RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $50 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
A.191
B.213
C.221
D.223
Answer: D.223
Explanation: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 10% of the cost:
Sell Price = Cost + $50
Sell Price = $500 + $50
Thus, the Sell Price is $550 for each item. Selling all 100 items gives the retailer...
100($50) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(550) = $27.5 discount
$522.5 = $500 + $22.5
Now, the retailer makes a profit of just $22.5 per item sold.
To earn $2,000 in profit, the retailer must sell....
$22.5(X) = $2,000
X = 2,000/22.5
X = 222.222222 items
You'll notice that this is not among the answer choices.... 221 and 223 are.
Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.
Final Answer:
D
Question: Local kennel has cats and dogs in the ratio of 3:4. If there are 8 fewer cats than dogs, how many dogs are in the kennel?
A.28
B.26
C.24
D.32
Answer: D.32
Explanation: Lets work with the data given to us. We know that there ratio of cats to dogs is 3:4 or
cats 3
dogs 4
we can write number of cats as 3x and number of dogs as 4x and we know that 4x-3x= 8 (therefore x = 8)
Then # of dogs = 4x8= 32
Answer is D
Question: The sum of digits of a two digit number is 8,The difference between the digits is 6. Find the number
A.85
B.94
C.83
D.71
Answer: D.71
Explanation: Description :
=> x+y=8, x-y=6
Adding these 2x =14
=> x=7, y=1.
Thus the number is 71
Answer D
Question: The remainder obtained when a prime number greater than 9 is divided by 9 is
A.a)2 or 4
B.b) 1 or 5
C.c) 3 or 5
D.d) 4 or 5
Answer: A.a)2 or 4
Explanation: The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 9, i.e. 13 and 11:
13/9 = 1 + remainder of 4
11 /9 = 1 + remainder of 2
This is already sufficient to see that answer choice a) is correct.
A
Question: If 0 < q < 1, what is the median of the values q, q^-1, q^2, q^1/2 and q^3?
A.q
B.q^-1
C.q^2
D.q^1/2
Answer: A.q
Explanation: A. To make the problem less confusing, I picked a number between 0 and 1 such as q = 1/4 and calculate:
q = 1/4
q^-1 = 4
q^2 = 1/16
q^(1/2) = 1/2
q^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is q. Answer A
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 266 m, what is its area?
A.4290
B.2535
C.2530
D.2515
Answer: A.4290
Explanation: length = breadth +23. Therefore,
4× breadth +2×23=266 m
⇒ breadth =55 m
length =55+23=78 m
Area =78×55=4290 m2
Answer is A.
Question: What are the last two digits of (301*401*503*604*646*547*448*349)^2
A. 96
B. 76
C. 56
D. 44
Answer: D. 44
Explanation: ((301*401*503*604*646)*(547*448*349))^2
If you observe above digits, last digit are: 1,1,3,4,6,7,8,9; 1&5 are missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,01,03,04,46 and final three as 47*48*49.
Solving for only last two digits and multiplying them we get:( (03*04*46)(56*49))^2 = (52*44)^2=88^2=44
Hence answer is D
Question: The simple interest on Rs.14000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest.
A.3052.82
B.3052.51
C.3028.31
D.3028.11
Answer: D.3028.11
Explanation: R = 100 I / PT
=> R = (100 * 7200)/ (14000 * 5) = 10.28%
CI = P{ [1 + R /100]n - 1}
= 14000 { [ 1 + 10.28 / 100]^2 - 1} = Rs.3028.11
Answer:D
Question: In the quadratic equation ax2 + 8x + 16 = 0, if the sum of two roots is -8, what is the product of the two roots?
A.16
B.14
C.20
D.15
Answer: A.16
Explanation: Explanation:
The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 +8 x + 40 = 0, where a = a, b = 8 and c = 16.
we get, sum of the roots = -8 / a= -8
a= 1
Product of the roots = 16 / 1 = 16
ANSWER: A
Question: A group of four women and four men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
A. 8! – 5!4!
B. 7! – 4!3!
C. 7! – 5!3!
D. 7 × 2!3!2!
Answer: A. 8! – 5!4!
Explanation: 8 people can sit in 8! different ways. But because 4 men cannot sit together, we take them as a unit.
This unit of men, among themselves can sit in 4! ways.
Hence, 8! - 4!.
This unit of men along with 4 women can sit in 5! different ways which also needs to be eliminated.
Hence 8! - 5!4!
A
Question: If F + A < F - A < A - F, which of the following is correct?
A.A < F < 0.
B.F < A < 0.
C.F < 0 < A.
D.0 < F < A.
Answer: B.F < A < 0.
Explanation: Check first inequality
F + A < F - A
A<-A
A is -ve
Check another equality
F - A < A - F
-2A<-2F
A>F
Combining both 0>A>F
Option B fits only
Ans B
Question: If 10, 12 and 'x' are sides of an acute angled triangle, how many integer values of 'x' are possible?
A.7
B.12
C.9
D.13
Answer: C.9
Explanation: Explanatory Answer
Key property about sides of an acute triangle
Finding the answer to this question requires that you know this key property about sides of an acute triangle.
For an acute angled triangle, the square of the LONGEST side MUST BE LESS than the sum of squares of the other two sides.
If 'a', 'b', and 'l' are the 3 sides of an acute triangle where 'l' is the longest side then l2 < a2 + b2
The sides are 10, 12, and 'x'.
Scenario 1: Among the 3 sides 10, 12, and x, for values of x ≤ 12, 12 is the longest side.
Scenario 2: For values of x > 12, x is the longest side
Possibilities in scenario 1: When x ≤ 12, let us find the number of values for x that will satisfy the inequality 122 < 102 + x2
i.e., 144 < 100 + x2
The least integer value of x that satisfies this inequality is 7.
The inequality will hold true for x = 7, 8, 9, 10, 11, and 12. i.e., 6 values.
Possibilities in scenario 1: When x > 12, x is the longest side.
Let us count the number of values of x that will satisfy the inequality x2 < 102 + 122
i.e., x2 < 244
x = 13, 14, and 15 satisfy the inequality. That is 3 more values.
Hence, the values of x for which 10, 12, and x will form sides of an acute triangle are x = 7, 8, 9, 10, 11, 12, 13, 14, 15. A total of 9 values.
Choice C
Question: At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 85. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?
A.2
B.5
C.6
D.15
Answer: C.6
Explanation: WITHOUTusing the formula, we can see that today the restaurant served 30 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 30 customers must offset the “deficit” below the average of 90 created on the x days the restaurant served only 85 customers per day.
30/5 = 6 days.Choice (A).
WITHthe formula, we can set up the following:
90 = (85x + 120)/(x + 1)
90x + 90 = 85x + 120
5x = 30
x = 6Answer Choice (C)
Question: The diagonals of the two squares are in the ratio of 7:9 find the ratio of their area
A.78:89
B.5:48
C.49:81
D.74:36
Answer: C.49:81
Explanation: let the diagonals of the square be 7x and 9x respectively .
ratio of their areas =1/2(7x)^2:1/2(9x)
= 49x^2:81x^2=49:81
Answer(C)
Question: The 8 leaders of the G8 nations convene in Rome and stand in a row as they get ready to have some pictures of them taken by the press. What is the probability that the picture that the New York Times' editors will randomly select for publishing the next day is one in which Berlusconi is not standing next to Obama? (assuming that there are pictures of all possible standing arrangements).
A.1/8
B.1/4
C.1/2
D.3/4
Answer: D.3/4
Explanation: We'd have 7 units: 1, 2, 3, 4, 5, 6, and {Berlusconi, Obama}. These 7 units can be arranged in 7! ways. Berlusconi and Obama within their unit can be arranged in 2! ways. Thus the total number of ways to arrange 8 leaders so that Berlusconi and Obama to stand together is 7!*2!.
8 people without any restriction can be arranged in 8! ways, thus in 8! - 7!*2! arrangements Berlusconi and Obama will not not be standing together.
P=8!−7!∗2!8!=1−7!∗2!8!=1−14=34P=8!−7!∗2!8!=1−7!∗2!8!=1−14=34.
Answer: D.
Question: Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6?
A.A=30000 B=40000 C=48000
B.A=30000 B=40000 C=48200
C.A=30000 B=40900 C=48000
D.A=30000 B=40090 C=48000
Answer: A.A=30000 B=40000 C=48000
Explanation: Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
----------
A:B:C = 15:20:24
We can divide Rs.118000 in this ratio.
Share of A = 15/59 * 118000 = 30000
Share of B = 20/59 * 118000 = 40000
Share of C = 24/59 * 118000 = 48000
Answer: A
Question: A man and his wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is (1/7) and the probability of wife’s selection is (1/5). What is the probability that only one of them is selected?
A.1/7
B.2/7
C.3/7
D.4/7
Answer: B.2/7
Explanation: P(A)=1/7
P(B)=1/5
P(A’)=6/7
P(B’)4/5
Required probability= P((A and B’) or ( B and A’))
=(1/7x4/5)+(1/5x6/7)
=2/7
ANSWER B 2/7
Question: A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
A.0.002%
B.0.02%
C.0.2%
D.2%
Answer: D.2%
Explanation: In 20 days 20*0.01=0.2 ounces of water evaporated, which is 0.2/10∗100=2 of the original amount of water.
Answer: D.
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 42 degrees. Find the temperature on Friday?
A.34 D
B.40 D
C.38 D
D.50 D
Answer: A.34 D
Explanation: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 â€“ 150 = 34
ANSWER A
Question: The height of a triangle is decreased by 25% and its base increased by 45%. Its area will
A.decrease by 12.5%
B.increase by 8.75%
C.decrease by 25%
D.Increase by 25%
Answer: B.increase by 8.75%
Explanation: Explanation :
Let the initial height be 100 and the base be 200 units.
âˆ´ Area = 1/2 x 100 x 200 = 1000sq units
Now, height = 75 units and base = 290 units
âˆ´ New area = 1/2 x 75 x 290 = 10875
âˆ´ Area is increased by (10875 - 10000)/10000 x 10
= 8.75%
Answer : Option B
Question: If 30% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
A.620
B.630
C.616
D.600
Answer: C.616
Explanation: We know 37.5 % people study biology,therefore the no of people not studying = 100 - 30 = 70%
> Therefore the people not studying biology out of a total 880 people are = 70 % of 880
> (70/100)*880 = 616 people
C
Question: What is the next number in this sequence, 1, 11, 21, 1211, 111221 , 312211 ?
A.1332123
B.1112321
C.2221313
D.1311222
Answer: D.1311222
Explanation: D
Next in sequence is 13112221.
This series describes each number that came before it:
1 [One]
11 [One One]
21 [Two One(s)]
1211 [One Two and One One(s)]
111221 [One One, One Two, and Two One(s)]
312211 [Three One(s), Two Two(s), and One One]
The next number in the series is:
13112221 [One Three, One One, Two Two(s), Two One(s)]
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
A.1988
B.1918
C.1910
D.1900
Answer: D.1900
Explanation: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: D
Question: A certain car can travel 72 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
A.52
B.65
C.117
D.91
Answer: C.117
Explanation: Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters
Time = 5.7 hours
1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile
Speed (km/hour)= D/T = 72 (km*) x 3.9 x 3.8 / 5.7
replace (km*) to miles ; multiply by 1/1.6 mile
Speed (miles/hour)= 72x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour
Ans :C
PS :i felt the factors were easy to cancel out ,so didn't require much rounding off
= 72 x 3.9 x 3.8 / 5.7 x 1.6
= 117 C
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with thrice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day?
A. $015
B. $0.20
C. $0.30
D. $0.40
Answer: C. $0.30
Explanation: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 3 units of water was used to make 4 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 4. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 4.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 4 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.6=4*x --> x=$0.3.
Answer: C.
Question: If 4c + 4/c + 6/c + 6c is an integer, which of the following must also be an integer?
A.10/c
B.10+c/c^2
C.10(c^2 + 1)/c
D.c+15/c^2
Answer: C.10(c^2 + 1)/c
Explanation: If 4c+6/c+4/c+6c is also integer.
i.e. 10(c^2 +1)/c is an integer.
Answer is C
Question: 230,246,271,307,..?..
A.412
B.356
C.518
D.612
Answer: B.356
Explanation: 230. 246. 271. 307 356
--------,-------,--------,-------
4^2 5^2. 6^2. 7^2
answer B
Question: In how many ways 3 Indians and 2 Englishmen can be seated in a row so that they are alternate?
A.11
B.96
C.12
D.18
Answer: C.12
Explanation: number of ways = 3!*2! = 12
Answer is C
Question: A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
A.180/63 days
B.160/13 days
C.180/13 days
D.680/13 days
Answer: C.180/13 days
Explanation: One day work of A and B = 1/12
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/12 + 1/30 + 1/36
2(A + B + C) = 13/90
(A + B + C) = 13/180
Number of days required = 180/13 days.
Answer:C
Question: A retailer bought a machine at a wholesale price of $81 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?
A.81
B.108
C.120
D.135
Answer: B.108
Explanation: My solution: Wholesale Price= 81
Retail Price, be = x
He provides 10 % discount on Retail price= x-10 x/100
This Retail price = 20 % profit on Wholesale price
x-10 x/100 = 81+ 1/5(81)
x=108;
ANSWER:B
Question: The cost of producing x tools by a company is given by
C(x) = 1200 x + 5500 (in $)
a) What is the cost of 100 tools?
A.125500 $
B.125800 $
C.125900 $
D.126500 $
Answer: A.125500 $
Explanation: Solution
C(100) = 1200*100 + 5500 = 125500 $
Answer A
Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
A.3
B.1
C.2
D.4
Answer: C.2
Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
C
Question: Diesel costs Rs.4per lit and petrol costs5.23 per litre.If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take untill a litre of Diesel costs more thatn a litre of petrol.
A.9 months
B.5 months
C.6 months
D.3 months
Answer: D.3 months
Explanation: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324 which is higher than the
price of the petrol!
Answer : D
Question: A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
A.27
B.26
C.29
D.25
Answer: A.27
Explanation: A:B=2:1
AB'S together wrk in 18 days
A;s alone is 1/18*2/3=27 days
ANSWER:A
Question: When a is divided by b, the quotient is c with remainder 2. What is a in terms of 2, b, and c?
A.2c-b
B.2b-c
C.bc+2
D.b-c
Answer: C.bc+2
Explanation: a/b =c with remainder 2
i.e, a-2 = bc
a= bc+2
Answer : C
Question: The price of Maruti car rises by 30 percent while the sales of the car come down by 20%. What is the percentage change in the total revenue?
A.- 4%
B.- 2%
C.+ 4%
D.+2%
Answer: C.+ 4%
Explanation: Solution: Let initial price of Maruti Car be Rs. 100.
As price increases 30%, price of car will become, (100 +30% of 100) = Rs. 130.
Due to increase in price, sales is down by 20%. It means, it is going make 20% less revenue as expected after increment of price.
So, New revenue = (130 - 20% of 130) = Rs. 104.
The initial revenue was Rs. 100 which becomes Rs. 104 at the end. It means there is 4% increment in the total revenue.
Mind Calculation Method:
100==30%↑(price effect)==>130==20%↓(sales effects)==>104.
Hence, 4% rises.
Answer: Option C
Question: Carolyn bought 15 gumballs, Lew bought 12 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought?
A.20
B.22
C.18
D.24
Answer: C.18
Explanation: Smallest gumballs = (19-15) + (19-12) +19= 30
Largest gumballs = (25-15) + (25-12) +25= 48
Difference = 48 - 30 = 18
C
Question: 2/3rd of the boys and 3/4th of the girls of a school participate in a function. If the no.of participating students is 550, out of which 150 are girls, what is the total no.of students in the school?
A.400
B.500
C.800
D.900
Answer: C.800
Explanation: Let total number of boys be x and total number of girls be y. y=400=>x = 600and^= I50=>y = 200 Now, x + y = 800
C
Question: In a business Ram invests Rs.60,000. After 6 months his uncle invests Rs.40,000. After one year they got a profit of Rs.12,000. Then uncle gets his share as
A.Rs.2500
B.Rs.2000
C.Rs.1000
D.Rs.3000
Answer: D.Rs.3000
Explanation: ram=60,000(12months)
uncle=(40000)(6months)
60000*12 : 40000*6
3 : 1
uncle share= (1/3+1)(12000)=3000
ANSWER:D
Question: If y > 0, (2y)/5 + (3y)/10 is what percent of y?
A.40%
B.50%
C.60%
D.70%
Answer: D.70%
Explanation: can be reduced to 2y/5+3y/10 =2y/5=70%
D
Question: The manufacturing cost of a shoe is Rs.200 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
A.s 222
B.s 246
C.s 220
D.s 210
Answer: B.s 246
Explanation: Explanation :
Total cost of a watch = 200 + (500/100) = 205.
Gain = 20% => SP = 1.2CP = 1.2 X 205 = 246
Answer : B
Question: My friend collects antique stamps. she purchased two, but found that she needed to raise money urgently. So she sold them for Rs. 800 each. On one she made 20% and on the other she lost 20%. How much did she gain or lose in the entire transaction?
A.66.66
B.66.69
C.66.68
D.66.67
Answer: A.66.66
Explanation: Explanation:
Selling prices were given. Assume that on the first stamp she made profit and on the second stamp she made loss.
So cost prices of the both stamps = 800120%+80080%800120%+80080% = 1666.66
So She incurred a loss of 66.66 rupees.
Answer: A
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
A.2999
B.3000
C.2777
D.2999
Answer: B.3000
Explanation: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer:B
Question: Look at this series: 90, 88, 86, 84, 82, 80, 78, 76, ... What number should come next?
A.72
B.70
C.77
D.74
Answer: D.74
Explanation: Explanation:
In this series, each number 2 is subtracted to arrive at the next number.
Answer: Option D
Question: The average price of three items of furniture is Rs. 12000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?
A.2379
B.2889
C.9288
D.7200
Answer: D.7200
Explanation: Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (12000 * 3) or x = 2400.
Cost of cheapest item = 3x = Rs. 7200.
Answer: D
Question: The smallest number which when diminished by 6, is divisible by 12, 16, 18, 21 and 28 is
A.1008
B.1014
C.1022
D.1032
Answer: B.1014
Explanation: Required Number = (L.C.M of 12, 16, 18,21,28)+6
= 1008 + 6
= 1014
Answer: B
Question: Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 50 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
A.250
B.300
C.350
D.400
Answer: A.250
Explanation: Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 50 meters, thus second time she runs 2*50 = 100 meters.
Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 100 + 150 = 250 meters.
Answer: A.
Question: The value of x + x(xx) when x = 2 is:
A.10
B.16
C.18
D.36
Answer: A.10
Explanation: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (A)
Question: What will be the remainder when 13^36 is divided by 2196?
A.0
B.1
C.12
D.2195
Answer: B.1
Explanation: In such Qs, best is to get the dividend and divisor in some friendly figures..
13^36=(13^3)^12=2197^12=(2196+1)^12
when (2196+1)^12 is divided by 2196, all terms in the expansion are divisible by 2196 except 1^12, so the remainder will be 1
ANSWER:B
Question: If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1?
A.a. 8
B.b. 9
C.c. 12
D.d. 7
Answer: D.d. 7
Explanation: Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30
We can write 30 as product of two numbers in following ways
1*30
2*15
3*10
5*6
4 cases = 4*2 i.e. 8 factors (including 1)
Factors greater than 1 = 7
Answer: Option D
Question: The average weight of 12 persons is 50 kg. On replacing a man whose weight is 53 kg. with a new man, new average becomes 49 kg. The weight of the new man is:
A.22
B.41
C.37
D.29
Answer: B.41
Explanation: Explanation:
Sum of the weights of all 12 persons = 12 × 50 = 600
Sum of the weights of all 12 persons after replacement = 12 × 49 = 588
The difference is because of one person with 53 kg is replaced by another one. So his weight must be 53 - 12 = 41
AnswerB
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 12. What is the total number of students in the school?
A.72
B.80
C.25
D.150
Answer: C.25
Explanation: Explanation: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 12 + 2/3 of 12
80/100x = 20
x = 25.
Answer: Option C