divelab/Sys2Bench huggingface dataset:
Question: Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 80% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
Options:
A)1 to 4
B)1 to 3
C)3 to 5
D)3 to 4
E)2 to 2
Rationale: Correct Answer: E
Solution: E. We know that when Pam and Stanley were both working, the ratio was 4 boxes by Pam to 1 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 4 to 2. Answer E is correct.
Answer: E
Question: Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $4.89 on lunch. What was her average daily cost?
Options:
A)a. $3.19
B)b. $3.75
C)c. $3.48
D)d. $4.08
E)e. $4.23
Rationale: On Monday and Thursday, she spent $5.43total.
On Tuesday and Wednesday, she spent $3.54on each day.
On Friday, she spent $4.89 on lunch.
The average = (5.43 + 2*3.54 + 4.89)/5 = 4.08.
Answer: C.
Answer: C
Question: The volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate R, in cubic meters per minutes, at which the water is flowing into the swimming pool?
Options:
A)0.125
B)0.25
C)0.5
D)0.75
E)Not enough information to determine the rate
Rationale: The correct answer is E.
There are not enough info to answer the question.
A 840 cubic meters rectangle is built from: height*length*width.
From the question we know the volume of the pool and the filling rate.
A pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = E
Answer: E
Question: The ratio of investments of two partners A and B is 7:5 and the ratio of their profits is 7:10. If A invested the money for 5 months, find for how much time did B invest the money ?
Options:
A)11 months
B)9 months
C)7 months
D)10 months
E)12 months
Rationale: Explanation:
7x5: 5xk = 7:10
k = 10 months
ANSWER IS D
Answer: D
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
Options:
A) 0.33
B) 0.44
C) 33
D) 44
E) 55
Rationale: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;
A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents.
Answer: C.
Answer: C
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
Options:
A)22
B)88
C)12
D)73
E)29
Rationale: Explanation:
S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
S.I. for 5 years = Rs. = Rs.3675
Principle = Rs.(9800-3675) = Rs.6125
Hence, Rate = =12%
Answer: C) 12%
Answer: C
Question: At a dinner party 3 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
Options:
A)2
B)10
C)24
D)32
E)120
Rationale: Hi there,
You can treat this as an ordering question except thatfor a circular arrangement you need to divide by the number of spaces.So in this case:
3!/3=2
If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.
Happy Studies,
HG.
A
Answer: A
Question: Find the lowest common multiple of 24, 36 and 42.
Options:
A)360
B)504
C)510
D)320
E)280
Rationale: LCM=2*2*2*3*3*7=504.
Answer is B
Answer: B
Question: Ray writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the sum of the digits of the number.
Options:
A)2
B)8
C)9
D)3
E)5
Rationale: Let the two digit number be xy.
4(x + y) +3 = 10x + y - - - (1)
10x + y + 18 = 10 y + x - - - (2)
Solving 1st equation,
4x + 4y + 3 = 10x + y
3y + 3 = 6x
6x – 3y = 3
Therefore, 2x – y = 1 - - - (3)
Solving 2nd equation,
xy + 18 = yx
⇒⇒ (10x + b) + 18 = 10y + x
⇒⇒ 18 = 9y – 9x
⇒⇒ 2 = y – x
we get y - x = 2 - - - (4)
adding 3 and 4, we get x = 3
By substituting in (4), we get y = 5
So the given number is 35. Sum of the digits = 8.
Answer:B
Answer: B
Question: 25% of 30% of 45% is equal to?
Options:
A)0.03375
B)0.3375
C)3.375
D)33.75
E)44.25
Rationale: Answer: Option A
(25/100) * (30/100) * (45/100)
1/4 * 3/10 * 9/20
27/800 = 0.03375
Answer: A
Question: In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:
A)5 : 6
B)3 : 4
C)7 : 8
D)8 : 9
E)None of these
Rationale: Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
ANSWER IS A
Answer: A
Question: A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent?
Options:
A)34 %
B)39 %
C)50 %
D)35 %
E)33 %
Rationale: The total number of mangoes bought by the shopkeeper be 24.
If he buys 6 a rupee, his CP = 4
He selling at 4 a rupee, his SP = 6
Profit = SP - CP = 6 - 4 = 2
Profit Percent = 2/4 * 100 = 50 %
Answer:C
Answer: C
Question: A boat running up stram takes 6 hours to cover a certain distance, while it takes 10 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
Options:
A)2 : 3
B)5 : 6
C)4 : 1
D)7 : 1
E)8 : 1
Rationale: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
6(x+y) = 10(x-y)
6x+6y = 10x-10y
16y = 4x
4y = x
x/y = 4/1
4 : 1
Answer: Option C
Answer: C
Question: A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 124 in his diary to remember his PIN. He also wrote out the way to calculate 124 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 124".
Once, Prafull saw his diary in which Pinaki wrote this number 124. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
Options:
A)874
B)875
C)876
D)877
E)873
Rationale: Explanation :
Let, the PIN is x.
According to the question,
The card number =996 and Remainder =124.
Thus, (996 × x)/997=124.
=>x= 873.
Answer : E
Answer: E
Question: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction K of time taken by the two wide pipes working together to fill the tank?
Options:
A) 1/2
B) 2/3
C) 3/4
D) 3/7
E) 4/7
Rationale: I always plug in for these questions.. I find them easier
Let 2 large pipes each work fill 10lts/hr
small ones = 1/2*10 = 5
total 5 = 10+10+5+5+5 = 35 lts/hrs
now assume the total capacity = 140 lts ( LCM of 20,35)
Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank
all working together will take 140/35 = 4 hrs
two large pipes working will take 140/20 = 7 hrs
hence ratio K= 4/7 = E
Answer: E
Question: A box measuring 36 inches long by 45 inches wide by 18 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
Options:
A)32
B)34
C)38
D)40
E)42
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
9 is the biggest number that could divide all three, 36, 45 and 18.
Thus side of cube must be 9, and total number of cubes = 36/9 * 45/9*18/9 =40
Ans D.
Answer: D
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
Options:
A)387
B)400
C)776
D)268
E)181
Rationale: 441 = P(21/20)2
P = 400
Answer:B
Answer: B
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
Options:
A)1/127
B)1/183
C)1/126
D)1/122
E)1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄ = 1/126
Answer: E
Answer: E
Question: If a, b, y are integers, 33 = aby, and a < b < y, what is the smallest possible value of a?
Options:
A)-33
B)-3
C)1
D)3
E)11
Rationale: Given : a * b * y = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.
Correct answer is A
Answer: A
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
Options:
A)15 sec
B)19 sec
C)12 sec
D)10 sec
E)11 sec
Rationale: Explanation:
D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: Option C
Answer: C
Question: A certain team has 8 members, including Joey. A three-member relay team will be selected as follows: one of the 8 members is to be chosen at random to run first, one of the remaining 7 members is to be chosen at random to run second, and one of the remaining 6 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
Options:
A)1/1320
B)1/132
C)1/110
D)1/12
E)1/4
Rationale: Total outcomes= 8*7*6
Favorable Outcomes= 7*1*6 and 7*6*1
P=2*7*6*1/8*7*6
P=1/4
Ans E
Answer: E
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is?
Options:
A)54
B)77
C)36
D)88
E)21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/8 => x = 15
Speed of each train = 15 m/sec.
= 15 * 18/5 =- 54 km/hr.Answer: A
Answer: A
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire?
Options:
A)7 meters
B)9 meters
C)8 meters
D)5 meters
E)3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 168,000 m : C is the circumference
C = 3 meters
correct answer A
Answer: A
Question: Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $105 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?
Options:
A)$2400
B)$3200
C)$3500
D)$6400
E)$9600
Rationale: let x be the monthly salary
15%of 1/5*x=105
x=3500
answer C
Answer: C
Question: 75 persons Major in physics, 83 major in chemistry, 10 not at major in these subjects u want to find number of students majoring in both subjects
Options:
A)65
B)66
C)67
D)68
E)69
Rationale: Consider the number of total students = n(T) = 100
number of persons Major in physics = n(P) = 75
number of persons Major in chemistry = n(C) = 83
According to the question ;
10 not at major in these subjects = n(P'∩ C') = 10
n(P'∩ C') = n(P U C)' = 10
n(P U C)' = n(T) - n(P U C)
10 = 100 - n(P U C)
n(P U C) = 90
n(P U C) = n(P) + n(C) - n(P ∩ C)
90 = 75 + 83 - n(P ∩ C)
n(P ∩ C) = 158 - 90
n(P ∩ C) = 68
number of students majoring in both subjects WILL be 68
ANSWER:D
Answer: D
Question: A man, his wife and daughter worked in a graden. The man worked for 3 days, his wife for 2 days and daughter for 4 days. The ratio of daily wages for man to women is 5 : 4 and the ratio for man to daughter is 5 : 3. If their total earnings is mounted to Rs. 105, then find the daily wage of the daughter.
Options:
A)Rs. 15
B)Rs. 12
C)Rs. 10
D)Rs. 9
E)NONE OF THE ABOVE
Rationale: EXPLANATION:
Assume that the daily wages of man, women and daughter are Rs 5x, Rs. 4x, Rs 3x respectively.
Multiply (no. of days) with (assumed daily wage) of each person to calculate the value of x.
[3 x (5x)] + [2 x (4x)] + [4 x (3x)] = 105
[15x + 8x + 12x] = 105
35x = 105
x = 3
Hence, man's daily wage = 5x = 5 x 3 = Rs. 15
Wife's daily wage = 4x = 4 x 3 = Rs. 12
Daughter's daily wage = 3x = 3 x 3 = Rs. 9
ANSWER IS D
Answer: D
Question: Of the 160 people at a party, 70 were women, and 50 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Total people at party=160
Women=70
so Men 160-70=90
No. of pple who tried appetizer=160-50 (given info)=110
No of women who tried appetizer=50
So Remaining ppl(men) who tried the appetizer =110-50=60
Correct Option C
Answer: C
Question: One pipe can fill a pool 1.5 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?
Options:
A)11.25
B)11.52
C)12.5
D)9
E)7.2
Rationale: Say the rate of the slower pipe is R pool/hour, then the rate of the faster pipe would be 1.5R=3R/2. Since when both pipes are opened, they fill the pool in five hours, then their combined rate is 1/5 pool/hour.
Thus we have that R + 3R/2 = 1/5 --> R = 2/25 pool/hour --> time is reciprocal of rate thus it's 25/2 =12.5 hours.
Answer: C.
Answer: C
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options:
A)49 m2
B)50 m2
C)53.5 m2
D)55 m2
E)58
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2.
Answer: Option A
Answer: A
Question: Find the ratio between 1hr 30 minutes and 2hrs 40 minutes.
Options:
A)9:16
B)5:9
C)12:17
D)13:24
E)None of these
Rationale: Solution: The ratio = 1hr 30 min : 2hr 40 min. 90 min : 160 min = 9 : 16.
ANSWER IS A
Answer: A
Question: A man can row upstream at 25 kmph and downstream at 31 kmph, and then find the speed of the man in still water?
Options:
A)22
B)28
C)30
D)27
E)18
Rationale: US = 25
DS = 31
M = (31 + 25)/2 = 28
Answer:B
Answer: B
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)187 m
B)279 m
C)245 m
D)279 m
E)222 m
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: C
Answer: C
Question: A, B AND C TOGETHER EARN RS. 300 PER DAY WHILE A AND C TOGETHER EARN RS. 188 AND B AND C TOGETHER EARN RS. 152. THE DAILY EARNING OF C IS:
Options:
A)RS. 40
B)RS. 68
C)RS. 112
D)RS. 150
E)NONE OF THESE
Rationale: B'S DAILY EARNING = RS. (300-188)=RS. 112
A'S DAILY EARNING = RS. (300=152)-RS. 148.
C'S DAILY EARNING = RS. (300-(112+148))=RS. 40
CORRECT OPTION: A
Answer: A
Question: A rectangular field has a length 10 meters more than it is width. If the area of the field is 119, what is the length (in meters) of the rectangular field?
Options:
A)13
B)15
C)17
D)19
E)21
Rationale: area = l * w = (L) * (L-10) = 171
trial and error:
20*10 = 200 (too high)
19*9 = 171 (too high)
18*8 = 144 (too high)
17*7 = 119
The length is 17 meters.
The answer is C.
Answer: C
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)3452
B)2343
C)2435
D)2578
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 80 square feet of cloth remain, what was the length of a side of the original piece of cloth?
Options:
A)16
B)18
C)20
D)24
E)32
Rationale: Let the original side of the square be x.
(x-12)*(x-10) = 80 = 8*10
x = 20
The answer is C.
Answer: C
Question: How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 28%?
Options:
A)100 ml
B)60 ml
C)120 ml
D)140 ml
E)150 ml
Rationale: we can also go by answer choices
Tke 100 ml for eg
400 (old)+100 (new concentr)ml
500*28/100 = 140 ml (40ml is de old concentration +100 ml (newly added)
Answer D
Answer: D
Question: The ratio of the ages of three people is 4:6:7. Six years ago, the sum of their ages was 50. Find their present ages.
Options:
A)12,18,21
B)16,24,28
C)20,30,35
D)24,36,42
E)28,42,49
Rationale: Let the present ages be 4x, 6x, 7x.
(4x-6) + (6x-6) + (7x-6) = 50
17x = 68
x = 4
Their present ages are 16, 24, and 28.
The answer is B.
Answer: B
Question: The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1800 in revenue from the sales. How many orchestra tickets did they sell?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Let x be the number of orchestra tickets.
Then 90-x is the number of upper tier tickets.
30x + 12(90-x) = 1800
18x = 1800-1080
x = 40
The answer is C.
Answer: C
Question: what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition
Options:
A)2599980
B)2699980
C)2799980
D)2509980
E)2499980
Rationale: There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum.
i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) }
so,here by putting the values as,
(0+1+2+3+4){(5-1)!*(11111)-(5-2)!*1111}
= 10{(4!*11111)-(3!*1111)}
= 10{266664-6666}
= 2599980
ANSWER:A
Answer: A
Question: A merchant sold two items for Rs.1700 each, and makes a profit of 25% from the first item and a loss of 20% from the second item. calculate the total gain or loss.
Options:
A)7
B)5
C)3
D)6
E)4
Rationale: (25*20)/100 = 5%loss
Answer: B
Answer: B
Question: I have only 1$ and 2$ note. I want to give 95$ to John. How many maximum number of 2$ note I need?
Options:
A)39
B)95
C)47
D)55
E)76
Rationale: Check whether 95 is divisible by 2 then that is maximum no of 2$ note
else check next maximum term before 95
so 94/2=47
ans is C
Answer: C
Question: An amount of money is to be divided among P, Q and R in the ratio of 4 : 9 : 16. If R gets 4 times more than P, what is Q’s share in it?
Options:
A)1,800
B)2,700
C)3,600
D)Data inadequate
E)None of these
Rationale: Here, neither the total amount nor the individual amount is given. So the share of Q cannot be determined.
Answer D
Answer: D
Question: If x is an integer and y = 3x + 7, which of the following CANNOT be a divisor of y?
Options:
A)4
B)5
C)7
D)9
E)8
Rationale: For any value of x, the expression 3x + 2 would never be divisible by 3,6,9...... onwards
So answer = 6 = D
Answer: D
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 25 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
Options:
A)10%
B)12%
C)15%
D)17%
E)33%
Rationale: Lets assume that candidate got 25% votes and total votes is 100.
Candidate won = 25
Remaining = 75
To get 50%, candidate requires 25 votes from 100 which is 25% and 25 votes from 75.
25/75 = 33.33%
Which is approx 33%. Hence the answer is E
Answer: E
Question: Addison High School’s senior class has 200 boys and 160 girls. If 60% of the boys and 75% of the girls attended college, what percentage of the total class that did not attend college?
Options:
A)33.33
B)60
C)80
D)66.67
E)64
Rationale: Number of boys attending the college: 0.60*200 = 120
number of girls attending the college: 0.75*160 = 120
Total attending = 120+120 = 240
Total people = 200+160 = 360
% of people attending = 240/360 = 66.67%. D is the correct answer
Answer: D
Question: How many seconds will a 500 metre long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
Options:
A)30
B)40
C)50
D)20
E)15
Rationale: Dist = 500 m
relative speed = (63-3) = 60 km/hr
60*5/18 = 50/3 m/s
time taken = 500/(50/3) = 30 sec
ANSWER A
Answer: A
Question: Two trains, one from Hyderabd to Bangalore and the other from Bangalore to Hyderabad, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is ?
Options:
A)2 : 3
B)3 : 2
C)3: 4
D)1 : 2
E)4 : 3
Rationale: Let us name the trains as A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
Answer : E
Answer: E
Question: If n^2 = m^2, which of the following must be true?
Options:
A)n = m
B)n = -m
C)n = |m|
D)|n| = |m|
E)n = -|m|
Rationale: Solution:
We are given that n^2 = m^2, and we can start by simplifying the equation by taking the square root of both sides.
√n^2 = √m^2
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
√n^2 = √m^2 is |n| = |m|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: D
Answer: D
Question: If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10?
Options:
A)7
B)2
C)4
D)6
E)8
Rationale: This one took me bout 3 1/2 min. Just testin numbers and what not.
First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.
1-7 stands for ^1 thru 6
1: 7*1=7
2: 7*7=9
3: 7*9=3
4: 7*3=1
5: 7*1=7
6: 7*7=9
7: 7*9=3
Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.
so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8
Now from here if id double check just to make sure.
7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit).
Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern)
so again 3*6=18/10 ---> R =7.
A or J in this problem.
Answer: A
Question: An amount of Rs. 55000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
Options:
A)s. 52500; Rs. 47500
B)s. 34375; Rs. 20625
C)s. 72500; Rs. 27500
D)s. 82500; Rs. 17500
E)s. 72500; Rs. 17500
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (55000 - x). Then,
(x * 9 * 1)/100 + [(55000 - x) * 11 * 1]/100 = (55000 * 39/4 * 1/100)
(9x + 605000 - 11x)/100 = 39000/4 = 10725/2
x =34375
Sum invested at 9% = Rs. 34375
Sum invested at 11% = Rs. (55000 - 34375) = Rs. 20625
ANSWER:B
Answer: B
Question: The greatest number of four digits which is divisible by 10, 13, 40 and 60 is:
Options:
A)9200
B)9300
C)9400
D)7800
E)8700
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10, 13, 40 and 60 is 600.
On dividing 9999 by 7800, the remainder is 2199.
Required number (9999 - 2199) = 7800.
ANSWER :D
Answer: D