divelab/Sys2Bench huggingface dataset:
Question: A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $50, how many pounds of premium chocolates are in the box?
Options:
A)[A] 1
B)[B] 2
C)[C] 3
D)[D] 4
E)[E] 5
Rationale: This question is a bit of Special equations with a single set of unique values.
the Equation stands : 5X + 4Y =50
Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4
31 - 5 = 26 -> Not divisible by 4
31 - 10 = 21 -> Not divisible by 4
31 - 15 =16 -> Divisible by 4
31 - 20 =11 -> Not divisible by 4
31 - 25 =6 -> Not divisible by 4
31 - 30 =1 -> Not divisible by 4
Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible
Thus Amount spent on regular chocolate= $16
Amount spent on Premium chocolate= $15
Price per premium chocolate = $5
No. Of boxes of premium chocolate bought = 25 / 5 = 5
Correct Option : E
Answer: E
Question: A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other half
Options:
A)15 mins
B)20 mins
C)25 mins
D)30 mins
E)None of these
Rationale: Explanation:
Let the total time be x mins.
Part filled in first half means in x/2 = 1/40
Part filled in second half means in x/2 =
1/60+1/40=1/24
Total = x/2∗1/40+x/2∗1/24=1
=>x/2(1/40+1/24)=1
=>x/2∗1/15=1
=>x=30mins
Option D
Answer: D
Question: Find the number of zeros in the product 5 x 10 x 25 x 40 x 50 x 55 x 65 x 125 x 80
Options:
A)8
B)9
C)12
D)13
E)16
Rationale: Explanation :
From the question understand whether number of 2's are more or number of 5's are more...count the lesser one only...the number of zero will be equal to that as they will be responsible in creating zeros by being multiplied by 5
Answer : B
Answer: B
Question: By selling a bat for Rs.810/- a man loses 10% what is that bat cost price
Options:
A)s.600/-
B)s.630/-
C)s.700/-
D)s.780/-
E)s.900/-
Rationale: 90 % ------> 810 (90 * 9 = 810)
100 % ------>900 (100 * 9 = 900)
Cost price = Rs.900/-
E)
Answer: E
Question: How many 7 in between 1 to 110?
Options:
A)18
B)21
C)22
D)23
E)24
Rationale: 7,17,27,37,47,57,67,
70,71,72,73,74,75,76,77(two 7's),78,79,87,97,107
21 7's between 1 to 110
ANSWER:B
Answer: B
Question: If the sides of a square are multiplied by sqrt(20), the area of the original square is how many times as large as the area of the resultant square?
Options:
A)2%
B)5%
C)20%
D)50%
E)150%
Rationale: Let x be the original length of one side.
Then the original area is x^2.
The new square has sides of length sqrt(20)*x, so the area is 20x^2.
The area of the original square is 1/20 = 5% times the area of the new square.
The answer is B.
Answer: B
Question: The forth proportional to 4,6,8 is?
Options:
A)12
B)15
C)16
D)18
E)20
Rationale: Let the fourth proportional to 4,6,8 be x
then 4:6::8:x
4x = 6*8
x = 12
Answer is A
Answer: A
Question: A mobile phone is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
Options:
A)18%
B)19%
C)21.2%
D)21.81%
E)22.07%
Rationale: For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Answer: D
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
Options:
A)Rs.482
B)Rs.424
C)Rs.842
D)Rs.512
E)Rs.524
Rationale: 20000(11/10)4 - 20000(6/5)2 = 482
ANSWER:A
Answer: A
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 25 hours respectively. The ratio of their speeds is?
Options:
A)4:9
B)4:3
C)5:4
D)4:1
E)4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √25 : √26
= 5:4
Answer:C
Answer: C
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)67 sec
B)6 sec
C)7 sec
D)5 sec
E)8.3 sec
Rationale: Answer: Option B
Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Question: Every month, a girl gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she had $7777 left. Assuming she only gets money by allowance, how much money does she earn every month?
Options:
A)$1592.33
B)$2692.33
C)$2492.33
D)$2592.33
E)$3592.33
Rationale: let the girl gets x$ per month,then
for 12 months she would get 12x$,she spent 12x/2 $ on clothes,now she will have 12x/2 $=6x$,1/3 of this is spent on games i.e (12x/2)*(1/3)=2x.then remaining money is 6x-2x=4x$.1/4 of this is spent on toys i.e 4x/4=x $.now she is left with 4x-x=3x$ which is given as 7777.so x=7777/3=2592.333$.so, she would get monthly allowance of $2592.33
ANSWER:D
Answer: D
Question: The bases of a hemisphere and a cone are equal. If their heights are also equal then ratio between their curved surface area is—
Options:
A)1 : √2
B)√2 ∶1
C)1 : 2
D)2 : 1
E)None of these
Rationale: both having same radius and the heights are same. So height of cone is same as the radius.
2πr^2 / πrl
2r/√(r^2+h^2) , where πr gets cancelled on both sides and l^2=r^2+h^2
2r/√(2r^2) , r=h
2/√2
√2/1
ANSWER:B
Answer: B
Question: The instructions state that Jansi needs 1/4 square yards of one type of material and 1/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 8/24 square yards left that she did not use. What is the total amount of square yards of material Jansi used?
Options:
A)1/4
B)1/9
C)2/3
D)1 1/9
E)2 1/9
Rationale: Total bought = 1/4+1/3
left part 8/24--->1/3
so used part 1/4+1/3-1/3=1/4
ANSWER:A
Answer: A
Question: Village P’s population is 800 greater than Village Q's population. If Village Q’s population were reduced by 700 people, then Village P’s population would be 7 times as large as Village Q's population. What is Village Q's current population?
Options:
A)910
B)920
C)930
D)940
E)950
Rationale: P = Q+800.
P=7(Q-700).
7(Q-700)=Q+800.
6Q=5700.
Q=950.
The answer is E.
Answer: E
Question: The least common multiple of positive integer w and 3-digit integer n is 690. If n is not divisible by 3 and w is not divisible by 2, what is the value of n?
Options:
A)115
B)230
C)460
D)575
E)690
Rationale: The LCM of n and w is 690 = 2*3*5*23.
w is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to w.
From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.
Answer: B.
Answer: B
Question: The number a yields a remainder p when divided by 11 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of a ?
Options:
A)45
B)43
C)72
D)85
E)100
Rationale: I solved this question in the following way:
Q<7 so Q can be from 0 to 6 and P<11 so P can be from 0 to 10, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 10.
a=11k + P or a= 11k + 7 to 10 and look at the answer as, place different values for k, B will give 43 which is 11*3 + 10, the other answers are out of the range
Answer: B
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?
Options:
A)1/38
B)1/36
C)1/35
D)1/389
E)1/31
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer:B
Answer: B
Question: How many 9 digit numbers are possible by using the digits 1, 2, 3, 4, 5 which are divisible by 4 if the repetition is allowed?
Options:
A)77
B)26
C)88
D)27
E)99
Rationale: : If A number has to be divisible by 4, the last two digits must be divisible by 4. So possibilities are, 12, 24, 32, 44, 52. And the of the remaining 7 places, each place got filled by any of the five digits. So these 7 places got filled by 5 x 5 x .....(7 times) = 5757 ways. So total ways are 5 x 5757 = 5/8
Answer:A
Answer: A
Question: A password for a computer uses nine digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
Options:
A)1/32
B)1/16
C)1/8
D)2/5
E)1/512
Rationale: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 × 10 × 10× 10 × 10 × 10 × 10 = 1,000,000,000 possible combinations.
Prime numbers constitute 2, 3, 5,7,11,13,17,19 and 23. In addition to zero, this is 5 total possibility for each digit. So the number of satisfactory variants is 9 × 9 × 9 × 9 × 9× 9 × 9 × 9 × 9. So the probability is 1/2 × 1/2 × 1/2 × 1/2 × 1/2× 1/2 × 1/2 × 1/2 × 1/2 = 1/512.
The right answer is choice (E).
Answer: E
Question: If in a $180 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
Options:
A)$60 mln
B)$80 mln
C)$100 mln
D)$120 mln
E)$150 mln
Rationale: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $180 mln portfolio, x+2x=3x=180 mln from where x=60 mln.
Answer: A
Answer: A
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)444 km
B)445 km
C)500 km
D)300 km
E)250 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
ANSWER A
Answer: A
Question: here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 83 and 92 respectively. the average of the whole class is 86, what is the value of x?
Options:
A)a) 6
B)b) 7
C)c) 8
D)d) 10
E)e) 12
Rationale: 12(83)+92x/12+x=86
996+92x/12+x=86
996+92x=86(12+x)
996+92x=1032+86x
X's one side, numbers one side we get,
92x - 86x=1032-996
6x=36
hence, x=6
Answer A
Answer: A
Question: In May Mrs Lee's earnings were 45 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
Options:
A)50%
B)68%
C)72%
D)76%
E)80%
Rationale: Let in May Lee family's total income =100
in May Mrs Lee's income =45
in May rest of the family's income = 55
In june Mrs Lees income = 45*120/100 = 54
In june Total income = 54+ 55= 109
% of Mrs Lee's income =54/109 =49.54
(A)
Answer: A
Question: The speed at which a man can row a boat in still water is 18 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)16 seconds
B)15.4 seconds
C)26 seconds
D)12 seconds
E)18 seconds
Rationale: Speed of the boat downstream = 18 + 3
= 21 kmph
= 21 * 5/18 = 35/9 m/s
Hence time taken to cover 60 m
= 60*9/35
= 15.4 seconds.
Answer: B
Answer: B
Question: If 5395 / 4.15 = 1300, then 539.5 / 41.5 is equal to ?
Options:
A)17
B)13
C)15
D)14
E)16
Rationale: Answer
Given expression 539.5 / 41.5 = 5395 / 415
= 5395 / (415 x 100)
= 1300 / 100
=13
Correct Option: B
Answer: B
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)2 min
B)8 min
C)9 min
D)3 min
E)5 min
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer: B
Answer: B
Question: An iron mining company depletes 1/11 of the iron ore in a pit it mines over a year. If the company opens a new iron ore mining pit in year 1 and if the initial reserves of the pit were estimated to be 9000 MT (million tons), what is the approximate total quantity of iron ore that would have been mined from that pit by the end of year 4?
Options:
A)5728 MT
B)2853 MT
C)4514 MT
D)3152 MT
E)1510 MT
Rationale: X is the initial quantity of the iron ore in the pit.
After a year of mining the quantity of iron ore left would be X1=X-1/11X i.e. X1=10/11X
Same thing for X2, X3, X4, respectively representing the quantity left after 2, 3, 4 years of mining. (quantity at the end of the year)
So we have:
X1=10/11 X
X2=10/11 X1
X3=10/11 X2
X4=10/11 X3
By multiplying both ends of the equations we get:
X1*X2*X3*X4 = (10/11)^4 X*X1*X2*X3
Simplification leaves us with:
X4 = (10/11)^4 X
X4 is the quantity left at the pit by the end of year4. So the cumulative quantity (Q4) that has been mined from the pit after 4 years is: Q4= X-X4=X-(10/11)^4X i.e. Q4 = X (1-(10/11)^4)
In this case, given X was: X=9000 MT
So we have Q4 = 9,000 * (1-(10/11)^4) = 9000 * (1- 10,000/14,641) = 9,000 * (14,641-10,000)/14,641 = 9,000 * 4,641/14641 = 2852.87 rounded to 2,853 So Q4 = 2,853 MT.
Answer: B
Answer: B
Question: What is it answer?& it is a letter.
Options:
A)22
B)77
C)397
D)27
E)922
Rationale: Explanation:
It is ASHOK as 01100101 10000011 01110010 01111001 01110101
65 83 72 79 75
A S H O K
Answer: B
Answer: B
Question: How many ways are there to split a group of 14 students into two groups of 7 students each? (The order of the groups does not matter)
Options:
A)1016
B)1218
C)1412
D)1716
E)1912
Rationale: 14C7 =3432
If we consider these groups, each group will be counted twice.
The number of ways to choose 2 groups of 7 is 3432/2 = 1716
The answer is D.
Answer: D
Question: If x=1/3, which expression has the greatest value?
Options:
A)x^(1/3)
B)x^(1/2)
C)1/(2x)
D)x/.03
E)x^(-3)
Rationale: Options A and B are both less than 1.
Option C: 1/(2(1/3)) = 3/2 = 1.5
Option D: (1/3) / 0.03 = 1/0.09 = 11.111...
Option E: (1/3)^(-3) = 3^3 = 27
The answer is E.
Answer: E
Question: How may 5 digit odd numbers can be formed from 1 2 3 4 5?
Options:
A)36
B)48
C)72
D)68
E)78
Rationale: Since the number is odd last digit is 1,3,or 5
When last digit is 1 , remaining 4 digits can be arranged in 4!= 24 ways
Similarly when last digit is 3, number of ways = 24
and last digit 5, number of ways = 24
Total number of 5 digit odd numbers = 24*3 = 72
ANSWER:C
Answer: C
Question: City A to city B, Ameer drove for 1 hour at 60 mph and for 3 hours at 50 mph. What was the average speed for the whole trip?
Options:
A)57
B)52.5
C)58.2
D)59
E)62
Rationale: The total distance is 1×60+3×50=210
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)=210/4=52.5
Answer : B
Answer: B
Question: An aeroplane covers a certain distance of 590 Kmph in 8 hours. to cover the same distance in 2 3/4 hours, it Must travel at a speed of
Options:
A)1780
B)1716
C)1890
D)1980
E)1450
Rationale: Speed of aeroplane = 590 Kmph
Distance travelled in 8 hours
= 590 * 8 = 4720 Km
Speed of aeroplane to acver 4720 Km in 11/4
= 4720*4/11 = 1716 Km
Answer B.
Answer: B
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
Options:
A)16 days
B)19 days
C)11 days
D)13 days
E)10 days
Rationale: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
Answer:D
Answer: D
Question: A train travelling 80kmph to pass through a tunnel of 70km at 5:12am. the train leaves the tunnel at 5:18am. find the length of train?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Distance=speed*time
let x is length of train
5:18-5:12=6minutes=6/60 hr=1/10hr
now D=(x+7)=80kmph*1/10
x=1km
ANSWER:A
Answer: A
Question: If Matthew and Fred are both offering Chemistry and Mathematics, which of the following could be true?
I. Matthew and Fred both offer Chemistry.
II. Fred does not love Chemistry but offers it.
III. Matthew loves Chemistry but Fred does not.
Options:
A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III
Rationale: Let’s check each statement.
Statement I:Matthew and Fred both offer Chemistry. Fred offers Chemistry, Matthew offers Chemistry in which case Statement I is TRUE.
Statement II: Fred does not love Chemistry but offers it. There is no mention of Fred's love for Chemistry in which case Statement II can NEVER BE TRUE.
Statement III: Matthew loves Chemistry but fred does not. There is no mention of Fred's and Matthew's love for Chemistry, in which case Statement III can NEVER BE TRUE.
Only Statement I is true.
So,the correct answer is A
Answer: A
Question: A cistern is filled by a tap in 4 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?
Options:
A)30
B)36
C)42
D)45
E)48
Rationale: filling rate - leak rate = net rate
1/4.5 - leak rate = 1/5
leak rate = 2/9 - 1/5 = 1/45
The answer is D.
Answer: D
Question: Find the odd man out. 5, 10, 40, 81, 320, 640, 2560
Options:
A)81
B)5
C)10
D)81
E)320
Rationale: Alternatively 2 and 4 are multiplied with the previous terms
5
5 × 2 = 10
10 × 4 = 40
40 × 2 = 80
80 × 4 = 320
320 × 2 = 640
640 × 4 = 2560
Hence, 81 is wrong. 80 should have come in place of 81.
Answer is A
Answer: A
Question: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference Q between n and m?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result Q will be 8 - 5 = 3
And answer B
Answer: B
Question: If the sum of a number and its square is 182, What is the number?
Options:
A)16
B)77
C)25
D)87
E)13
Rationale: Explanation:
Let the integer be x.
Then, x + x2 = 182
x2 + x - 182 = 0
(x + 14) (x – 13) = 0
x = 13
ANSWER: E
Answer: E
Question: Today is Wednesday. After 29 days, it will be:
Options:
A)Sunday
B)Saturday
C)Friday
D)Thursday
E)Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 28 days, it will be Wednesday.
After 29 days, it will be Thursday.
Answer :D
Answer: D
Question: 4.036 divided by 0.04 gives :
Options:
A)10.09
B)1.06
C)10.06
D)100.9
E)100.6
Rationale: = 4.036/0.04
= 403.6/4
= 100.9
Answer is D.
Answer: D
Question: The average age of 5 girls is 7. The oldest among them is 15 years old. What is the average age of others?
Options:
A)9
B)6
C)7
D)8
E)5
Rationale: sum of ages of girls = 35
sum of ages of rest of 4 girls=20
average=20/4=5
ANSWER:E
Answer: E
Question: A = {10, 1, -3, 6, -8,-5}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
Options:
A)1/4
B)1/3
C)2/5
D)4/9
E)1/2
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 3/6 *2/4 = 6/24;
P(negative, negative) = 3/6*2/4 = 6/24.
P = 6/24 + 6/24
= 12/24
= 1/2
Answer: E
Answer: E
Question: Anne can do a piece of work in 2 days and Emma alone can do it in 5 days. How much time will both take to finish the work ?
Options:
A)A)5
B)B)6.56
C)C)1.42
D)D)8.333
E)E)9.3333
Rationale: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 2 x 5 / (2 + 5)
= 10 / 7
= 1.42 days
Answer: C
Answer: C
Question: What would be the length of the diagonal of a square plot whose area is equal to the area of a rectangular plot of 45 m length and 40 m width?
Options:
A)42.5 m
B)60 m
C)4800 m
D)Data inadequate
E)None of these
Rationale: a2 = 45 × 40 = 1800
∴ a = √1800=30√2
∴ Diagonal of the square = √2 a = √2 × 30√2
= 30 × 2 = 60 m
Answer B
Answer: B
Question: What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
Options:
A)2000
B)2300
C)3000
D)3300
E)3400
Rationale: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
Answer: C
Question: Insert the missing number.
3, 6, 6, 12, 9, 18, 12, 24, 15, (....)
Options:
A)30
B)36
C)42
D)40
E)38
Rationale: Explanation:
There are two series, beginning respectively with 3 and 6. In one 3 is added and in another 6 is added.
The next number is 24+ 6 = 30.
Answer: A) 30
Answer: A
Question: If 3a – 2b – 2c = 30 and √3a-√(2b+2c)=4, what is the value of a + b + c?
Options:
A)3
B)9
C)10
D)12
E)14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
C
Answer: C
Question: If Henry were to add 7 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
Options:
A)25
B)40
C)64
D)80
E)56
Rationale: 7/8x-3/4x=7galls
1/8*x=7gallons
x=56 gallons
ANswer E
Answer: E
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is:
Options:
A)11
B)14
C)15
D)13
E)18
Rationale: Age of the 15th student=
[15 * 15 - (14 * 5 + 16 * 9)] = (225 - 214) = 11 years.
ANSWER A
Answer: A
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?
Options:
A)56m
B)52m
C)27m
D)28m
E)19m
Rationale: Length of the wire fencing = perimeter = 2(90 + 50) = 280 metres
Two poles will be kept 5 metres apart. Also remember that the poles will be placed
along the perimeter of the rectangular plot, not in a single straight line which is
very important.
Hence number of poles required = 280 / 5 = 56
Answer: A
Answer: A