divelab/Sys2Bench huggingface dataset:
Question: At an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?
Options:
A)239
B)700
C)278
D)260
E)1711
Rationale: Explanation:
Let the total votes are 100x. Then winning candidate got 84x, and losing candidate got 16x.
⇒ 84x – 16 x = 476
⇒ 68 x = 476
⇒ x = 7
Total votes are 700.
Answer: B
Answer: B
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Options:
A)144º
B)150º
C)168º
D)180º
E)190º
Rationale: Angle traced by the hour hand in 6 hours =360/12x 6º= 180º.
Answer: Option D
Answer: D
Question: A cistern which could be filled in 4 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
Options:
A)76 hrs
B)99 hrs
C)55 hrs
D)20/3 hrs
E)11 hrs
Rationale: 1/4 - 1/x = 1/10
=> 20/3 hrs
Answer: D
Answer: D
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1:96
B)1:97
C)1:99
D)1:28
E)1:29
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144
= 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas
= 3x : 12x2 = 1 : 4x
= 1:96.
Answer:A
Answer: A
Question: The average mark obtained by 22 candidates in an examination is 45. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
Options:
A)2
B)0
C)9
D)8
E)6
Rationale: It is clear that 22 x 45 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 0
Answer:B
Answer: B
Question: If the product of the integers a, b, c and d is 770, and if 1 < a< b< c< d, what is the value of a+ d?
Options:
A)10
B)13
C)16
D)18
E)21
Rationale: 770 = 2 * 5 * 7 * 11
So a= 2, x = 5, c= 7, d= 11
a+ d= 2 + 11 = 13
Answer - B
Answer: B
Question: If a2 - b2 =11 and a*b = 5, find a4 + b4.
Options:
A)62
B)181
C)170
D)171
E)50
Rationale: a2 - b2 = 11 : given
a4 + b4 - 2a2b2 = 112 : square both sides and expand.
a*b = 2 : given
a2b2 = 52 : square both sides.
a4 + b4 - 2(25) = 121 : substitute
a4 + b4 = 171
correct answer D
Answer: D
Question: What number should replace the question mark?
16, 23, 19, 22, 15, 25, ?
Options:
A)10
B)18
C)11
D)22
E)26
Rationale: C
11
There are two alternate sequences: +3 and -4.
Answer: C
Question: At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 16.9 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?
Options:
A)13.0
B)13.3
C)13.6
D)13.9
E)14.2
Rationale: Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 16.9
x^2=1.69
x=1.3
At 4:00 pm, the amount of bacteria was 10(1.3)=13 grams.
The answer is A.
Answer: A
Question: In a certain Gun shooting competition prizes were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points . No other points were awarded. John participated several times in the competition. The product of all the points he received was 84700. How many times did he participate in the competition.
Options:
A)7
B)5
C)3
D)2
E)cannot be determined
Rationale: 84700 = 2*2*5*5*7*11*11
If the question stated that John atleast came 4th each time he participated, then we can say that John participated 7 times.
But, it is not stated how many times did John come fifth, sixth, seventh, etc.
Hence, Answer will be E.
Answer: E
Question: If each of 3 digit code is formed of integers from 1 to 25, inclusively, and each of the digits are different, how many possible codes are there?
Options:
A)13600
B)13500
C)13400
D)13800
E)13900
Rationale: Code consists of 3 digits and no digit is repeated.
First digit of the code can have 25 possibilities
Second digit can have 24 possibilities
Third digit can have 23 possibilities
Total number of possible codes = 25*24*23 = 13800
Answer: D
Answer: D
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)3
B)4
C)5
D)2
E)7
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: Option D
Answer: D
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 twice 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 $0.82 per glass on the first day, what was the price per glass on the second day?
Options:
A) $015
B) $0.20
C) $0.30
D) $0.40
E) $0.55
Rationale: 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 2 units of water was used to make 3 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 3. 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 3.
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 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.82=3*x --> x=$0.55.
Answer: E.
Answer: E
Question: A car starts 2/5 of a mile behind a bus that is traveling at 60 miles per hour. If the car catches up to the bus after 2 minutes, how many miles does the car travel in that time?
Options:
A)2 1/10
B)2 2/5
C)2 1/2
D)2 7/8
E)3
Rationale: Car is travelling at a speed of 2/5 miles per 2 mins faster than the bus
i.e 12 mph faster than the buse
= 72 mph
So in 2 mins = 72 * 2/60 = 2.4
Answer is B.
Answer: B
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)28 seconds
B)27 seconds
C)40 seconds
D)128 seconds
E)18 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: C
Question: Find the odd man out
74, 24, 82, 61, 10, 4
Options:
A)61
B)24
C)10
D)82
E)74
Rationale: 61 is the only odd number in the series.
ANSWER:A
Answer: A
Question: Tracey sold her house for 40 percent more than the amount that she bought it for. If she has to pay a brokerage fee of 5 percent of the selling price of the home, and then has to pay 40 percent of the leftover profit in taxes, what is the net after-tax percent profit Tracey makes on the sale?
Options:
A)12%
B)14.4%
C)16%
D)19.8%
E)21%
Rationale: Lets assume Cost price is 100. Then the selling price will be 1.4*100= 140.
5% brokerage fee= 5% of 140 = 7
After brokerage amount left is 140-7=133.
Next, taxes are 40% of left over profit which is 40% of (133-100)=40% of 33 which is 19.8.
Hence answer is D.
Answer: D
Question: If the ratio of the roots of the equation 16x2+px-32=0 is equal to that of the roots 8x2+rx-16=0, then:
Options:
A)2r=p
B)r=p
C)2p=r
D)3p=2r
E)None
Rationale: 16x2+px-32=0 for this eqn... roots are R1=-p/16 R2=2
8x2+rx-16=0 for this eqn... roots are R3=-r/8 R4=2
As per Question, p/-32=r/-16
=> 2r=p
ANSWER:A
Answer: A
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150m
B)170m
C)180m
D)158m
E)350m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: There are 13 hearts in a full deck of 52 cards. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws it took before the person picked a heart and, thereby, won. What is the probability that one will pick the first heart on the third draw or later?
Options:
A)1/2
B)9/16
C)11/16
D)13/16
E)15/16
Rationale: Here, we're told that 13 of the 52 cards are "hearts" - this is 1/4 of the deck. We're also told that after drawing a card, the card is PUT BACK in to the deck (so there will always be 52 cards to draw from).
To draw a heart for the first time on the 3rd draw (or later), the FIRST TWO draws MUST NOT be hearts....
Probability of NOT drawing a heart on the first draw = 3/4
Probability of NOT drawing a heart on the second draw = 3/4
(3/4)(3/4) = 9/16
From this point, you will eventually draw a heart (which is what the question is asking for), so the probability is 9/16.
ANSWER:B
Answer: B
Question: The value of {(.87)3 + (.13)3 + .87 × .39}0.5 is:
Options:
A)0.6
B)1
C)0
D)3
E)4
Rationale: (a^3 + b^3)=(a+b)(a^2-ab+b^2)
so, (a^2-ab+3ab+b^2) ^0.5 , here a+b=1
(0.87+0.13)^2*0.5
=1
ANSWER:B
Answer: B
Question: The difference between simple and compound interests on a certain sum for 2 years at 4% per annum is Rs.50. The sum is
Options:
A)Rs.20,400
B)Rs.25,000
C)Rs.31,250
D)Rs.38,000
E)Rs.48,000
Rationale: difference between 2yr CI and SI is given by PR^2 ..
PR^2= 50
P*R/100*R/100=50
P*4/100*4/100 =50
P=(50*100*100)/4*4
P= 31,250
ANSWER:C
Answer: C
Question: The sum of two consecutive even integers is 26. What are the two numbers?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: Solution
Let 2n be the first even integer and let 2n + 2 be the second integer
2n + 2n + 2 = 26
4n + 2 = 26
4n + 2 - 2 = 26 - 2
4n = 24
n = 6
So the first even integer is 2n = 2 × 6 = 12 and the second is 12 + 2 = 14
Answer A
Answer: A
Question: How many batteries will remain unboxed if in a factory that manufactures batteries 2 types of boxes are used to store batteries. the bigger box can store 25 batteries while the smaller box can store 18 batteries. The total number of batteries to be stored is 217.
Options:
A)0
B)1
C)2
D)7
E)5
Rationale: Total batteries to be stored 218
The big box can store 25
small box can store 18
storing 217 batteries in big box 218/25 =8 r 18
store remainder in small box 18/18=1 r 0
least number of batteries that will be left unboxed=0
Answer: A
Answer: A
Question: A packet of 10 electronic components is known to include 3 defectives. If 4 components are randomly chosen and tested, what is the probability of finding among them not more than one defective component.
Options:
A)0.6517
B)0.868
C)0.4483
D)None of these
E)Cannot be determined
Rationale: Explanation :
Here, the trials are independent , since the probability of defective component in any trial is not affected by the occurrence or non-occurrence of a defective component in any other trial. So, it is a case of binomial distribution.
No. of trials = n = 4.
Occurrence of a defective component is a success.
Then, the probability of success = p = 3/10.
the probability of failure = 1- p = 7/10.
Components not more than one defective one means x ≤ 1 i.e x = 0.
Using the formula,
P(x) = ncxPx(1-P)n-x.
Since,
=> P(x ≤ 1) = P(x = 0) or P(x = 1)
= P(0) + P(1) .
= 4c0(3/10)0 x (7/10)4 + 4c1(3/10)1x (7/10)3 .
= (7/10)4 + 4 x (3/10) x (7/10)3.
= 0.6517
Hence, the required probability is 0.6517.
Answer : A
Answer: A
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 22 years(the child was born during the interval). What is the present age of the child?
Options:
A)6
B)5
C)10
D)4
E)2
Rationale: 28 * 2 = 56
22 * 3 = 66
-----------
10 years.Answer: C
Answer: C
Question: The area of a parallelogram is 200sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)8
B)9
C)7
D)10
E)5
Rationale: 2x * x = 200 => x= 10
Answer: D
Answer: D
Question: The sum of three integers is 19. The largest integer is 3 times the middle integer, and the smallest integer is 9 less than the largest integer. What is the product of the three integers?
Options:
A)132
B)144
C)156
D)168
E)180
Rationale: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 9.
3x - 9 + x + 3x = 19
x = 4
The three integers are 3, 4, and 12.
The product is 3*4*12 = 144
The answer is B.
Answer: B
Question: Which is the smallest fraction:
Options:
A)11/13
B)9/11
C)5/4
D)5/7
E)6/7
Rationale: 11/13=.846
9/11=.818
5/4=1.25
5/7=.714
So smallest is 5/7
ANSWER:D
Answer: D
Question: What is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5v2 cm?
Options:
A)20v2
B)10
C)10v2
D)20
E)25
Rationale: SOLUTION : 10v2
Area of square = 1/2 * (length of diagonal)2
Area of square 1 = * (5v2)2 = 25
Area of square 2 = 4*25 = 100
Length of diagonal of square 2 = v2 * area = v2 * 100 = v200 = 10v2 cm
ANSWER IS C
Answer: C
Question: The largest four digit number which is a perfect cube, is:
Options:
A)7000
B)8000
C)9261
D)9999
E)None of these
Rationale: Explanation:
21*21*21 = 9261
Option C
Answer: C
Question: A large box contains 15 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
Options:
A)A)220
B)B)490
C)C)375
D)D)450
E)E)690
Rationale: the only thing you have to do is a simple multiply
we have:
15*25
=375
correct answer is:
C) 375
Answer: C
Question: A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 10% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
Options:
A)A)266666.7
B)B)562000
C)C)800000
D)D)500000
E)E)652000
Rationale: 3 children got = 3*15% = 45%
wife got = 30%
orphan house = 10%
total = 45+30+10 = 85%
remaining = 100-85 = 15%
15% = 40000
100% = 40000*100/15 = $266666.7
Answer is A
Answer: A
Question: In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 100 more than the correct answer. Find the number.
Options:
A)192
B)280
C)384
D)400
E)500
Rationale: Explanation:
Let the number be x.
5*x/6 = 5*x/16 + 100
25*x/48 = 100
x = 192
ANSWER A
Answer: A
Question: One day Eesha started 30 min late from home and reached her office 50 min late while driving 25% slower than her usual speed. How much time in min does eesha usually take to reach her office from home?
Options:
A)22
B)60
C)99
D)17
E)18
Rationale: We know that Speed is inversely proportional to time
While she drives 25% slower means she drove at 3434(S)
We know that D = S x T
When speed became 3434(S) then Time taken should be 4343(T)
i.e, She has taken 4343(T) - T extra to cover the distance.
Extra Time = T3T3 = 20 min (as 20 min late due to slow driving)
Actual time T = 60 Minutes
Answer:B
Answer: B
Question: A dealer originally bought 70 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
Options:
A)3q/140
B)3q/2
C)105q
D)q/70
E)105/q
Rationale: The cost of each battery was q/70.
Each battery was sold for 1.5q/70 = 3q/140.
The answer is A.
Answer: A
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/18
B)30/29
C)30/12
D)30/13
E)30/82
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26
= 30/13 hours.
Answer:D
Answer: D
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 5 days and left the job. how many days does X alone need to finish the remaining work?
Options:
A)12
B)5
C)6
D)8
E)9
Rationale: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 5 days = 5/15 = 1/3
Remaining work = 1 – 1/3 = 2/3
Number of days in which X can finish the remaining work = (2/3) / (1/18) = 12
A
Answer: A
Question: A tank can supply water to a village for 30 days. If a leak at the bottom of the tank drains out 15 liters per day, the supply lasts for 20 days only. For how many days will the supply last if the leak drains out 20 liters per day?
Options:
A)12
B)14
C)15
D)16
E)18
Rationale: Losing 15 liters per day results in a loss of 300 liters in 20 days. So, those 300 liters were for 10 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*30 = 900 liters.
Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 900/50 = 18 days.
The answer is E.
Answer: E
Question: If the least common addition of two prime numbers x and y is 10, where x > y, then the value of 2x + y is
Options:
A)7
B)9
C)14
D)17
E)21
Rationale: (x+y) = 10 and both x an y are prime.
The only values of x and y can be 7 and 3 (x = 7 and y = 3)
2x + y = 2*7 + 3 = 17
Correct Option: D
Answer: D
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 15 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)76 km/hr
B)66 km/hr
C)60 km/hr
D)67 km/hr
E)32 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/15 = 3x => x = 40/9.
So, speed of the faster train = 80/9 = 80/9 * 18/5 = 32 km/hr.
Answer:E
Answer: E
Question: The area of the floor of a class room is 10 m2 that of a longer wall 15 m2 and of the shorter wall 6 m2, find the edge of the new cube?
Options:
A)50 m3
B)30 m2
C)60 m3
D)40 m3
E)900 m3
Rationale: lb = 10 ; lh = 15 ; fh = 6
(lbh)2 = 10 * 15 * 6 => lbh = 30 m3
ANSWER:B
Answer: B
Question: If x is an integer and 1 ≤ x ≤ 100, what is the probability that x(x + 1) is a multiple of 12 and 9?
Options:
A)1/25
B)1/20
C)2/25
D)11/100
E)1
Rationale: x(x+1) is a number that is divisible by both 12 and 9
for x = 27, 71,72, 80 we get number ie divisible by both 12 and 9
so probability would be 4/100 = 1/25
ANSWER:A
Answer: A
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 3 years ago ? (RBI Assistant 2015)
Options:
A)24
B)20
C)12
D)15
E)18
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 3 years ago = 21 - 3 = 18 years
answer :E
Answer: E
Question: If log4 (x) = 12 , then log2 (x/4) is equal to what?
Options:
A)55
B)21
C)31
D)11
E)22
Rationale: Explanation:
log(4) x = 12. We need to find log(2) (x/4)
log(2) (x/4) = log (2) x - log(2) 4
=> log(2) x - log(2) 2^2
use log a^b = a*log b
=> log(2) x - 2 ...(1)
log(4) x = 12
=> x = 4^12
=> x = 2^2^12
=> x = 2^24
take log to base 2 of both the sides
=> log(2) x = 24
Substituting in (1)
log(2) x - 2
=> 24 - 2
=> 22
The required value of log(2)(x/4) = 22
Answer E
Answer: E
Question: 100 identical coins each with probability 'pp' showingup heads & tossed. If 0
Options:
A)21/311
B)23/321
C)51/101
D)55/413
E)47/321
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: C
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 272 runs?
Options:
A)6
B)6.25
C)7.25
D)7.5
E)8
Rationale: Required run rate = 272 - (3.2 x 10) =	240 = 6
40	40
A
Answer: A
Question: When 15 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
Options:
A)20
B)24
C)36
D)48
E)45
Rationale: Explanation:
Let the number be x. Then,
x - 15 = 7x/12 => x - 7x/12 = 15
5x/12 = 15 => x = 36
Answer: Option C
Answer: C
Question: From the integer n, if n*n*n is odd, then what is true from below options?
Options:
A)n is odd and n*n is even
B)n*n is even
C)n is odd
D)n is even
E)n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: A
Question: 860% of 50 + 50% of 860 =?
Options:
A)430
B)516
C)660
D)860
E)None
Rationale: Solution
Given expression
= [860 / 100 x 50 + 50 / 100 x 860]
= 430 + 430
= 860.
Answer D
Answer: D
Question: The sum of first 45 natural numbers is:
Options:
A)1035
B)1038
C)1040
D)1045
E)1050
Rationale: Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.
Sn = n [2a + (n - 1)d] = 45 x [2 x 1 + (45 - 1) x 1] = 45 x 46 = (45 x 23)
2 2 2
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035.
Shorcut Method:
Sn = n(n + 1) = 45(45 + 1) = 1035.
2 2
A
Answer: A
Question: Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
Options:
A)60
B)150
C)1800
D)700
E)7,500
Rationale: I'd use backsolving for this question.
Check C:
1800 lenses = 900 usable lenses = 450 tubes = 450 eyepieces. We CAN buy 450 tubes and 450 eyepieces, so that not to have leftovers.
Answer: C.
Answer: C
Question: The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is
Options:
A)A)2.4%
B)B)2.6%
C)C)2.0%
D)D)0.3%
E)E)1.3%
Rationale: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350
R1 - R2 = 0.3%
Answer:D
Answer: D
Question: A restaurant meal cost $40 and there was no tax. If the tip was more than 12 percent but less than 13 percent of the cost of the meal, then the total amount paid must have been between
Options:
A)$40 and $42
B)$39 and $41
C)$38 and $40
D)$44 and $45
E)$36 and $37
Rationale: The total amount for the meal was between 40*1.12=44.8 and 40*1.13=~45.2. Only option which covers all possible values of the meal is D.
Answer: D.
Answer: D
Question: A meal cost $ 35.50 adn there was no tax. If the tip was more than 15 pc but less than 25pc of the price, then the total amount paid should be:
Options:
A)41-44
B)39-41
C)38-40
D)37-39
E)36-37
Rationale: 15%(35.5) = 5.325
25%(35.5) = 8.875
total amount could have been 35.5+5.325 and 35.5+8.875
=> could have been between 40.825 and 44.375
=> approximately between 41 and 44
Answer is A.
Answer: A
Question: One half of a two digit number exceeds its one third by 4. What is the sum of the digits of the number?
Options:
A)6
B)9
C)11
D)12
E)15
Rationale: Explanation:
x/2 – x/3 = 4 => x =24
2 + 4 =6
A
Answer: A
Question: It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If seven beavers start to build the same dam at noon, and one beaver per hour is added beginning at 6:00 PM, at what time will the dam be complete?
Options:
A)7:24 PM
B)7:48 PM
C)8:06 PM
D)8:32 PM
E)9:12 PM
Rationale: The rate of 1 beaver is 1/60.
The amount of work done by 7 beavers in 6 hours is 7/60 *6 = 42/60
In the next hour, 8 beavers do 8/60 for a total of 50/60.
In the next hour, 9 beavers do 9/60 for a total of 59/60.
In the next 6 minutes, 10 beavers do 10/60 * 6/60 = 1/60 for a total of 60/60.
The dam will be completed at 8:06 pm.
The answer is C.
Answer: C