RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If a quarter kg of onions costs 80 paise, how many paise will 100 gm cost?
A.32 paise
B.65 paise
C.56 paise
D.87 paise
Answer: A.32 paise
Explanation: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 80 : x
250 * x = (100 * 80)
x = (100 * 80) / 250
x = 32
ANSWER: A
Question: 39! is divided by 41. Then what is the remainder?
A.1
B.3
C.4
D.6
Answer: A.1
Explanation: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Question: A library contains 90671 books in English and 405063 books in other languages. What is the total number of books available in the library?
A.494947
B.494044
C.495734
D.493734
Answer: C.495734
Explanation: Number of English Books = 90671
Number of in other Language Books = 405063
total number of books 90671 + 405063 = 495734 books
answer :C
Question: what is probabability that 5 envelope can not put in to the right envelope?
A.11/30
B.12/30
C.13/30
D.14/30
Answer: A.11/30
Explanation: Number of derangements = n! (1/2! - 1/3! + 1/4! + ... + ((-1)^n)/n!)
Given 5 letters A, B, C, D and E:
Total number of derangements = 5! (1/2! - 1/3! + 1/4! - 1/5!) = 60-20+5-1 = 44.
Total possible arrangements = 5! = 120.
P(no letter is in the correct position) = 44/120 = 11/30.
ANSWER:A
Question: There are 15 students in a class. On the day the test was given, Cara was absent. The other 14 students took the test and their average was 76. The next day, Cara took the test, and with this grade included, the new average was 77. What was Cara's grade on the test?
A.89
B.90
C.91
D.92
Answer: C.91
Explanation: 14*76+Cara's grade=15*77
Cara's grade is 15*77-14*76=91.
The answer is C.
Question: If the quantity (p + 5) is 5 times the quantity (q − 5), then what is the relationship between p and q?
A.p = 5q + 30
B.p = 5q − 30
C.5p = q + 20
D.p = 5q
Answer: B.p = 5q − 30
Explanation: p+5=5(q-5)
p+5=5q-25
p=5q-30
option B
Question: In a camp, there is a meal for 120 men or 200 children. If 120 children have taken the meal, how many men will be catered to with remaining meal?
A.30
B.42
C.40
D.57
Answer: B.42
Explanation: There is a meal for 200 children.
120 children have taken the meal.
Remaining meal is to be catered to 70 children.
Now, 200 children 120 men.
70 children = (120/200)x 70 = 42 men.
B
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
A.1/26
B.1/25
C.1/21
D.1/29
Answer: A.1/26
Explanation: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
A.245
B.255
C.260
D.268
Answer: B.255
Explanation: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Question: John bought 2 shares and sold them for $36 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
A.a profit of $10
B.a profit of $3
C.a loss of $3
D.a loss of $10
Answer: C.a loss of $3
Explanation: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 36*2 = $72
Total Cost Price = 72/(0.96) = $75
Loss = 75-72 = $3
Answer: Option C
Question: A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/5 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
A.2.5%
B.17.67%
C.28.3%
D.36%
Answer: D.36%
Explanation: Fiction Novels = 5,508
Transferred to another location = 6,120
Transferred fiction novels =1,101
Non Transferred Fiction Novels = 4,407
Percent of the remaining collection was fiction novels = 4,407/(18360 - 6120 ) * 100 => 36.004...%
Hence answer will be (D)
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 10 seconds. Find the length of the faster train?
A.270
B.288
C.100
D.299
Answer: C.100
Explanation: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 10 * 10 = 100 m.
The length of the faster train = 100 m.
Answer: C
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. four years from today, the difference between the age of the boy and the combined ages of the girls will be
A.1
B.2
C.3
D.–3
Answer: D.–3
Explanation: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 4 years there ages are
5 ....................... 5 ............................ 7
Difference = 7 - (5+5) = 7 - 10 = -3
Answer = D
Question: A coin is tossed 3 times. What is the probability of getting exactly 2 heads?
A.1/2
B.1/4
C.3/8
D.5/8
Answer: C.3/8
Explanation: The number of possible outcomes is 2^3 = 8
There are 3 ways to get exactly 2 heads.
P(exactly 2 heads) = 3/8
The answer is C.
Question: A can do a piece of work in 5 days and B can do it in 4 days how long will they both work together to complete the work?
A.6/11
B.8/11
C.7/9
D.2/9
Answer: D.2/9
Explanation: Explanation:
A’s one day work = 1/5
B’s one day work = 1/4
(A+B)’s one day work = 1/5 + 1/4 = 9/20 => time = 20/9 = 2 2/9 days
Answer: Option D
Question: Find the probability that a non leap year selected at random will have 53 Wednesdays.
A.6/7
B.5/7
C.1/7
D.3/7
Answer: C.1/7
Explanation: There are 365 days in a leap year: 52 weeks and 1 more days. So, 52 Sundays and 1 days.
This 1 days can be {Mon, Tue, Wed, Thu, Fri, Sat,Sun} (7 cases). In order to have 53 Mondays we should have Mon case.
The probability of that is 1/7.
Answer: C.
Question: A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 13, 21, and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box?
A.7/72
B.1/6
C.7/36
D.5/28
Answer: D.5/28
Explanation: Probability = No: of desired outcomes / Total No: of outcomes.
You are picking two slips out of 8 slips. So
Total No: of outcomes = 8C2 = 28
Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?
If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.
(1,2) (2,3) (3,5) (5,8) (8,13) . There are 5 such pairs. If the two numbers which I pick is from any of these 5 pairs, then I get my desired outcome.
So No: of desired outcomes = 5
Probability = 5/28
Answer :D
Question: A man can do a piece of work in 15 days and his son do the same work in 12 days, both are working together for 5 days after that son left the job. then in how many days a man alone complete the remaining work?
A.2.58 DAYS
B.2.33 DAYS
C.5.69 DAYS
D.8.85 DAYS
Answer: B.2.33 DAYS
Explanation: First take LCM of (15,12) = 60; Total work =60; A man one day work = 60/15 =4; son's one day work =60/12 = 5; One day work of both man+son= 4+5 = 9; Total work completed in 5 days = 5*5=25; remaining work is = 60 - 25 = 35; remaining work completed by a man in = 35/15= 2.33 days. Answer =B
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.11
B.12
C.15
D.10
Answer: D.10
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer: D
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
A.200
B.250
C.260
D.270
Answer: D.270
Explanation: Sol.
Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 26 sec.
Let the length of the train be x metres.
Then, x + 250 / 26 = 20 ⇔ x + 250 = 520 ⇔ x = 270.
Answer D
Question: Find the HCF of 2.1, 1.05 and 0.63
A.0.44
B.0.64
C.0.21
D.None of above
Answer: C.0.21
Explanation: Explanation:
To solve this question quickly, first remove decimal by multiplying each term with 100,
Then terms become 210, 105, 63
Then HCF of above terms is 21,
So Answer is 0.21
Option C
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is
A.1/4
B.1/10
C.7/15
D.8/15
Answer: D.8/15
Explanation: A's 1 day's work =1/15
B's 1 day's work =1/20
(A + B)'s 1 day's work =(1/15+1/20)=7/60,
(A + B)'s 4 day's work =(7/60x 4)=7/15.
Therefore, Remaining work =(1-7/15) = 8/15
Answer: Option D
Question: Michael cashed a check for $1,270 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
A. $830
B. $800
C. $770
D. $730
Answer: B. $800
Explanation: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1270 - 470 = 800.
Answer B
Question: The surface of a cube is 384sq cm. Find its volume?
A.8cc
B.9cc
C.512cc
D.4cc
Answer: C.512cc
Explanation: 6a2 = 384 = 6*64
a = 8 => a3 = 512cc
Answer: C
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $45,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
A.$10,000
B.$11,200
C.$12,000
D.$13,600
Answer: D.$13,600
Explanation: 1 machine of type B will cost: 20% down payment of 45,000 = 9,000plusremaining sum (50,000-9,000=41,000) with 40% of finance charges 41,000*1.4=57,400 --> 9,000+57,400=66,400;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 66,400 - 52,800 = 13,600.
Answer: D.
Question: Three unbased coins are tossed. the probability of getting at most three T is ?
A.1/2
B.7/8
C.3/4
D.1/8
Answer: D.1/8
Explanation: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {TTT}
P(E)=n(E)/n(S)=1/8
Answer(D)
Question: If 130/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer
A.I only
B.III only
C.I and II only
D.II and III only
Answer: A.I only
Explanation: I think, here we should use the greatest common factor.
The greatest common factor for 144 and 108 is 36.
So 36/x is an integer.
For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.
Ans is A.
Question: A clock is started at noon. By 10 minutes past 7, the hour hand has turned through how many degrees?
A.205Â°
B.210Â°
C.215Â°
D.220Â°
Answer: C.215Â°
Explanation: The angle traced by the hour hand in 12 hrs is 360Â°
The angle traced by the hour hand in 1 hour is 30Â°
The angle traced by the hour hand in 10 minutes is 5Â°
The angle traced by the hour hand in 7 hours and 10 minutes is 7*30Â° + 5Â° = 215Â°
The answer is C.
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
A.20:23
B.34:43
C.32:45
D.37:45
Answer: C.32:45
Explanation: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
ANSWER:C
Question: The difference between the place value and the face value of 6 in the numeral 856973 is
A.973
B.6973
C.5994
D.6084
Answer: C.5994
Explanation: (Place value of 6) - (Face value of 6) = (6000 - 6) = 5994
Answer: Option C
Question: A group of people were given 2 puzzles. 77% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?
A. 11%, 0%
B. 77%, 63%
C. 68%, 57%
D. 79%, 68%
Answer: B. 77%, 63%
Explanation: To solve this question, we don't need any formulas. Just read the question carefully. If 77% of the people solved puzzle X and 89% solved puzzle Y, then maximum % that can solve both correctly can only be 77%. From the given options, only D looks good
Answer B
Question: There is an antique clock exhibition. So many clock are piled up with distinct numbers tagged with them. The person managing it hangs different clocks numbers periodically on the main wall. At 9:20 am, he hung the clock number 200; at 11:00 am, he hung the clock number 30; at 4:00 pm, he hung the clock number 240.
Which numbered clock will he hang on the wall when the time is 7:30pm ?
A.313
B.314
C.315
D.316
Answer: C.315
Explanation: Solution:
He will hang clock number 315 at 7:30pm. The person has been hanging the clock number which corresponds with the angle between the hour hand and the minute hand of the clock at that time.
Answer C
Question: In your classes you counted 124 hands. How many students were at the class?
A.62
B.61
C.85
D.86
Answer: A.62
Explanation: Total number of hands = 124
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 124 by 2
124 ÷ 2 = 62
Therefore, there were 62 students at the class.
ANSWER IS A
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
A.587
B.287
C.585
D.658
Answer: C.585
Explanation: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135
=585
Answer:C
Question: Sachin is 40 years old and Ajith is 60 years old. How many decades ago was the proportion of their ages 3 : 5?
A.10
B.69
C.37
D.21
Answer: A.10
Explanation: A
10
If the ratio was 3 : 5, ‘A’ years ago.
Then, 7A – 6A = 4
A = 4
Then, {( 40 – A)/(60 – A)}= (3/5)
5 (40 – A) = 3(60 – A)
2A = 20
A = 10
Question: There are 14 students in a class. On the day the test was given, Dan was absent. The other 13 students took the test and their average was 75. The next day, Dan took the test, and with this grade included, the new average was 76. What was Dan's grade on the test?
A.86
B.87
C.88
D.89
Answer: D.89
Explanation: 13*75+Dan's grade=14*76
Dan's grade is 14*76-13*75=89.
The answer is D.
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?
A.36.7
B.36.1
C.36.5
D.36.9
Answer: C.36.5
Explanation: Correct sum
= (36 * 50 + 48 - 23)
= 1825.
Correct mean = 1825/50
= 36.5
Answer:C
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 96. Find their present ages.
A.24,42,54
B.8,20,28
C.16,28,36
D.16,28,46
Answer: A.24,42,54
Explanation: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 96
20K = 120
K = 6
Therefore, then present ages are 24,42,54.
ANSWER:A
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.31/38
C.21/32
D.31/33
Answer: A.31/32
Explanation: 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
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 61?
A.68
B.69
C.144
D.68^2
Answer: C.144
Explanation: In order to get the lowest LCM, we have to take the first number as 62 and the next number as its multiple.
So, I can take 62 and 144 as two distinct numbers, such that Lowest LCM = 144.
Answer should be C.
Question: Clara is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of waffle. The pattern repeats after she leaves the morsel of rye. If Clara drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
A.waffle − wheat − wheat
B.wheat − wheat − white
C.white − waffle − wheat
D.white − white − white
Answer: A.waffle − wheat − wheat
Explanation: In a single round Clara drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 9?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: 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 C
Question: A store sells chairs and tables. If the price of 3 chairs and 1 table is 60% of the price of 1 chair and 3 tables, and the price of 1 table and 1 chair is $80, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
A.68
B.84
C.72
D.60
Answer: D.60
Explanation: LET C= CHAIR ; T =TABLE
3C+1T = 0.6 (1C + 3T) OR C( 3-0.6) = 1.8T -1T OR 2.4C = 0.8 T THEREFORE C= 0.8/2.4 T = 1/3 T
IC +1T =80 OR 1/3T + 1T =80 THEREFORE T= 80*3/4 = 60
D
Question: 300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 35% of the customers that had purchased clothes for less than $100 reported they were overall satisfied with their purchase. What percent of the customers surveyed purchased clothes for at least $100 and reported that they were NOT overall satisfied with their purchase?
A.19
B.25
C.35
D.45
Answer: A.19
Explanation: Out of 300 - 180 purchased for less than 100$120 for more
Out of 300 - 120 responded as satisfied and 180 responded disatisfied
Out of 180 ( Purchased less than 100$) - 35% = 63 responded as satisfied, So remaining Satisfied are 120 - 63 = 57
so 57 is what percentage of 300 - 19%
So the answer should be A
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 240 vote’s majority. What is the total number of votes polled?
A.600
B.700
C.800
D.850
Answer: A.600
Explanation: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 280 (40*6 = 240)
100% -----> 600 (100*6 = 600)
Answer: Option A
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 35%. Staff are allowed a further 30% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
A.0.555D
B.0.765D
C.0.455D
D.0.785D
Answer: C.0.455D
Explanation: Effective discount = a + b + ab/100 = - 35 - 30 + (-35)(-30)/100 = -54.5
Sale price = D * ( 1 - 54.5/100)
Sale price = .455 * D
Answer (C)
Question: A sum of money at simple interest amounts to Rs. 800 in 3 years and to Rs. 850 in 4 years. The sum is:
A.Rs. 670
B.Rs. 690
C.Rs. 600
D.Rs. 625
Answer: C.Rs. 600
Explanation: Explanation:
S.I. for 1 year = Rs. (850 - 800) = Rs. 50.
S.I. for 3 years = Rs.(50 x 3) = Rs. 150.
Principal = Rs. (800 - 150) = Rs. 600.
Answer: Option C
Question: The cost of an item was reduced from its usual selling price of $23.99 to $16.99. Which of the following is closest to the percent decrease in the price of the item?
A.17%
B.21%
C.24%
D.29%
Answer: D.29%
Explanation: The price decreased by 23.99 - 16.99 = $7.
$7 is a bit more than 29% of original price of $24.
Answer: D.
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
A.7232
B.828
C.12
D.83
Answer: C.12
Explanation: Explanation:
T = 9/45 * 60 = 12
Answer: Option C
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
A.56%
B.57%
C.60%
D.61%
Answer: B.57%
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage = 11628	x 100	% = 57%.
20400
Option B
Question: Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
A.9680
B.9800
C.8000
D.7500
Answer: A.9680
Explanation: (8000*3*2)/100 = 480
9200
--------
9680
ANSWER A
Question: If the radius of a circle is increased by 40% then the area is increased by:
A.44%
B.120%
C.96%
D.40%
Answer: C.96%
Explanation: initially A=pi*r2
now R2=140/100r
then area=Pi*(140R/100)2
area=196R/100
that is area increases from 100 to 196=increase in area=96%
ANSWER:C
Question: What is the unit digit in {(6374)^1793 x (625)^317 x (341^491)}?
A.5
B.1
C.0
D.7
Answer: C.0
Explanation: Unit digit in (6374)^1793 = Unit digit in (4)^1793
Unit digit in [(4^2)^896 x 4]
= Unit digit in (6 x 4) = 4.
Unit digit in (625)^317 = Unit digit in (5)^317 = 5.
Unit digit in (341)^491 = Unit digit in (1)^491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Answer C)0.
Question: The regular price per can of a certain brand of soda is $0.30. If the regular price per can is discounted 15 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases?
A.$16.32
B.$18.36
C.$21.60
D.$24.48
Answer: B.$18.36
Explanation: The discounted price of one can of soda is (0.85)($0.30), or $0.255.
Therefore, the price of 72 cans of soda at the discounted price would be (72)($0.255) = 18.36
Answer: B.
Question: If a fast song has 160 beats per minute, and a slow song has 90 beats per minute, how many minutes total would you play a fast and a slow song to have a stream of music that had a total of 1,020 beats?
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: We can determine quickly that total number should range between 1,020/160<= N <= 1,020/90 , so ans should be between 6 and 12.
Now solving the expression 160A+90B = 1,020
decreasing 1,020 by multiples of 160 and checking divisibility of that number by 9, we get
fast song plays for 3 minutes and slow somg plays for 6 minutes, 3*160 + 6*90 = 1,020
Hence total number of minutes stream of music plays is 3 + 6 = 9 minutes
Ans D
Question: Find the 25th term of an arithmetic progression whose first term is 5 and the common difference is 7.
A.145
B.38
C.173
D.156
Answer: C.173
Explanation: n th term of A.P = a +(n-1) *d
= 5+(25-1)*7 , = 5 + 168 = 173.
ANSWER:C
Question: What is the greatest prime factor of 6^8−3^8 ?
A.3
B.11
C.17
D.19
Answer: C.17
Explanation: 6⁸ − 3⁸ is a DIFFERENCE OF SQUARES. So we can factor it.
6⁸ − 3⁸ = (6⁴ + 3⁴)(6⁴ - 3⁴)
= (6⁴ + 3⁴)(6² + 3²)(6² - 3²)
= (6⁴ + 3⁴)(6² + 3²)(6 + 3)(6 - 3)
= (6⁴ + 3⁴)(45)(9)(3)
= (6⁴ + 3⁴)(3)(3)(5)(3)(3)(3)
Hmmmm, we can see that the correct answer is "hiding" in the first number (6⁴ + 3⁴)
Let's factor out the 3⁴, to get:
6⁴ + 3⁴ = 3⁴(2⁴ + 1)
= 3⁴(16 + 1)
= 3⁴(17)
= (3)(3)(3)(3)(17)
So, 6⁸ − 3⁸ = (3)(3)(3)(3)(17)(3)(3)(5)(3)(3)(3)
So the correct answer is C