) 116
Question: In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 248. What is the sum of all the integers in the sequence?
(A) 528
(B) 568
(C) 574
(D) 586
(E) 590
Rationale: let the first term of the sequence be x
since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms)
now,
sum of first 4 terms =248
or,
4x+12=248
x=236/4=59
Thus the answer can now be calculated by either summing up 59+61+63+... 8th term
or
s=n/2(2a+(n-1)d
=8/2(2*59+(7*2))
=4(118+14)=528
A
Answer: (A) 528
Question: Find the average of all the numbers between 11 and 36 which are divisible by 5
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Average = (15 + 20 + 25 + 30 + 35) / 5 = 125/5 = 25
ANSWER C
Answer: (C) 25
Question: If log10 2 = 0.3010, the value of log10 80 is:
(A) 1.5252
(B) 1.903
(C) 3.9252
(D) 3.903
(E) 2.5252
Rationale: = log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
ANSWER B
Answer: (B) 1.903
Question: In how many ways can 3 black and 5 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
(A) 720
(B) 30
(C) 120
(D) 15
(E) 60
Rationale: 3 black chess pieces can be arranged in 3! ways and 5 white pieces can be arranged in 5! ways.
W_W_W_W
Number of ways = 3!*5! = 6 * 120 = 720
Answer A
Answer: (A) 720
Question: A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 36 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?
(A) 36
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)
T=144
n(A)=T-n(A')=144-89=55
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=36-6=30
n(All 3 Events)=6
144=55+44+53-30-2*6+n(None of the events)
n(None of the events)=144-55-44-53+30+12=34
Ans:E
Answer: (E) 34
Question: A man whose speed is 3.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 2.0
(B) 2.5
(C) 3.0
(D) 2.1
(E) 4.0
Rationale: M = 3.5
S = 1.5
DS = 5
US = 2
AS = (2 * 5 * 2) /5 = 4
Answer: E
Answer: (E) 4.0
Question: In the coordinate plane, one of the vertices of a square is the point (-3, -4). If the diagonals of that square intersect at point (5, 3), what is the area of that square?
(A) 100
(B) 169
(C) 225
(D) 324
(E) 256
Rationale: One point (-3-4), Intersection (3,2) so the distance from the first point -3-5=-8 is the midpoint of the square --> whole side 16, 16*16=256
E
Answer: (E) 256
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 338
(B) 278
(C) 800
(D) 269
(E) 112
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Answer: (C) 800
Question: Village X has a population of 68000, Which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year. In how many years will the population of the two villages be equal ?
(A) 7 years
(B) 6 years
(C) 9 years
(D) 13 years
(E) 12 years
Rationale: Let the population of village X and Y be equal after p years
Then, 68000-1200P=42000 + 800P
2000P=2600
P=13
so, their population will be equal after 13 years
ANSWER: D
Answer: (D) 13 years
Question: Dividing by 3⁄7 and then multiplying by 5⁄6 is the same as dividing by what number?
(A) 35⁄18
(B) 16⁄5
(C) 20⁄9
(D) 9⁄20
(E) 5⁄16
Rationale: say X/3/7*5/6 = x*7/3*5/6 = x*35/18
A
Answer: (A) 35⁄18
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: x ----- 9
(x + 10) --- 6
x * 9 = (x + 10)6
x = 20
ANSWER B
Answer: (B) 20
Question: If each side of a right triangle is increased by 10% and the base(b) is half of the height, find the percentage change in its area?
(A) 26%
(B) 21%
(C) 15%
(D) 18%
(E) 12%
Rationale: a =1/2 x b x h or 1/2 x 2a x a(for simplification)
New h = 220a / 100 = 22a / 10
New b =(110a x 100) ==11a/10
New area = 1/2 (22a x 11a) / (10 x 10) = (121a²/100)
increased area== (121a²/100) - a²
Increase %= [(21a²/100 ) x (1/a² ) x 100]% = 21%
answer :B
Answer: (B) 21%
Question: A dog takes 5 leaps for every 6 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 1:6
(B) 5:6
(C) 6:1
(D) 5:1
(E) 9:1
Rationale: Explanation:
Dog : Hare = (5*3) leaps of hare : 6 leaps of hare = 15 : 3-->5:1
Answer: D
Answer: (D) 5:1
Question: On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.50 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027
(B) 0.09
(C) 0.417
(D) 0.657
(E) 0.875
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.5
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.5 * 0.5 = 0.25
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.5^3 = 0.125
Total = 0.875
Ans E
Answer: (E) 0.875
Question: Ram professes to sell his goods at the cost price but he made use of 750 grms instead of a kg, what is the gain percent?
(A) 11 1/7%
(B) 11 7/7%
(C) 11 1/9%
(D) 33.33%
(E) 11 1/2%
Rationale: 750 --- 250
100 --- ? => 33.33%
Answer:D
Answer: (D) 33.33%
Question: John has on his shelf three books of poetry, four novels, and three reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
(A) 12/45
(B) 2/5
(C) 3/10
(D) 7/20
(E) 8/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/10*3/9 + 3/10*4/9 = 12/45.
Answer: A
Answer: (A) 12/45
Question: In how many ways a committee,consisting of 5 men and 6 women can be formed from 8 men and 10 women?
(A) 266
(B) 5040
(C) 11760
(D) 86400
(E) None
Rationale: Solution
Required number of way = (8 C 5 × 10 C 6) = (8 C 3 × 10 C 4)
=( 8x7x6/3x2x1x 10x9x8x7/4x3x2x1) = 11760
Answer C
Answer: (C) 11760
Question: In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.78 per kg?
(A) 5:8
(B) 4:7
(C) 3:7
(D) 9:5
(E) 9:8
Rationale: (96-78)/(78-68)=18/10=9/5
ANSWER:D
Answer: (D) 9:5
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 45 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17 minutes
(B) 87 minutes
(C) 36 minutes
(D) 27 minutes
(E) 11 minutes
Rationale: 1/20 - 1/45 = 1/36
36 minutes
Answer:C
Answer: (C) 36 minutes
Question: If NOIDA is written as STNIF, how MEERUT can be written in that code?
(A) RJJWZY
(B) RIJWZY
(C) RJJWZX
(D) RJJWZZ
(E) RJJWZW
Rationale: N + 5 = S
O + 5 = T
I + 5 = N
D + 5 = F
SO,
M + 5 = R
E + 5 = J
E + 5 = J
R + 5 = W
U + 5 = Z
T + 5 = Y
RJJWZY ANSWER:A
Answer: (A) RJJWZY
Question: If a rectangle have length 16 cm and diagonal 20cm.calculate its area.
(A) 185
(B) 132
(C) 165
(D) 192
(E) 212
Rationale: breadth=√20^2-16^2=√144=12cm
Area=16*12=192 sq.cm
Answer D
Answer: (D) 192
Question: Painter A can paint a house in 16 days, and painter B can do the same work in 20 days. With the help of painter C, they paint the house in 8 days only. Then, Painter C alone can do this task in
(A) 90 days
(B) 45 days
(C) 20 days
(D) 50 days
(E) 80 days
Rationale: Work done by Painter A per day =1/16
Work done by Painter B per day =1/20
Work done by Painter A, Painter B, Painter C per day=1/10
Work done by Painter C per day = 1/10 - (1/16+1/20)=1/80
C can paint the house in 80 days.
E
Answer: (E) 80 days
Question: In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number?
(A) 376
(B) 286
(C) 126
(D) 297
(E) 864
Rationale: Explanation:
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b - 2
a + b + c = 3b = 18 => b = 6
So a = 8 and b = 4
Hence the three digit number is: 864
Answer: E
Answer: (E) 864
Question: How many total numbers of seven-digit numbers can be formed having sum of whose digits is even is
(A) 9000000
(B) 4500000
(C) 8100000
(D) 4400000
(E) None of these
Rationale: Suppose x1 x2 x3 x4 x5 x6 x7 represents a seven digit number. Then x1 takes the value 1, 2, 3, ....., 9 and x2, x3,....., x7 all take values 0, 1, 2, 3, ......, 9.
If we keep x1, x2, ......, x6 fixed, then the sum x1 + x2 + ......+ x6 is either even or odd. Since x7 takes 10 values 0, 1, 2, ....., 9, five of the numbers so formed will have sum of digits even and 5 have sum odd.
Hence the required number of numbers
= 9 . 10 . 10 . 10 . 10 . 10 . 5 = 4500000
Answer B
Answer: (B) 4500000
Question: Which fraction should be added to:
1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ....... + 1/(29 Ã— 30)
so that the result is equal to 1?
(A) 4/15
(B) 7/15
(C) 8/15
(D) 11/30
(E) 13/30
Rationale: The given expression
= 1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ...... + 1/(29 Ã— 30)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/29 - 1/30)
= 1/2 - 1/30 = 14/30
Thus, the fraction we should add = 1 - 14/30 = 16/30 = 8/15
The answer is C.
Answer: (C) 8/15
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,30) and (-5,15). Which can be the coordinate of fourth vertex?
(A) (-5,-5)
(B) (5,15)
(C) (-5,-30)
(D) (-5,10)
(E) (15,30)
Rationale: A(-5, 15)
B(5, 15)
C(5, 30)
X(-5, 30): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 30): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:E
Answer: (E) (15,30)
Question: The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 3 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 12 seconds?
(A) 18 miles per hour
(B) 90 miles per hour
(C) 216 miles per hour
(D) 288 miles per hour
(E) 360 miles per hour
Rationale: Since Velocity is proportional to Time
Velocity =k*Timewhere k is the constant of proportionality
Time= 3 seconds
Velocity = 3k = 90 miles per Hour
i.e. k = 30
i.e. The relation between Velocity and Time becomes
Velocity =30*Time
Time= 12 seconds
Velocity = 30*12 = 360 miles per hour
Answer: Option E
Answer: (E) 360 miles per hour
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 384 votes. Find the number of votes casted to the winning candidate?
(A) 288
(B) 744
(C) 992
(D) 298
(E) 177
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 384
62% -------- ? => 992
Answer: C
Answer: (C) 992
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 4
Rationale: (30*30)/100 = 9%loss.Answer: A
Answer: (A) 9
Question: How many of the positive factors of 24 are not factors of 30
(A) 2
(B) 3
(C) 4
(D) 1
(E) 5
Rationale: factors of 24 - 1, 2, 3, 4, 6, 8, 12,24
factors of 30 -1, 2, 3, 5, 6, 10, 15 and 30.
Comparing both, we have four factors of 24 which are not factors of 30- 4,8,12,24
Answer(C)
Answer: (C) 4
Question: How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?
(A) 8
(B) 12
(C) 60
(D) 118
(E) 120
Rationale: ways in which 3 seats out 5 can be selected = 5C3
ways in which 3 people can be arranged in 3 seats = 3!
Total ways of arrangement = 5C3*3!
=5*4/2*6
=10*6
=60
Ans = C
Answer: (C) 60
Question: Find the number of zeroes at the end of 50!
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: calculate division by 5 and 25
50/5=10
50/25=2
total=12
ANSWER:C
Answer: (C) 12
Question: A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 60$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?
(A) 39.55$
(B) 40.63$
(C) 41.63$
(D) 42.15$
(E) 48.7$
Rationale: let x is the cost of the food
1.07x is the gross bill after including sales tax
1.15* 1.07x=60
x=48.7
Hence, the correct option is E
Answer: (E) 48.7$
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^7) + (23)?
(A) 2
(B) 5
(C) 9
(D) 10
(E) 25
Rationale: (21)(3^7) is divisible by 3 but 23 is not divisible by 3.
Therefore (21)(3^7) + 23 is not divisible by 3 and thus not divisible by 9.
The answer is C.
Answer: (C) 9
Question: A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B's contribution in the capital
(A) Rs 9000
(B) Rs 7000
(C) Rs 5000
(D) Rs 4000
(E) None of these
Rationale: Explanation:
Let B contribution is x.
3500*12/7x =2/3
=>14x=126000=>x=Rs9000
Option A
Answer: (A) Rs 9000
Question: A Private Limited company have 20 staffs and they celebrated one festival. Director gives Rs.10000/- to his accountant and told him to 4500/- to each staff Rs. 2000/- each to cleaning staff and cooking staff and balance for you. Then how much amount accountant received?
(A) 10500
(B) 20000
(C) 4500
(D) 6500
(E) 5000
Rationale: Total amount paid for 20 Staffs : 4500 * 19= 85500/-
Paid to Cleaning & Cooking Staff : 2000/- * 2 = 4000/-
Total amount paid for both : 85500/- + 4000/- =89500/-
Balance with Accountant : 100000 - 89500 = 10500/-
Answer is (A)
Answer: (A) 10500
Question: What is the decimal equivalent of (1/4)^3?
(A) 0.0016
(B) 0.0625
(C) 0.16
(D) 0.25
(E) 0.0156
Rationale: (1/4)^3 = 1/64 =0.0156
Answer : E
Answer: (E) 0.0156
Question: What is the sum of natural numbers between 50 and 100
(A) 4800
(B) 4860
(C) 3825
(D) 5500
(E) 5550
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 50 and 100 numbers = 51 => 100 - 50 = 50 + 1 = 51
Sn = 51/2 Ã— 150 = 51 Ã— 75 = 3825
Answer : C
Answer: (C) 3825
Question: if log10 7 = a then log10 (1/70) equal to
(A) -(1+a)
(B) (1+a)
(C) (1+2a)
(D) (2+a)
(E) (2+2a)
Rationale: log10(1/70) = log10 1 - log10 70
= - log10 (7*10)
= -(log10 7 + log10 10) = -(a+1)
ANSWER A
Answer: (A) -(1+a)
Question: A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?
(A) 3 : 4
(B) 4 : 3
(C) 1 : 4
(D) 2 : 3
(E) 4 : 5
Rationale: Since S # 1/t
S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4
Answer : A
Answer: (A) 3 : 4
Question: The three digits of a number add up to 20. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?
(A) 175
(B) 250
(C) 78
(D) 225
(E) 125
Rationale: Say the three-digit number is abc.
The leftmost digit is double the middle digit --> a=2b;
The number is divisible by 5 --> c is either 0 or 5;
The three digits of a number add up to 20 --> a+b+c=20
So, either a+b+c=2b+b+0=20 or a+b+c=2b+b+5=20. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=5 --> a=10 and c=5 --> a*b*c=250.
Answer: B.
Answer: (B) 250
Question: During a Pizza buffet where A eats more times 2.5 than B, and B eats 7 times less than C.find the least number of times all the three has to eat
(A) 50
(B) 60
(C) 70
(D) 80
(E) 85
Rationale: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.5:1 or 5:2 and as B eat 7 times less the C the the ratio of B : C is 2:14 the the least number of times all three has eat is the LCM of A,B,C that is 70 ..
ANSWER:C
Answer: (C) 70
Question: A sum of Rs.5000 was divided into 30 persons such that each man gets Rs.200 and each woman gets Rs.150. Find the number of women.
(A) 20
(B) 15
(C) 18
(D) 24
(E) 26
Rationale: m+w=30,
200m+150w=5000
By solving we get men=10,women=20
ANSWER:A
Answer: (A) 20
Question: What least number must be added to 3000 to obtain a number exactly divisible by 19 ?
(A) 2
(B) 1
(C) 4
(D) 18
(E) 17
Rationale: On dividing 3000 by 19, we get 17 as remainder.
Number to be added = (19 - 17) = 2.
ANSWER A 2
Answer: (A) 2
Question: A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 9 minutes. Then the speed of the current is :
(A) 1 kmph
(B) 2 kmph
(C) 3 kmph
(D) 2.5 kmph
(E) 1.85 kmph
Rationale: Rate upstream = (1/20 *60) = 3 kmph
Rate dowm stream = 1/9 * 60 = 6.7 kmph
Rate of the current = ½ (6.7-3) = 1.85 kmph
ANSWER:E
Answer: (E) 1.85 kmph
Question: A vessel has 300 ml of pure milk. 30 ml of milk is removed and 30 ml of water is added into the vessel. If this operation is repeated another 2 times, what is the % of milk in the vessel at the end?.
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Total MIlk Removed= 30+30+30=90 ml
Remaining Milk= 300-90 = 210 ml
% of Milk = 210/300=7/10=70%
ANSWER:C
Answer: (C) 70
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the p measure in inches of the width of the foil covered prism?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 = 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2 =p=10
Ans E.
Answer: (E) 10
Question: A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?
(A) 11
(B) 13
(C) 66
(D) 77
(E) 88
Rationale: Let the number of men initially be x. we have M1 D1 H1= M2 D2 H2
So, x * 65 * 6 = (3x)/4 * 40 * h2
=> h2 = (65 * 6 * 4)/(3 * 40) = 13.
Answer: B
Answer: (B) 13
Question: Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract?
(A) 90
(B) 180
(C) 225
(D) 450
(E) 900
Rationale: We need to select
M M W C = four people
M - 10C2 = 45
W = 5C1 = 5
C = 2C1 = 2
Now 45*5*2 = 450
ANS option D
Answer: (D) 450
Question: If a man can cover 16 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 118 km
(B) 162 km
(C) 216 km
(D) 1887 km
(E) 177 km
Rationale: 16 m/s = 16 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 16 * 18/5 * 15/4 km = 216 km.
Answer: C
Answer: (C) 216 km
Question: A class of 40 students has an average height of 120 cm. four students whose average height is 160 cm, left the class and four others whose average height is 124 cm, joined. Calculate the new average height of the students of the class (in cm) is?
(A) 292.4 cm
(B) 296.4 cm
(C) 206.4 cm
(D) 294.4 cm
(E) 236.4 cm
Rationale: Total height = 120 * 40 = 4800 cm.
Total height of those who left = 160 * 4 = 640
Total height of those who joined = 124 * 4 = 496
New average
= [12000 - 640 + 496 ] / 40 = 11856/40 cm.
= 296.4 cm
Answer:B
Answer: (B) 296.4 cm
Question: At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes?
(A) 2150
(B) 2600
(C) 3120
(D) 1500
(E) 1895
Rationale: Winner votes = 100-30 = 70
polled votes = [(100*1000)/2*70-100]+100 = 2600
Answer is B
Answer: (B) 2600
Question: A class has a ratio of 3:6:7 of children with red hair, blonde hair and black hair respectively. If the class has 9 kids with red hair, how many kids are in the class?
(A) 99
(B) 48
(C) 16
(D) 22
(E) 60
Rationale: Since there are 9 children with red hair, and the class exists in a 3:6:7 ratio, there are 3 times more children than the unit ratio. Therefore
9 red-haired children
3*(6) blonde-haired children
3*(7) black-haired children
9+18+21 = 48
Alternatively, a part-to-whole ratio can be set up. Since the whole is 3+6+7=16,
9/3=X/16
3*16=48
Answer: B)
Answer: (B) 48
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 400 that is both a prime and a palindrome. What is the sum of the digits of p?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Given that p is smallest integer greater than 400 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
A
Answer: (A) 3
Question: 300 liters of a mixture contains milk and water in the ratio 3:2 If 15 liters of this mixture be replaced by 15 liters of milk, the ratio of milk to water in the new mixture would be?
(A) 12:8
(B) 12:4
(C) 13:8
(D) 14:5
(E) 13:5
Rationale: Quantity of milk in 300 liters if mix = 300*3/5 =180 liters
Quantity of milk in 315liters of new mix = 180+15 = 195 liters
Quantity of water in it = 315-195 = 120 liters
Ratio of milk and water in new mix = 90:20 = 13:8
Answer isC
Answer: (C) 13:8
Question: 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
(A) 334
(B) 377
(C) 495
(D) 766
(E) 261
Rationale: Explanation:
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is \inline {\color{Black}12C_4{}} = 495.
Therefore, we can draw 495 quadrilaterals
Answer: C) 495
Answer: (C) 495