mathewhe/aqua_rat huggingface dataset:
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 6 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 6
(B) 8
(C) 16
(D) 24
(E) 52
Rationale: Notepads of the same color = 6 (we have 6 colors). As we have two sizes then total for the same color=6*2=12
Notepads of the different colors = 6C3=20 (we should choose 3 different colors out of 6). As we have two sizes then total for the different color=20*2=40
Total=40+12=52
Answer: E.
Answer: (E) 52
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
(A) Rs.90
(B) Rs.76
(C) Rs.98
(D) Rs.18
(E) Rs.02
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15 = Rs.90.
Answer:C
Answer: (C) Rs.98
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
(A) 384
(B) 882
(C) 270
(D) 377
(E) 262
Rationale: Average mark scored by all the three boys
= [64/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 384
Answer:A
Answer: (A) 384
Question: The strength of a school increases and decreases every alternate year. It starts with increase by 10% and there-after the percentage of increase/decrease is the same. Which of the following is definitely true about the strength of the school in 2001 as compared to that in 1996?
(A) Increase approximately by 2%
(B) Decrease approximately by 2%
(C) Increase approximately by 20%
(D) Decrease approximately by 20%
(E) None of these
Rationale: Let the strength of school was x in 1998
∴ strength in 2001 will be
= x110⁄100 × 90⁄100 × 110⁄100 × 90⁄100 × 110⁄100 = 1.07811 x
increment = 1.07811 x – x = 0.07811 x
∴ % increase = 7.811 ≈ 8%
Answer E
Answer: (E) None of these
Question: The area of a square is equal to twice the area of a rectangle of dimensions 32 cm * 64 cm. What is the perimeter of the square?
(A) 236
(B) 256
(C) 456
(D) 656
(E) 756
Rationale: Area of the square = s * s = 2(32 * 64)
=> s = 64 cm
Perimeter of the square = 4 * 64= 256cm.
Answer: Option B
Answer: (B) 256
Question: If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
(A) -5
(B) 4
(C) 2
(D) 8
(E) 9
Rationale: 9x-3y=12---1
3x-5y=7----2
multiplying second equation with 3 and solving the two equations we get
x=1 and y=-1
6*1-2*-1=8 ANSWER:D
Answer: (D) 8
Question: The average of six numbers is X and the average of three of these is Y.If the average of the remaining
three is z, then
(A) x = y + z
(B) 2x = y + z
(C) x = 2y + z
(D) x = y + 2z
(E) None of these
Rationale: Explanation:
X =((3y+3z)/6)
or
2X= y + z
Answer: Option B
Answer: (B) 2x = y + z
Question: L = {3, 4, 5, 5, 6, 7}
M = {2, 2, 2, 8, 8, 8}
N = {15, 15, 15, 15, 15, 15}
Rank those three sets from least standard D eviation to greatest standard deviation.
(A) L, M, N
(B) M, L, N
(C) M, N, L
(D) RANKING=N, L, M
(E) N, M,
Rationale: Square of Standard deviation is sum of squares of deviation from the mean divided by the number of terms.
If deviation from the mean is higher for the same number of elements, standard deviation will be higher.
L = {3, 4, 5, 5, 6, 7}
Mean is 5 and deviation of 2 elements from mean is 0, of 2 elements is 1 and of 2 elements is 2.
M = {2, 2, 2, 8, 8, 8}
Mean is 5 and deviation of all elements from the mean is 3. So SD here will be higher than SD of L.
N = {15, 15, 15, 15, 15, 15}
Mean is 15 here and all elements have 0 deviation from mean so SD = 0 here. This is the minimum possible SD.
Answer N, L, M
Answer (D)
Answer: (D) RANKING=N, L, M
Question: The arithmetic mean of 5 negative integers is -100. If the average of 3 of these integers is -90, what is the least possible value that one of the other 2 integers can have?
(A) 229
(B) -1
(C) -229
(D) 90
(E) -90
Rationale: The Arithmetic Mean of 5 negative integers is (a+b+c+d+e)/5=-100
So, The sum of 5 negative integers would be a+b+c+d+e=-100*5 = -500
Similarly, The sum of 3 negative integers would be a+b+c= -90*3 = -270
Thus, the sum of the other 2 integers is -500 + 270= -230. Since we know that the integers are negative then the least one from these two can be -229, the other one being -1.
Hence, the correct ans is C
Answer: (C) -229
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 75 terms?
(A) 25/26
(B) 40/41
(C) 75/76
(D) 150/151
(E) 151/75
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a75 = 1/75 - 1/76
The sum of these terms is 1-1/76 = 75/76
The answer is C.
Answer: (C) 75/76
Question: A wheel rotates 20 times every minute and moves 30 cm during each rotation. How many metres does the wheel move in one hour?
(A) 360 metre
(B) 12 metre
(C) 320 metre
(D) 1200 metre
(E) 260 metre
Rationale: Number of times wheel moves in 1 hour = 20 * 30 = 1200
:. Distance moves = (1200*30) cms = 36000 cms
In metres = 360 metre
ANSWER:A
Answer: (A) 360 metre
Question: In a one km race A gives B a start of 100m and in a one km race B gives a start of 80 m to C. In a 1 km race who will win and by how much distance from the worst performer between two losers?
(A) 172 m
(B) 372 m
(C) 172 m
(D) 772 m
(E) 632 m
Rationale: Ratio of speeds of A:B = 1000:900 = 100:90
Ratio of speeds of B:C = 1000:920 = 100:92
Therefore, when A moves 1000m , B moves 900 m and when B moves 900m, C moves 828m
Thus,
Since , C moves 8 % less than B in the same time . Thus, C is the worst performer and A will win by him by 172 m
ANSWER=A
Answer: (A) 172 m
Question: How many 4-digit numbers contain no.2?
(A) 22
(B) 98
(C) 28
(D) 29
(E) 22
Rationale: Answer:B
Answer: (B) 98
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 300 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 300xy
(B) 300y - x
(C) 300x - y
(D) 300y/x
(E) 300x/y
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
300 = d/(x*pi)
d = 300 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (300 * x * pi) / (y*pi) = 300x/y
Answer (E)
Answer: (E) 300x/y
Question: If you divide 7^84 by 5, which remainder do you get?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of 7^1 is 7.
The units digit of 7^2 is 9.
The units digit of 7^3 is 3.
The units digit of 7^4 is 1.
The units digit of 7^5 is 7.
etc...
The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}
The remainder of 84/4 is 0.
So the units digit of 7^84 is 1.
The remainder of 7^84 / 5 is 1.
The answer is B.
Answer: (B) 1
Question: In how many ways can 4 boys and 2 girls sit around a table in such a way that no two girls sit together?
(A) 74
(B) 72
(C) 78
(D) 82
(E) 68
Rationale: The 4 boys can be seated around a table in 3! Ways. In between them there are 4 places.
The 2 girls can be placed in the 4 places in 4P2 ways.
Therefore, Required number of ways= 3!* 4P2
=6*12
=72
ANSWER:B
Answer: (B) 72
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?
(A) 8 days
(B) 10 days
(C) 12 days
(D) 14 days
(E) 16 days
Rationale: If A can complete a work in x days and B 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 = 12 × 24/ 36 = 8 days.
A)
Answer: (A) 8 days
Question: The sum of three consecutive even numbers is 20 more than the first of these numbers. What is the middle number?
(A) 7
(B) 9
(C) 11
(D) Cannot be determined
(E) None of these
Rationale: Solution
Let the numbers be x, x + 2 and x + 4.
Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.
∴ Middle number = x + 2 = 9.
Answer B
Answer: (B) 9
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 9 men and 9 women?
(A) 9C4 9C5
(B) 4C9 5C9
(C) 7C5 9C4
(D) 9C4 7C5
(E) NONE
Rationale: Group consisting of 9 men and 9 women
4 men can be selected from 9 men in 9C4 ways
5 women can be selected from 9 women in 9C5 ways
Therefore, Total number of ways= 9C4 9C5
ANSWER:A
Answer: (A) 9C4 9C5
Question: a number when divided by 899 gives a remainder 63. what remainder will be obtained by dividing the same number by 29
(A) 8
(B) 5
(C) 7
(D) 6
(E) 9
Rationale: 63 / 29, thereforerequired number is: 5, correct answer (B)
Answer: (B) 5
Question: For the integer n, if n*n*n is odd, then what is true
(A) n is odd and n*n is even
(B) n*n is odd
(C) n is even
(D) n*n is odd
(E) None of these
Rationale: Option A
Answer: (A) n is odd and n*n is even
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 5, and the digit 2 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 300
(E) 320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 5.
Four digit # possible without the restriction (about the digit 2): 4*5*4*2=160
Numbers with two 2-s, 2X2X 1*5*1*2=10.
Thus there are 160-10=150 such numbers.
Answer: B.
Answer: (B) 150
Question: A fellow borrowed a certain sum of money at 6% per annum at simple interest and in 6 years the interest amounted to Rs.672 less than the sum lent. What was the sum lent?
(A) 1050
(B) 1220
(C) 1250
(D) 1060
(E) 1110
Rationale: P - 672 = (P*6*6)/100
P = 1050
Answer: A
Answer: (A) 1050
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is:
(A) 338
(B) 278
(C) 322
(D) 231
(E) 121
Rationale: Clearly, the numbers are (23 * 13) and (23 * 14). Larger number
= (23 * 14) = 322.
Answer: C
Answer: (C) 322
Question: In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
(A) 7:3
(B) 3:7
(C) 4:6
(D) 5:7
(E) 8:9
Rationale: Required rate = 3.50 : 1.50 = 7 : 3.
ANSWER A
Answer: (A) 7:3
Question: The reflex angle between the hands of a clock at 10.25 is
(A) 180°
(B) 192 ½°
(C) 195°
(D) 197 ½°
(E) None
Rationale: Solution
Angle traced by hour hand in 125 / 12 hrs.	=[360/12 x 125/12]°
= 312½°.
Angle traced by minute hand in 25 min.	= [360/60 x 25]°
=150°.
Reflex angle	= 360 - (312½ -150)°
=360° - 162 ½°
= 197½°.
Answer D
Answer: (D) 197 ½°
Question: John and David can finish a job together in 3 hours. If John can do the job by himself in 4 hours, what percent of the job does David do?
(A) 35%
(B) 28%
(C) 26%
(D) 20%
(E) 25%
Rationale: You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 12 donuts which is the job ( I picked this as a SMART number).
John on his own works 12/4 = 3 donuts per hour.
John and David work 12/3 = 4 donuts per hour so David works 1 donuts/hour
To find out the percentage, David works 1 donuts/hr x 3 hours = 3 donuts per hour.
Therefore 3 donuts/12donuts = 1/4 = 25%
Answer : E
Answer: (E) 25%
Question: During a certain week, a seal ate 55% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
(A) 32
(B) 80
(C) 55
(D) 64
(E) 80
Rationale: Total smelt = x.
Then, 0.55*80+0.3(x-80)=0.4*x --> x=200 --> 0.4*x=80.
Answer: B.
Answer: (B) 80
Question: The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?
(A) 18750 sq.m
(B) 37500 sq.m
(C) 40000 sq.m
(D) 48000 sq.m
(E) None of these
Rationale: Solution
So length =250 m; breadth=150m
Area	= (250 x 150)m²
= 37500 m²
Answer B
Answer: (B) 37500 sq.m
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
(A) 42 6/4%
(B) 42 9/7%
(C) 42 2/7%
(D) 42 6/7%
(E) 42 6/8%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: (D) 42 6/7%
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 3:1 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
(A) 26:11
(B) 23:11
(C) 21:11
(D) 24:11
(E) 25:11
Rationale: Vessel A = 300 gallons --> milk = 225, water = 75;
Vessel B = 500 gallons --> milk = 300, water = 200;
Vessel A + B = 800 gallons --> milk = 525, water 275
The ratio =525/275 -->21:11
Answer: C
Answer: (C) 21:11
Question: How many two digit numbers of distinct digits can be formed by using digits 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
Answer: option E
Answer: (E) 6
Question: The G.C.D. of 1.08, 0.36 and 0.9 is:
(A) 0.03
(B) 0.9
(C) 0.18
(D) 0.2
(E) 0.21
Rationale: Given numbers are 1.08, 0.36 and 0.90.
H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer: Option C
Answer: (C) 0.18
Question: Set A: {1, 3, 4, 6, 9, 12, 16}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 4?
(A) 3/14
(B) 2/7
(C) 9/14
(D) 5/7
(E) 1/35
Rationale: using probability you can solve: 3/7*2/6*1/5=1/35.
Ans E
Answer: (E) 1/35
Question: There are 12 pieces of radioactive metal K that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.
Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.
If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}
The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=B
Answer: (B) 3
Question: The unit digit in the product 1457*7863*4575*9719 is?
(A) 5
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Unit digit in the given product = unit digit in 7*3*5*9 = 5
Answer is A
Answer: (A) 5
Question: A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.4 hours, then the distance covered at 40 kmph is
(A) 130 km
(B) 120km
(C) 100km
(D) 140km
(E) 148
Rationale: Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 5.4
or, x/40 + (250 - x)/60 = 5.4
or, (3x + 500 - 2x)//120 = 5.4
or 500 + x = 648
x=148
ANSWER:E
Answer: (E) 148
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 39 degrees. Find the temperature on Friday?
(A) 65 degrees
(B) 73 degrees
(C) 31 degrees
(D) 34 degrees
(E) 74 degrees
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 39
Tu + W + Th = 192 -39 = 153
F = 184 – 153 = 31
Answer:C
Answer: (C) 31 degrees
Question: The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
(A) 42.85
(B) 44
(C) 46
(D) 48
(E) 50
Rationale: The time it takes Cara to drive to City B is 150 / 30 = 5 hours.
Dan needs to take less than 3.5 hours for the trip.
Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour.
The answer is A.
Answer: (A) 42.85
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 17 min
(B) 10 min
(C) 90 min
(D) 18 min
(E) 20 min
Rationale: 4/12 + x/15 = 1
x = 10
Answer: B
Answer: (B) 10 min
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 4: 00 p.m., at what time were there 32 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 8: 00 p.m.
(C) 6: 00 a.m.
(D) 8: 00 a.m.
(E) 10: 00 a.m.
Rationale: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 4 PM, we get 10 AM as the answer.
Option E
Answer: (E) 10: 00 a.m.
Question: Three interviewers, E, F, and G are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer E admitted F applicants, G admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
(A)  12
(B)  2
(C)  6
(D)  8
(E)  0
Rationale: If E admitted 15 are overlapping with F admission of 17 But G does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : E
Answer: (E)  0
Question: There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 7 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?
(A) 45,000
(B) 360,000
(C) 354,300
(D) 392,000
(E) 396,900
Rationale: Say x was the # of hardback copies sold from the time the first paperback copy was sold.
Then the total # of paperback copies sold was 9x;
Hence the total # of copies sold was (hardback)+(paperback)=(36+x)+(7x)=441 --> x=50.6.
So, the total # of paperback copies sold was 7x=7*50.6=354.3 or 354,300.
Answer: C.
Answer: (C) 354,300
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
(A) 9 3/9
(B) 9 3/7
(C) 9 3/8
(D) 9 3/2
(E) 9 3/1
Rationale: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Answer:C
Answer: (C) 9 3/8
Question: A glass was filled with 24 ounces of water, and 0.06 ounce of the water evaporated each day during a 12-day period. What percent of the original amount of water evaporated during this period?
(A) 0.003%
(B) 0.03%
(C) 3%
(D) 2%
(E) 30%
Rationale: In 12 days 12*0.06=0.72 ounces of water evaporated, which is 0.72/24âˆ—100=3 of the original amount of water.
Answer: C.
Answer: (C) 3%
Question: Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?
(A) 9:30
(B) 9:00
(C) 8:40
(D) 7:50
(E) 7:00
Rationale: Relative speed =jan - Tom =10 pages per hour = 1/6 page per minute
time diff =50 minutes
by the time Jan started ToM already finished (30/60)*50 = 25 pages
time taken = 25 /(1/6) =25*6= 150 minutes=7:50
ANSWER:D
Answer: (D) 7:50
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 30, what is the sum of the first 15 terms of the progression?
(A) 250
(B) 275
(C) 260
(D) 225
(E) 230
Rationale: 4th term + 12th term = 30
i.e., (a+3d)+(a+11d) = 30
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 30 --------------- From (1)
=225
Answer : D
Answer: (D) 225
Question: four children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
(A) 24
(B) 480
(C) 540
(D) 720
(E) 840
Rationale: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 6!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 4 can sit in 5! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 6!-2*5!=24..
ans A
Answer: (A) 24
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 59.4 meters. How many times did the ball bounce?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Ans: 6
Division of total diatance travelled will be 20+20+10+5+2.5+1.25+0.6 ANS B
Answer: (B) 6
Question: Jonathan’s grandparents lend $20,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
(A) 20,000∗0.1^5
(B) 20,000∗1.5
(C) 20,000∗0.5
(D) 20,000∗1.1^5
(E) (20,000∗0.1)^5
Rationale: if you are like me and have used S.I = P x R x T formula in school, then while the question is asking for Amount in 5 years. so (B) 20,000∗ 1.5
Ans : B
Answer: (B) 20,000∗1.5
Question: Find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2?
(A) 1:2
(B) 2:3
(C) 2:9
(D) 2:1
(E) 2:2
Rationale: 1:2
Answer: A
Answer: (A) 1:2
Question: Look at this series: 42, 36, 39, __, 42, 45, 42, 48, ... What number should fill the blank?
(A) 40
(B) 48
(C) 46
(D) 42
(E) 52
Rationale: D
42
In this series, 3 is added to the previous number; the number 42 is inserted as every third number.
Answer: (D) 42