divelab/Sys2Bench huggingface dataset:
Question: If a and b are nonzero integers such that a = 5b/2, then each of the following must be true EXCEPT
Options:
A)0 < b/a < 1
B)ab is positive.
C)On the number line, b lies between 0 and a.
D)The ratio of a to b is equivalent to 10/4.
E)a – b is positive.
Rationale: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.
We're told that A and B are NONZERO INTEGERS and that A = 5B/2 or 2A = 5B. We're told that each of the answer is always true EXCEPT for one of them...
Before we get to the actual work, it's important to note a few details:
1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.
Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...
A = 5
B = 2
AND
A = -5
B = -2
Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.
Answer B: AB is positive
(2)(5) and (-2)(-5) both = +10. Answer B appears true.
Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0
Answer C appears true.
Answer D: A/B = 10/4
5/2 = -5/-2
10/4 = 5/2
Answer D appears true.
Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.
Final Answer:
E
Answer: E
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 52 units per day, what is the value of n ?
Options:
A)30
B)19
C)10
D)9
E)7
Rationale: (average production for n days) * n = (total production for n days) --> 50n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 52 * (n+1) --> n=19.
Or as 40 extra units increased the average for n+1 days by 2 units per day then 40/(n+1)=2 --> n=19.
Answer:B.
Answer: B
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)855 1/2 grams
B)833 1/3 grams
C)833 1/2 grams
D)875 2/7 grams
E)865 2/7 grams
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
ANSWER:B
Answer: B
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 7 years?
Options:
A)4x (1+n/100)^6 - x
B)5x (1+n/100)^5- x
C)3x (1+n/100)^4 - x
D)x (1+n/100)^4 - x
E)x (1+n/100)^7 - x
Rationale: Amount after 7 years compounded yearly = x (1+n/100)^7
Thus profit = Final amount - original principle = x (1+n/100)^7 - x . Answer : E
Answer: E
Question: A starts a business with a capital of Rs. 5,000. B joins in the business with Rs.2000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)5 months
B)6 months
C)7 months
D)10 months
E)None of these
Rationale: Explanation :
Let B joins for x months. Then
A:B = 5000*12 : x* 2000 = 3 : 1
=> 5*12 : 2x= 3 : 1
=> 5*12/ 2x = 3/1 = 3
=> 5*4 /2x = 1
=> 10/x = 1
=> x = 10. Answer : Option D
Answer: D
Question: A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?
Options:
A)23
B)22
C)21
D)36
E)48
Rationale: C
21
WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer: C
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9
B)10.7
C)10.3
D)10.8
E)10.2
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
'Answer: D
Answer: D
Question: There has been successive increases of 20% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
Options:
A)16%
B)20%
C)24%
D)28%
E)32%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.1*1.2*P = x*P
y = x / (1.1*1.2) which is about 0.76x which is a decrease of about 24%.
The answer is C.
Answer: C
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 17 terms of the arithmetic progression?
Options:
A)300
B)120
C)150
D)170
E)270
Rationale: n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 17 ...we get 17/2[ 2a + 14d] = 17 [a+7d] = 17*10 = 170...
Answer is D...
Answer: D
Question: What is the least number which when divided by 6, 7, 9 and 18 leaves remainder 4 in each care?
Options:
A)130
B)140
C)136
D)156
E)166
Rationale: Explanation:
LCM of 6, 7, 9 and 18 is 126
Required number = 126 + 4 = 130
Answer: Option A
Answer: A
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 2(x+ y) > 2z
III. yz > xz
IV. xy > y + z
Options:
A) I only
B) II only
C) II and III only
D) II and IV only
E) III and IV only
Rationale: we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 2(x+ y) > 2z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B
Answer: B
Question: If Rs 1050 is divided into three parts, proportional to (1 / 3) : (3 / 4) : ( 4 / 6), then what is the first part?
Options:
A)500
B)300
C)200
D)100
E)150
Rationale: EXPLANATION:
Given:
1050 =	1/3	:	3/4	:	4/6
1) L.C.M. of 3, 4 and 6 is 12
Therefore, multiply numerator and denominator of (1/3) with 4, to obtain denominator 12. Similarly multiply (3/4) with 3 and (4/6) with 2
4/12	:	9/12	:	8/12 = 4 : 9 : 8
2) If a number a is divided in three ratios x : y : z,
First Part:	ax/(x + y + z) ------- (a is the number divided)
Therefore,
First Part:	(1050 x 4) /(4 + 9 + 8)=200
ANSWER IS C
Answer: C
Question: A charity collected $1,499 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
Options:
A)77
B)78
C)79
D)74
E)65
Rationale: Min fund = 20
Total = 1499
The closest multiple of 20 to 1499 is : 73
Which implies 73 people gave 20 and 1 person gave 39
Ans. D
Answer: D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)299
B)200
C)240
D)111
E)161
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m. Answer:C
Answer: C
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
Options:
A)3
B)15
C)27
D)127
E)255
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: C
Question: If the number 52,1n6, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?
Options:
A)6
B)5
C)3
D)4
E)0
Rationale: The sum of the digits 5 + 2 + 1 + n + 6 must be a multiple of 3
14 + n must be a multiple of 3
substituting the numbers n must = 4
Answer D
Answer: D
Question: P,Q and R started a business in which P invested Rs.10,000/- for 2year, Q invested Rs.20,000/- for 3 years, R invested Rs.30,000/- for 4 years. At the end of the profit received by them is Rs.10,000/-. What is Q’s share?
Options:
A)Rs. 2,500
B)Rs. 2,000
C)Rs. 1,000
D)Rs. 1,500
E)Rs. 3,000
Rationale: Solution: A : B : C = (10,000 * 2) : (20,000 * 3) : (30,000 * 4) = 1 : 3 : 6.
So Q's share = Rs. (10,000 * 3/10) = Rs. 3,000.
Answer: Option E
Answer: E
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^20, then n =
Options:
A)3
B)6
C)19
D)23
E)24
Rationale: 2^2n + 2^2n + 2^2n + 2^2n = 4^20
=> 4 x 2^2n = 4^20 = 2^40
=> 2^2 x 2^2n = 2^40
=> 2^(2n+2) = 2^40
=> 2n+2 = 40=> n =19
So. Answer will be C.
Answer: C
Question: When a certain number X is divided by 63, the remainder is 25. What is the remainder when X is divided by 8?
Options:
A)1
B)3
C)4
D)5
E)6
Rationale: When a certain number X is divided by 63, the remainder is 25. What is the remainder when X is divided by 8?
Putting a value say x = 255 we get remainder as 25 when divided by 63.
When 25 divided by 8 we get 1 as remainder.
A is the answer.
Answer: A
Question: In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
Options:
A)L(L-N) / L-M
B)M+
C)L-N
D)M-N
E)L(N-M)/ L-M
Rationale: For my work, i took the following numbers:
L = 100
M = 10
N =20.
So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, leaving us with just two options..A and B.
Out of which, i choose E.
Answer: E
Question: John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?
Options:
A)1/16
B)2/16
C)3/16
D)7/16
E)9/16
Rationale: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2 & #3 & #4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
H-T-T-T ----> P = (1/2)^4 = 1/16
T-H-H-H ----> P = (1/2)^4 = 1/16
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/16 + 1/16 = 2/16
Answer (B).
Answer: B
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 264 is divisible by 3, 4 and 11
=> 264 is divisible by 132
396 is divisible by 3, 4 and 11
=> 396 is divisible by 132
462 is divisible by 3 and 11, but not divisible by 4
=> 462 is not divisible by 132
792 is divisible by 3, 4 and 11
=> 792 is divisible by 132
968 is divisible by 4 and 11, but not divisible by 3
=> 968 is not divisible by 132
2178 is divisible by 3 and 11, but not divisible by 4
=> 2178 is not divisible by 132
5184 is divisible by 3 and 4, but not divisible by 11
=> 5184 is not divisible by 132
6336 is divisible by 3, 4 and 11
=> 6336 is divisible by 132
Hence, only 264, 396 ,792 and 6336 are divisible by 132. So the answer is 4
B)
Answer: B
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 5000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
Options:
A)100000
B)100500
C)105000
D)Data inadequate
E)None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 5000) From the question,
(x - 500) × 126⁄100 = 6⁄5x ⇒ x = 105000
Answer C
Answer: C
Question: A man has some hens and cows. If the number of heads be 44 and the number of feet equals 128, then the number of hens will be
Options:
A)22
B)24
C)26
D)20
E)28
Rationale: Explanation :
Let number of hens = h and number of cows = c
number of heads = 44
=> h + c = 44 ---(Equation 1)
number of feet = 128
=> 2h + 4c = 128
=> h + 2c = 64 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 64 - 44
=> c = 20
Substituting the value of c in Equation 1, we get
h + 22 = 44
=> h = 44 - 20 = 24
i.e., number of hens = 24
Answer : B
Answer: B
Question: 4, 7, 16, 43, 124, (...)
Options:
A)22
B)367
C)27
D)32
E)25
Rationale: Explanation :
4
4 × 3 - 5 = 7
7 × 3 - 5 = 16
16 × 3 - 5 = 43
43 × 3 - 5 = 124
124 × 3 - 5 = 367
Answer : Option B
Answer: B
Question: The average of 11 results is 20. The average of first 5 of them is 15 and that of last 5 is 22 . Find the 6th result?
Options:
A)35
B)50
C)100
D)120
E)150
Rationale: 6th result = sum of 11 results - sum of 10 results
= 11*20-5*15-5*22
= 220-75-110
= 35
Answer is A
Answer: A
Question: The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 30%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
Options:
A)20%
B)24%
C)30%
D)32%
E)79%
Rationale: take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 30% then output equals 143
To restore new holidy demand output to original 100.
final -initial/final*100
=43/143*100=30% approxiamately.
option C is correct.
Answer: C
Question: Three taps A, B and C can fill a tank in 24, 30 and 40 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in :
Options:
A)8 hours
B)10 hours
C)14 hours
D)16 hours
E)18 hours
Rationale: (A+B)'s 1 hour's work = (1/24 + 1/30) = 9/120 = 3/40.
(A+C)'s 1 hour's work = (1/24 + 1/40) = 8/120 = 2/30.
Part filled in 2 hours = (3/40 + 2/30) = 17/120.
Part filled in 12 hours = (6 * 17/120) = 17/20.
Remaining part = (1 - 17/20) = 3/20.
now, it is the time of A and B and 3/20 part is filled by A and B in 1 hour, then, 3/40 part will filled in 2 hours.
.'. total time taken to fill the tank = (12 + 2) = 14 hours Answer : C
Answer: C
Question: If a and b are positive integers such that a/b = 4.37, which of the following must be a divisor of a?
Options:
A)19
B)13
C)12
D)7
E)17
Rationale: 1) A and B are positive INTEGERS
2) A/B = 4.37
A = 437
B = 100
437/100 = 4.37
These values are the smallest values as 437 is neither divisible by 5 or 2, the factors of 100.
The value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 437, we have to 'factor-down' 437. This gives us (19)(23). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Answer: A
Answer: A
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 12% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
Options:
A)22%
B)23%
C)24%
D)25%
E)34%
Rationale: Since 12% of the customers who sample the candy are not caught, then 88% of the customers who sample the candy are caught:
{% of customers who sample candy}*0.88 = 0.22;
{% of customers who sample candy} = 0.25.
Answer: D.
Answer: D
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 200. Find the total worth of the stock?
Options:
A)20029
B)20000
C)10000
D)20027
E)20026
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 200 => x = 10000
Answer: C
Answer: C
Question: A is B's sister. C is B's mother. D is C's father. E is D's mother. Then, how is A related to D?
Options:
A)Grandfather
B)Daughter
C)Grandmother
D)Granddaughter
E)SISTER
Rationale: A is the sister of B and B is the daughter of C.
So, A is the daughter of C. Also, D is the father of C.
So, A is the granddaughter of D.
Answer: D
Answer: D
Question: In the diagram shown, the number of rectangles of all
sizes is
Options:
A)11
B)15
C)7
D)13
E)9
Rationale: We systematically count rectangles by searching for groups of rectangles that are of similar size.
The largest rectangles in the diagram are all roughly the same size and overlap in pairs.
There are 3 of these; each is shaded black and shown below
Rectangle 2 (shown above) consists of 4 small rectangles.
We shade these rectangles black and label them 4; 5; 6; 7, as shown below
Together, Rectangle 4 and Rectangle 5 (shown above) create Rectangle 8, shown below.
Similarly, Rectangle 6 and Rectangle 7 together create Rectangle 9, shown below.
Finally, Rectangle 4 and Rectangle 6 (shown above) together create Rectangle 10, shown below.
Similarly, Rectangle 5 and Rectangle 7 together create Rectangle 11, shown below.
There are no other rectangles that can be formed.
In total, there are 11 rectangles in the given diagram.
correct answer A
Answer: A
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 5% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
Options:
A)5%
B)10%
C)15%
D)25%
E)35%
Rationale: 60-(x+5+z) + 50-(x+5+y) + 35-(z+5+y) + x + +y + z +5 = 100
where x = people who bought MilkChicken
y = people who bought chickenApples
z= people who bought Milk and Apples
x+y+z= the number of people who bought just exactly two products.
Hence solving the above equation we get,
135 -(x+y+z) = 100
Thus, x+y+z= 35
Answer: E
Answer: E
Question: If one-third of one fourth of a number is 15, then three-tenth of that number is:
Options:
A)35
B)25
C)45
D)54
E)52
Rationale: Let the number be x. Then,
1/3 of 1/4 of x = 15
x = 15 * 12 = 180
So, required number = (3/10 * 180) = 54.
ANSWER:D
Answer: D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.9 sec
C)1.3 sec
D)2.9 sec
E)1.8 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer:A
Answer: A
Question: If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?
Options:
A)30%
B)40%
C)50%
D)70%
E)80%
Rationale: (Explanation:Friends, we know we will need gain amount to get gain percent, right.
So lets get gain first.
Let the cost price of 1 pen is Re 1 Cost of 8 pens = Rs 8 Selling price of 8 pens = 12
Gain = 12 - 8 = 4 Gain%=(GainCost*100)%=(48*100)%=50%
C
Answer: C
Question: Today is Monday. After 29 days, it will be :
Options:
A)Tuesday
B)Saturday
C)Monday
D)Sunday
E)Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 28 days, it will be Monday
After 29 days, it will be Tuesday
Answer is A
Answer: A
Question: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 36 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
Options:
A)6 2/3
B)15
C)20
D)25
E)40
Rationale: Here is how I did it:
The cyclist travels 36 miles in 60 mins, so in 5 mins he will travel [(36*5)/60] miles, which equals 3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 3 miles, he will take [(60*3)/4] = 45 mins.
Hence 45-5 = 40 mins
E
Answer: E
Question: Pipe A can fill a tank in 4 hours, pipe B in 12 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled ?
Options:
A)2.8 hours
B)2 hours
C)3.5 hours
D)3 hours
E)None of these
Rationale: Explanation:
Part filled by A in 1 hour = 1/4
Part filled by B in 1 hour = 1/12
Part filled by C in 1 hour = 1/40
Part filled by (A+B+C) in 1 hour =
1/4+1/12+1/40=43/120
So all pipes will fill the tank in 2.8 hours.
Option A
Answer: A
Question: Two letters from the word FARTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Two letters from the word FARTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Options:
A)1/500
B)1/28
C)27/28
D)124/125
E)499/500
Rationale: There are 6 consonants and 2 vowels in FARTHING.
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So, Answer is 1 - 1/28 = 27/28 ------> C.
Answer: C
Question: A cube of edge 15cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
Options:
A)6cm
B)8.25cm
C)11.25cm
D)15.12cm
E)20.62cm
Rationale: Increase in volume = volume of the cube = 15*15*15 cm^3
Rise in water level = volume / area = 15*15*15/20*15 = 11.25cm
Answer is C
Answer: C
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
A)226
B)992
C)665
D)771
E)211
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
Answer: B
Answer: B
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 6 m, the volume of the box (in m3) is:
Options:
A)4830
B)5184
C)6420
D)8960
E)7960
Rationale: Clearly, l = (48 - 12)m = 36 m,
b = (36 -12)m = 24 m,
h = 8 m.
Volume of the box = (36 x 24 x 12) m3 = 5184 m3. Answer: Option B
Answer: B
Question: Two people are playing with a pair of dice. Instead of numbers, the dice have different colors on their sides. The first person
wins if the same color appears on both the dice and the second person wins if the colors are different. The odds of their winning
are equal. If the first dice has 5 red sides and 1 blue side, find the colour(s) on the second one.
Options:
A)12
B)2
C)3
D)4
E)7
Rationale: Let no of red sides in second dice = x
No of blue sides = 6-x
Now since their odds are equal
(5/6)X(x/6)+(1/6)X((6-x)/6)=(5/6)X((6-x)/6)+(1/6)X(x/6)
=>x=3
So No. of red and blue faces on second dice will be equal i.e. 3
ANSWER:C
Answer: C
Question: When the integer k is divided by 7, the remainder is 4. Which of the following expressions below when divided by 7, will have a remainder of 5?
I. 4k + 3
II. 6k + 2
III. 8k + 4
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II and III
Rationale: k = 7j + 4
4k + 3 = 28j + 16 + 3 = 28j + 14 + 5
6k + 2 = 42j + 24 + 2 = 42j + 21 + 5
8k + 4 = 56j + 32 + 4 = 56j + 35 + 1
The answer is D.
Answer: D
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?
Options:
A)3
B)6
C)9
D)18
E)22
Rationale: The trains will travel the perimeter of the circle which is 12π miles. The relative speed of the trains is 2π miles per hour. Time taken to meet = 12π/2π = 6 hours
ANSWER:B
Answer: B
Question: What simple interest will produce Rs.84000 as in 4 years at 3 1/2 percent?
Options:
A)11500
B)12660
C)15220
D)11760
E)16520
Rationale: (84000*4*7/2)/100 = i
i = 11760
Answer: D
Answer: D