mathewhe/aqua_rat huggingface dataset:
Question: The parameter of a square is equal to the perimeter of a rectangle of length 4 cm and breadth 2 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 4.51
(B) 4.71
(C) 4.32
(D) 4.21
(E) 4.68
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(4+ 2) = 12 cm Parameter of the square = 12 cm
i.e. 4a = 12
a = 3
Diameter of the semicircle = 3 cm
Circimference of the semicircle
= 1/2(âˆ)(3)
= 1/2(22/7)(3) = 66/14 = 4.71 cm to two decimal places
Answer: B
Answer: (B) 4.71
Question: A group of 6 volunteers is to be interviewed and selected from a pool of 9 candidates. How many different volunteer groups are possible?
(A) 102
(B) 52
(C) 84
(D) 56
(E) 336
Rationale: Note that the volunteer groups must consist of 6 members, not at least 6 members. Hence, all you have to do is 9C6 = 84
Answer (C)
Answer: (C) 84
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
(A) 37
(B) 85
(C) 48
(D) 43
(E) 84
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer: Option C
Answer: (C) 48
Question: Six children — A, B, C, D, E, F — are going to sit in seven chairs in a row. The children CF have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
(A) 600
(B) 240
(C) 1440
(D) 4320
(E) 4800
Rationale: for such questions , we can treat both as one then total person=5..
these 5 can be arranged in 6! ways.. but within these 6 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =5!*2=240
ans B
Answer: (B) 240
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 14 charts have been brought to the meeting, how many people are present?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 10
Total charts are 11 so A + 2B = 14
Add both: 3A + 3B = 24 so A + B = 8
Total number of people = 8
C
Answer: (C) 8
Question: Find the cost price of an item if by selling at Rs.1255, a profit of 10% is made?
(A) Rs. 1000
(B) Rs.3000
(C) Rs.2100
(D) Rs.1129
(E) Rs.1985
Rationale: SP = 1255
CP = (SP)*[100/(100+P)]
= 1255 * [100/(100+10)]
= Rs.1129
Answer: D
Answer: (D) Rs.1129
Question: The avg. age of a group of 24 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
(A) 22 years
(B) 23 years
(C) 24 years
(D) 25 years
(E) 27 years
Rationale: Total age of 12 students=24*20=480
If total age of 4 students=x
Then, (480+x)/(24+4) =(20+1), x=108
So average age of new students=108/4= 27 years
ANSWER:E
Answer: (E) 27 years
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 40% goods during theft. His loss percent is:
(A) 72%
(B) 42%
(C) 34%
(D) 12%
(E) 22%
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 60.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 60 = Rs. 66
Hence, loss % = 34/100 * 100 = 34%
Answer:C
Answer: (C) 34%
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
(A) 90
(B) 100
(C) 120
(D) 160
(E) 200
Rationale: Solution:
Let x be the number he chose, then
2*x*138=102
2x=240
x=120
correct answer C
Answer: (C) 120
Question: The price of rice has increased by 60%. In order to restore to the original price, the new price must be reduced by ?
(A) 33 1/3%
(B) 37 1/2%
(C) 40%
(D) 45%
(E) NONE
Rationale: Answer
Let original price = Rs. 100
⇒ Increase price = Rs. 160
⇒ Decrease on Rs. 160 = Rs. 60
∴ Decrease on Rs. 100 = (60/160) x 100 % = 37 1/2%
Correct Option: B
Answer: (B) 37 1/2%
Question: If Feb 12th,1986 falls on Wednesday then Jan 1st,1987 falls on which day?
(A) monday
(B) friday
(C) Thursday
(D) saturday
(E) 0
Rationale: Explanation:
First,we count the number of odd days for the left over days in the given period.
Here,given period is 12.2.1986 to 1.1.1987
Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan
16 31 30 31 30 31 31 30 31 30 31 1 (left days)
2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 1(odd days) = 1 odd day
So,given day Wednesday + 1 = Thursday is the required result.
Answer: C) Thursday
Answer: (C) Thursday
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3400, A will get:
(A) Rs.1200
(B) Rs.1500
(C) Rs. 2040
(D) Rs.2000
(E) None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 136
So, A’s amount = 120 × 15 = Rs.2040.
Answer: Option C
Answer: (C) Rs. 2040
Question: 6 people can do work in 80 days how much people they required to complete the work in 16
days ?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Man and days concept ...
6M * 80D=M * 16D
solve it,
total no of people required is 30;
ANSWER:C
Answer: (C) 30
Question: A clock shows 5.20. After how much time both hands will coincide together?
(A) 6 2/11 minutes
(B) 5 5/11 minutes
(C) 3 2/11 minutes
(D) 4 2/11 minutes
(E) 7 2/11 minutes
Rationale: 60/55*(5)=5 5/11
ANSWER:B
Answer: (B) 5 5/11 minutes
Question: In an examination 35% of the students passed and 351 failed. How many students appeared for the examination?
(A) A)540
(B) B)400
(C) C)700
(D) D)650
(E) E)840
Rationale: Let the number of students appeared be x
then, 65% of x = 351
65x/100 = 351
x = 351*100/65 = 540
Answer is A
Answer: (A) A)540
Question: A boy rides his bicycle 10km at an average speed of 12km/hr and again travels 12km at an average speed of 10km/hr. His average speed for the entire trip is approximately?
(A) 8km/hr
(B) 10.8km/hr
(C) 12.6km/hr
(D) 15.6km/hr
(E) 14km/hr
Rationale: Total distance traveled = 10+12 = 22km
Total time taken = 10/12 + 12/10 = 61/30 hrs
Average speed = 22*30/61 = 10.8km/hr
Answer is B
Answer: (B) 10.8km/hr
Question: A grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ?
(A) 4991
(B) 5467
(C) 5987
(D) 6453
(E) None of these
Rationale: Explanation:
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991. Answer: A
Answer: (A) 4991
Question: Two persons enter the lift of a five storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
(A) 7
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Each person out of 2 has 4 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 4*4=4^2=16.
Answer: E.
Answer: (E) 16
Question: Rose and John had the same number of candies. Rose gave John 24 candies so that now John has five times as many candies as Tina has. John has now how many candies?
(A) 36
(B) 48
(C) 54
(D) 60
(E) 65
Rationale: T = R
T - 24 ;R + 24
R + 24 = 5 ( T - 24 )
R + 24 =5T - 120
R - 5T = - 144
We knowR = T, so
R - 5T = - 144
Or, R - 5R = -144
Or, - 4R = - 144
Or, R = 36( This is the initital no of Candies Rebecca had)
Candles now she possesses is36 + 24 = 60
So , Rebecca now has 60 candies.
Answer will be (D) 60
Answer: (D) 60
Question: X completes a work in 70 days and Y complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be?
(A) 20 days.
(B) 22 days.
(C) 25 days.
(D) 36 days.
(E) 21 days.
Rationale: If X can complete a work in x days and Y can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 70Ã— 30/ 100 = 21 days.
E)
Answer: (E) 21 days.
Question: What is the length of the longest pole which can be kept in a room 6 m long, 4 m broad and 3 m high?
(A) 7
(B) 9
(C) 11
(D) 13
(E) None
Rationale: Explanation:
d2 = 62 + 42 + 32 = 7.8
E)
Answer: (E) None
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 26 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
(A) 32
(B) 40
(C) 48
(D) 54
(E) 60
Rationale: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.26(800) = 232
The answer is A.
Answer: (A) 32
Question: How many integers n are there such that 1< 4n + 4 < 16?
(A) 5
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 1< 4n + 4 < 16
1< 4n + 4 < 16
We first subtract 4 from all three parts of the inequality, and we obtain:
-3/4 < 4n < 12
Next, we divide both sides of the inequality by 4 and we get:
-4/4 < n < 3
The answer is D
Answer: (D) 3
Question: Fom the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd and n*n is even
(B) n is odd
(C) n*n is even
(D) n is even
(E) n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: A can have a piece of work done in 7 days, B can work five times faster than the A, C can work six times faster than A. How many days will they take to do the work together ?
(A) 3/2 days
(B) 8/9 days
(C) 4/3 days
(D) can't say
(E) none
Rationale: A's 1 day work is 1/18
B's 1 day work is 5/18
C's 1 day work is 6/18
(A+B+C)'s 1 day work(1/18+5/18+6/18) is 2/3
so, they can finish the work in 3/2 days
ANSWER:A
Answer: (A) 3/2 days
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) Rs.229
(B) Rs.285
(C) Rs.228
(D) Rs.217
(E) Rs.123
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160
= Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100]
= Rs.285.
Answer:D
Answer: (D) Rs.217
Question: Mandrake has to choose from 4 from 14 people. There are 3 girls, 5 boys , 6 children. What is total probability that he will choose 1G , 2B , 1C?
(A) 1/7
(B) 2/7
(C) 3/7
(D) 4/7
(E) 16/89
Rationale: (3C1 * 5C2 * 6C1)/ 14C4 = 3*10*6/1001 = 180/1001=16/89
ANSWER:E
Answer: (E) 16/89
Question: How many numbers between 1000 and 5000 are exactly divisible by 225?
(A) 16
(B) 18
(C) 19
(D) 12
(E) 21
Rationale: Explanation: First multiple of 225 after 1000 is 1125 (225 Ã— 5 ) and last multiple of 225 before 5000 is 4950 (225 Ã— 22)
Total number are l+a/d=4950-1125/225+1=18
ANSWER IS B
Answer: (B) 18
Question: Doughnuts, Cookies and Muffins in a pastry shop are in the ratio of 5: 3 : 1. If there are 50 Doughnuts, the number of Muffins in the shop is:.
(A) 25
(B) 30
(C) 10
(D) 15
(E) 20
Rationale: Explanation :
Let Doughnuts = 5x, Cookies = 3x & Muffins = 1x. Now, 5x = 50 hence x = 10.
Number of Muffins = 1x which is 10.
Answer : C
Answer: (C) 10
Question: Exactly 36% of the numbers in set R are even multiples of 3. If 40% of the even integers in set R are not multiples of 3, what percent of the numbers in set R are not even integers?
(A)  76%
(B)  60%
(C)  50%
(D)  40%
(E)  24%
Rationale: Everything is correct except the red part with a typo: it should be N=0.6R --> even numbers are 60% of R --> 40% of R are not even integers.
Answer: D.
Answer: (D)  40%
Question: A man walking at a rate of 15km/hr crosses a bridge in 40 minutes. The length of the bridge is?
(A) 1250m
(B) 1110m
(C) 2000m
(D) 1000m
(E) 1300m
Rationale: Speed = 15*5/18 = 15/18 m/sec
Distance covered in 40 minutes = 15/18 *40 *60 = 2000m
Answer is C
Answer: (C) 2000m
Question: A box contains 3 yellow balls and 7 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 3/5
(B) 7/10
(C) 5/8
(D) 2/3
(E) 3/7
Rationale: Each ball has an equal chance (1/10) of being selected fourth.
The probability that a black ball is selected fourth is 7/10.
The answer is B.
Answer: (B) 7/10
Question: A circle graph shows how the budget of a certain company was spent: 15 percent for transportation, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for salaries. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent salaries?
(A) 216°
(B) 222°
(C) 228°
(D) 234°
(E) 240°
Rationale: The percent of the budget for salaries is 100 - (15+9+5+4+2)= 65%
100% of the circle is 360 degrees.
Then (65%/100%)*360 = 234 degrees
The answer is D.
Answer: (D) 234°
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
(A) 1:2
(B) 4:5
(C) 1:3
(D) 1:1
(E) 1:4
Rationale: Let the third number be x.
Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2
Therefore, Ratio of first two numbers = (6x/5 : 3x/2)
= 12x : 15x = 4 : 5.
Answer is B.
Answer: (B) 4:5
Question: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 16 cm height. What is the diameter of each sphere?
(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm
(E) 12 cm
Rationale: Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
12*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 16 = 64 cm^3
R = 4 cm
D = 8 cm
The answer is C.
Answer: (C) 8 cm
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 5
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer:E
Answer: (E) 5
Question: Two members of a certain club are selected to speak at the next club meeting. If there are 15 different possible selections of the 2 club members, how many members does the club have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Method-1
Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]
i.e. If total member = n
then nC2 = n! / [(2!)(n-2)!] = 15
i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 15
i.e. n*(n-1) = 30
(for Positive Values of n)
therefore, n*(n-1) = 30
i.e. n= 6
Answer: Option B
Answer: (B) 6
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 2000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
(A) 100000
(B) 12500
(C) 42000
(D) Data inadequate
(E) None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 2000) From the question,
(x - 2000) × 126⁄100 = 6⁄5x ⇒ x = 42000
Answer C
Answer: (C) 42000
Question: If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be 10?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
(A) 8/2652
(B) 18/2652
(C) 1/2652
(D) 12/2652
(E) 16/2652
Rationale: 2 possible cases:
King - 10 or 10 -King (4 kings and 4 10).
Either way,
the total probability = 2( King -10) = 2 (4/52 * 4/51) = 18/2652. B is the correct answer.
Answer: (B) 18/2652
Question: Ayesha's father was 35 years of age when she was born while her mother was 30 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 9 years
Rationale: Mother's age when Ayesha's brother was born = 30 years.
Father's age when Ayesha's brother was born = (35 + 4) years = 39 years.
Required difference = (39 - 30) years = 9 years. Answer: Option E
Answer: (E) 9 years
Question: sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6700 ?
(A) 4966
(B) 6191
(C) 2877
(D) 2676
(E) 1881
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6700 x 6) - 34009]
= Rs. (40200 - 34009)
= Rs. 6191
Answer: B
Answer: (B) 6191
Question: In one can of mixed nuts, 10% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?
(A) 16 2/3%
(B) 20%
(C) 25%
(D) 33 1/3%
(E) 35%
Rationale: Can 1: size 1; 10% nuts
Can 2: size 0.5 and 40% nuts
(1x0.1+0.5x0.4)/1.5=33.33
D
Answer: (D) 33 1/3%
Question: There is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save. Auggie was very curious to test this theory.
Auggie spent all of his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?
(A) 248
(B) 120
(C) 252
(D) 250
(E) 350
Rationale: Amount left = 0.5x−4
For fifth store this is zero. So x = 8. That means he entered fifth store with 8.
Now for fourth store, amount left = 8 so 0.5x−4=8⇒ x = 24
For third store, amount left = 24 so 12x−4=24⇒ x = 56
For Second store, amount left = 56 so 0.5x−4=56⇒ x = 120
For first store, amount left = 120 so 0.5x−4=120⇒ x = 248
So he entered first store with 248.
ANSWER:A
Answer: (A) 248
Question: What is the sum of the odd integers from 25 to 55, inclusive?
(A) 495
(B) 550
(C) 555
(D) 600
(E) 640
Rationale: The mean is 40.
Sum=Mean(# of elements)
There are 16 odd numbers between 25-55 inclusive. 16*40=640
E
Answer: (E) 640
Question: A farmer is having a total of 20 fruits (apples or oranges). He made two type packets with these fruits. All the fruits are in either apple packets of orange packets. Apple Packets contain 3 apples each and Orange packets contain 2 oranges each.
If |apple packets| < 4
Then How many packets of apples the farmer can have. When number of apple and orange packets are both positive integers above zero.
(A) 2
(B) 3
(C) 4
(D) 7
(E) 6
Rationale: Let us start by understand the meaning of 4 > |Number of Apples|
1) when we write |-x| this means the same as |x|.
2) Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b'.
Now come to the question. Let number of apple packets be ‘a’ and number of oranges packets be ‘b’. First its given |a| < 4 ==> |a-0| < 4 ==> the distance from zero is less than 4. So the point ‘a’ will be -3,-2,-1,0,1,2,3 as distance from 0 to these values is less than 4. Number of apple packets is above zero so possible values of ‘a’ left are 1,2,3.
As per the given information there are total of 20 fruits and they are in packets (3 per packet for apples and 2 per packets for oranges) so we can write it as follows:
3a + 2b = 20 ==> b = 10 – (3*a)/2. If b is an integer then ‘a’ must be divisible by 2. If we take only those values of ‘a’ that are divisible by 2 then we are left with 2 only. So there are two packets of apples. If there are two packets of apples then b = 10 – (3*2)/2 ==> b = 7. So we have 7 packets of oranges and 2 packets of apples. So A is the answer. 7 packets (2 orange each) and 2 packets of apples (3 apples each) make 20 fruits in total.
Answer: (A) 2
Question: A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?
(A) 20
(B) 10
(C) 60
(D) 50
(E) 40
Rationale: Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above.
[sum(Xi) + sum(Yi)] / 20 = 70 : class average
sum(Xi) / n = 50 : average for less that 60
sum(Yi) / N = 75 : average for 60 or more
50n + 75N = 1400 : combine the above equations
n + N = 20 : total number of students
n = 4 and N = 16 : solve the above system
correct answer A
Answer: (A) 20
Question: The average (arithmetic mean)R of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) None of the above
Rationale: Given :
p + q = EVEN (odd + odd =even)
p + q + s + t = EVEN (even + even = even) nothing more....
(p + q + s + t) / 4 = x
I.
x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.
II.
Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.
III.
As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.
Answer E, None.
Answer: (E) None of the above
Question: A grocer stacked oranges in a pile. The bottom layer was rectangular with 4 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?
(A)  6
(B)  4
(C)  3
(D)  2
(E)  1
Rationale: Bottom Layer = 5 x 4 = 20
IInd Layer = (5-1) x (4-1) = 12
IIIrd Layer = (4-1) x (3-1) = 6
Answer = 6 = A
Answer: (A)  6
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
(A) 3 1/5 Km
(B) 4 Km
(C) 4 1/5 Km
(D) 3 2/5 Km
(E) 3 3/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A
Answer: (A) 3 1/5 Km
Question: Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 23 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
(A) 64
(B) 72
(C) 86
(D) 98
(E) 102
Rationale: Use the options.
The options which after getting added to 23 shows a cube of a number could be right.
Here
64+23 = 87
72+23= 95
86+23= 109
98+23 = 121
102+23=125 ---(5*5*5)
So we have 102 as the answer!
E
Answer: (E) 102