divelab/Sys2Bench huggingface dataset:
Question: If
1 = 3
2 = 6
3 = 9
4 = 12
5 = 15
Then 9 = ?
Hint: Its a logic Riddle not a mathematical riddle
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: C
3
As stated
3=9 => 9=3
Answer is C
Answer: C
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80.The compound interest on the same sum for the same period is :
Options:
A)Rs.81.60
B)Rs.160
C)Rs.1081.60
D)None of these
E)Cannot be determined
Rationale: Explanation:
Principal = Rs. (100×80/4×2) = Rs.1000
C.I = Rs. [{1000×(1+4/100)2−1000}] = Rs.81.60
Correct Option: A
Answer: A
Question: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
Options:
A)15%
B)20%
C)40%
D)50%
E)150%
Rationale: Let rate in R = 100x
then P = 75x
G = 100y
P = 90y
Thus
75 x=90y
or x = 1.20 y
Ans R = 120y
so increase = 20%
Answer: B.
Answer: B
Question: If a = 105 and a^3= 21 * 25 * 35 * b, what is the value of b?
Options:
A)35
B)42
C)45
D)49
E)63
Rationale: First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
25 = 5 * 5
35 = 7 * 5
so, (105)^3 = 3 * 7 * 5 * 5 * 7 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3 * 5^3 * 7^2 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 * 5 ^3 * 7^2
b = 3^2*7 = 9*7=63
Correct answer E.
Answer: E
Question: What is the scope including 1/41+1/42+1/43+......+1/50?
Options:
A)1/6~1/5
B)1/5~1/4
C)1/4~1/3
D)1/3~1/2
E)1/2~1
Rationale: For Maximum value : It should be less than 1/41 + 1/41 +1/41... 10 times = 10/41 ~ 1/4
For Minimum Value : It should be greater than 1/50+ 1/50+ 1/50 .. 10 times = 10/50 = 1/5.
Thus, the answer should lie between 1/5 and 1/4. Correct ans : B.
Answer: B
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 20 years(the child was born during the interval). What is the present age of the child?
Options:
A)2 years
B)3 years
C)5 years
D)4 years
E)1 years
Rationale: Answer: Option D
28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: D
Question: A can do a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together on the Dec. 15, 2000, but A left 8 days and B 12 days before the completion of the work. If C took the rest for a week then in how many days, the work was finished from the day it started ? Sol. Let the total time taken be x days.
Options:
A)1
B)70
C)5
D)7
E)776
Rationale: Answer:E
Answer: E
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 30 percent of the drive from the center, what percent of the round-trip has the technician completed?
Options:
A)5%
B)10%
C)25%
D)40%
E)65%
Rationale: The complete round trip consists of driving to the service center and then back home again.
So, once the technician drives to the service center he/she has already competed 50% of the entire trip.
Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%
so 0.5+0.5*0.3=0.65
Answer:
E
Answer: E
Question: If x^2+(1/x^2)=5, x^4+(1/x^4)=?
Options:
A)23
B)11
C)12
D)14
E)15
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=5^2-2=23.
Thus, the answer is A.
Answer: A
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = d is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-d, -k), then what are the coordinates of the point P?
Options:
A)(-5d, -5k)
B)(-3d, -3k)
C)(2d, 2k)
D)(3d, 3k)
E)(5d, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-d, -k), so R is at a distance of 2d from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4d and coord (3d,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3d,3k).ans D
Answer: D
Question: Ross has 60 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
Options:
A)9 ; 15.
B)2 ; 15.
C)4 ; 10.
D)5 ; 25.
E)3 ; 10.
Rationale: Total shirts = 60
Green shirts = 3/4*60 = 45, Non green shirts = 15
Shirts without button = 1/10*60 = 6, shirts with button = 24
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 15
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 15 - 6 = 6
Hence the range would be (9, 15)
Correct Option: A
Answer: A
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
Options:
A)1978
B)2707
C)7728
D)4200
E)7291
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer: D
Answer: D
Question: What is the sum of the integers 45 through 175 inclusive?
Options:
A)12,295
B)13,000
C)14,300
D)14,410
E)28,820
Rationale: sum of n consecutive positive integers=n(n+1)/2..
in one case n=44 and other 175... subtract the sum to get the answer
sum of first 175 +ive numbers=175*176/2=15400..
sum of first 45 +i've numbers=45*44/2=990..
answer=15400-990=14410
ANSWER:D
Answer: D
Question: which of the following options must be accurate if given the equation below: h=-e^7
I. h is positive.
II. If e is negative then h is negative.
III. e is non-negative.
Options:
A)I only
B)II and III only
C)I and III only
D)II only
E)III only
Rationale: I. h is positive --> not true;
II. If h is negative then e is negative. h is negative means that e is not zero. ;
III. e is non-negative.
Answer: D (I only).
Answer: D
Question: The side of a square has the length of 9. What is the area of the region shaded?
Options:
A)48-8π
B)48-6 π
C)24+6π
D)16+8π
E)64-9π
Rationale: The area of a square whose side is 9 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is E.
Answer: E
Question: 2 students appeared at an examination. 1 of them secured 9 marks more than the other one and hismarks was 56% of the sum of their marks. Find the marks obtained by them are?
Options:
A)39 and 31
B)40 and 33
C)42 and 33
D)37 and 31
E)35 and 32
Rationale: Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)
=> 14 (2x + 9)
=> 3x = 99
=> x = 33.
So, their marks are 42 and 33
C
Answer: C
Question: a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find b=?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: adding 1 to all equqtions.,we get them modified to the following form
(a^2+1)(b^2+1)=260
(b^2+1)(c^2+1)=1300
(c^2+1)(a^2+1)=500
by corresponding mul and div we get a=3,b=5,c=7
ANSWER:D
Answer: D
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.36 more than Jane, what was the original price of the dish?
Options:
A) 24
B) 34.8
C) 37.8
D) 42
E) 84
Rationale: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.36 --> 15p - 13.5p = 36 --> p = 24.
Answer: A.
Answer: A
Question: If a population of women in a town is 50% of men . What is the population of men as a percentage of population of women ?
Options:
A)100%
B)120%
C)200%
D)150%
E)180%
Rationale: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.
Men = 10
Women = 5
We're asked for the number of Men, as a percentage of the number of Women.
M/W %= 10/5 = 200%
Answer is C
Answer: C
Question: A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?
Options:
A)Rs. 4000
B)Rs. 4056
C)Rs. 4060
D)Rs. 4100
E)Rs. 4150
Rationale: Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
Answer: B
Question: Train X and train Y pass one another traveling in opposite directions. Twenty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
Options:
A)28
B)40
C)55
D)72
E)80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 20 min i.e 20/60 hr
using RTD table, (2R+30) * 20/60 = 100 ==> R= 135 miles/hr
So the rate of train X is 165 miles/hr (since R+30)
The distance traveled by Train X in 20 min is R*T = 165 * 20/60 = 55 miles (C)
Answer: C
Question: The speed of a boat in still water in 42 km/hr and the rate of current is 7 km/hr. The distance travelled downstream in 44 minutes is:
Options:
A)86.6 km
B)46.6 km
C)35.9 km
D)35.6 km
E)26.6 km
Rationale: Speed downstream = (42 + 7) = 49 kmph
Time = 44 minutes =44/60 hour = 11/15 hour
Distance travelled = Time × speed =11/15×49 = 35.9 km
ANSWER:C
Answer: C
Question: A man buys 60 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
Options:
A)7.6 %
B)7.7 %
C)29.13 %
D)33.6 %
E)37.82 %
Rationale: Explanation:
Let Marked price be Re. 1 each
C.P. of 60 pens = Rs. 46
S.P. of 60 pens = 99% of Rs. 60 = Rs. 59.4
Profit % = (Profit /C.P.) x 100
Profit% = (13.4/46) x 100 = 29.13%
ANSWER: C
Answer: C
Question: What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
Options:
A)64.98
B)64.29
C)53.98
D)64.1
E)22.13
Rationale: n:
S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000]
= Rs. 464.10 Difference
= (464.10 - 400)
= Rs. 64.10
Answer:D
Answer: D
Question: Two faces of a fair die are Yellow, two faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
Options:
A)1/36
B)1/18
C)1/32
D)1/54
E)None of these
Rationale: Probability of getting yellow color = P(Y) = 2/6 = 1/3
Probability of getting red color = P(R) = 2/6 = 1/3
Probability of getting blue color = P(B) = 1/6
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/3 x 1/3 x 1/6 = 1/54
ANSWER:D
Answer: D
Question: A big container is 30% full with water. If 36 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
Options:
A)36 liters
B)40 liters
C)45 liters
D)54 liters
E)80 liters
Rationale: A big container is 30% full with water and after 36 liters of water is added, the container becomes 75% full. Hence these 36 liters account for 45% of the container, which means that the capacity of it is 36/0.45=80 liters.
OR: if the capacity of the container is x liters then: 0.3x+36=0.75x --> x=80 liters.
Answer: E.
Answer: E
Question: Find the middle one when The sum of three consecutive even numbers is 36?
Options:
A)10
B)12
C)13
D)15
E)16
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: B
Question: 10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
Options:
A)5
B)6
C)7
D)8
E)10
Rationale: Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
= 5 men and 10 women can complete the work in 7 days Answer : Option C
Answer: C
Question: A couple decides to have 3 children. If they succeed in having 3 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 1 girl and 2 boys?
Options:
A)3/4
B)1/2
C)5/8
D)1
E)1/4
Rationale: Sample space = 2^3 = 8
Favourable events = {bgg}, {bgb}, {bbb}, {ggg}, {gbg},
Probability = 5/8 = 5/8.
Ans (C).
Answer: C
Question: The average of first five multiples of 3 is
Options:
A)3
B)6
C)9
D)12
E)15
Rationale: Solution
Average	= 3(1+2+3+4+5) / 5
= 45 / 5.
= 9.
Answer C
Answer: C
Question: In how many years, Rs. 200 will produce the same interest @ 5 % as Rs. 900 produce in 2 years @ 3 ½ %?
Options:
A)6.3 years
B)8.2 years
C)9 years
D)12 years
E)None of these
Rationale: Explanation:
P = Rs 900, R = 3 ½ % = 7/2 %, T = 2 years.
Therefore,
S.I. = PRT/100
S.I. = Rs. (900 x 7/2 x 2/100) = Rs. 63
Now, P = Rs. 200, S.I. = Rs. 63, R = 5 %
Time = ((100 x 63) / (200 x 5) ) years = 6.3 years
ANSWER A
Answer: A
Question: In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
Options:
A)16.67%
B)25%
C)20.45%
D)31.56%
E)40%
Rationale: Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67%
Answer is A
Answer: A
Question: At what price must an article costing Rs.57 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)69.5
C)62.3
D)62.1
E)75
Rationale: CP = 57
SP = 57*(125/100) = 71.25
MP*(95/100) = 71.25
MP = 75
Answer:E
Answer: E
Question: If the diameter of circle R is 20% of the diameter of circle S, the area of circle R is what percent of the area of circle S?
Options:
A)5%
B)10%
C)15%
D)14%
E)4%
Rationale: Let diameter of circle R , dr = 20
and diameter of circle S , ds = 100
Radius of circle R , Rr = 10
Radius of circle S , Rs = 50
Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )
= (10/50)^2 = (2/10)^2
=4%
Answer :E
Answer: E
Question: If 3^e- 3^(e-1) = 162 then e(e-1) =
Options:
A)12
B)16
C)20
D)30
E)81
Rationale: It seems like you were really close but you solved for e - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of e(e -1), e.g. (3)(4) = 12. Even then, had you figured e has to be a little bigger (plugging in 4 for e gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (e - 1) exponent place.
Again, a quick plugging in should get you (C) 20 as the only other answer with consecutive integers as factors is far too big.
Answer: C
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 6 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (14 * 6 + 16 * 8)] = 13 years. Answer: C
Answer: C
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)40, 68 kmph
B)40, 30 kmph
C)90, 60 kmph
D)40, 60 kmph
E)20, 60 kmph
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph
Answer: D
Answer: D
Question: A woman has three blouses of different colors, two skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
Options:
A)8
B)12
C)16
D)10
E)18
Rationale: total ways = 3*2*2=12..
now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..
the ways in which the pink blose and green skirty are together=1*1*2=2..
total ways =12-2=10..
D
Answer: D
Question: How many halves are there in one-fourth?
Options:
A)0.02
B)12
C)32
D)0.7
E)0.5
Rationale: divide 1/4 by 1/2
=1/4÷1/2
=1/4*2/1
=2/4
=0.5.
Answer is E.
Answer: E
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)88
C)77
D)66
E)51
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer:A
Answer: A
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 10%?
Options:
A)25%
B)28%
C)21%
D)30%
E)32%
Rationale: The question is very easy. My logic is the following:
A surface = 6*a^2
After 10% increase A surface = 6* ((1.1a)^2) = 6*1.21*a^2
The increase in the surface area = (6*1.21*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.21-1))/(6*a^2) = 1.21-1=0.21 = 21%
Answer : C
Answer: C
Question: In a colony of 50 residents, the ratio of the number of men and women is 3:2. Among the women, the ratio of the educated to the uneducated is 1:3. If the ratio of the number of education to uneducated persons is 4:6, then find the ratio of the number of educated and uneducated men in the colony?
Options:
A)1:1
B)3:2
C)1:3
D)2:5
E)5:7
Rationale: Number of men in the colony = 3/5 (50) = 30
Number of women in the colony = 2/5 (50) = 20
Number of educated women in the colony = 1/4 (20) = 5
Number of uneducated women in the colony = 3/4 (20) = 15
Number of educated persons in the colony = 4/10 (50) = 20
As 5 females are educated, remaining 15 educated persons must be men.
Number of uneducated men in the colony = 30 - 15 = 15
Number of educated men and uneducated men are in the ratio 15:15 => 1:1
Answer:A
Answer: A
Question: Two dice are tossed. The probability that the total score is a prime number is:
Options:
A)5/5
B)5/9
C)5/1
D)5/7
E)5/12
Rationale: n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.
Then E	= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) }
n(E) = 15
The total cases are 6 * 6 * 6 = 216.
The probability = 15/36 = 5/12.
Answer: E
Answer: E
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z<(x − 1)/y
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)
Options:
A)I only
B)I and II
C)II and III
D)II only
E)None of these
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z<(x − 1)/y --> 2/3 < 1/3 --> False
II. z<(x − 1)/(y − 1) --> 2/3 < 1/2 --> False
III. z>(x + 1)/(y + 1) --> 2/3 > 3/4 --> False
Answer: E
Answer: E
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)638
B)738
C)375
D)98
E)8303
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer:C
Answer: C
Question: Ten stickers numbered 1 to 10 are placed in a bowl, mixed up thoroughly and then one sticker is drawn
randomly. If it is known that the number on the drawn sticker is more than 3, what is the probability
that it is an even number?
Options:
A)3/7
B)4/7
C)5/7
D)7/11
E)9/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7
B)
Answer: B
Question: In a renowned city, the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
Options:
A)32,300
B)172,800
C)345,600
D)338,200
E)259,200
Rationale: Every 2 seconds, 8 persons are added (10-2). Every second 4 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 4 = 345600
Option C
Answer: C
Question: A man can row his boat with the stream at 6 km/h and against the stream in 3 km/h. The man's rate is?
Options:
A)1.5 kmph
B)3 kmph
C)8 kmph
D)7 kmph
E)5 kmph
Rationale: DS = 6
US = 3
S = ?
S = (6 - 3)/2 = 1.5 kmph
Answer: A
Answer: A
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The sum of the first 53 positive even integers is 2550. What is the sum of the even integers from 96 to 200 inclusive?
Options:
A)5,100
B)7,844
C)10,100
D)15,500
E)20,100
Rationale: even numbers from 96 to 200=104/2+1=53
Sum= (200+96)x53/2=7844
So B is the ans.
Answer: B
Question: Carmelo and LeBron participate in a five-person footrace on the basketball court during All-Star Weekend. If all five contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
Options:
A)5040
B)2520
C)720
D)120
E)60
Rationale: 5! = 120
120/2=60 half the time carmelo is in front, vice versa
Answer:
(E) 60
Answer: E
Question: Given the equation 7^p-3^(-p)=6.7, which of the following options is the correct value of p?
Options:
A)1
B)2
C)3
D)5
E)0
Rationale: Plugging in the various option into the equation to find out which is correct:
7^p-3^(-p)=6.7
7^1-3^(-1)=6.7 Ans. A
Answer: A
Question: There is a 50 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 50 cm, how many insects were still left after the race was over?
Options:
A)0
B)4
C)6
D)8
E)11
Rationale: Only the prime numbers greater than 10 and less than 50 were left.
That is 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
The total is 11.
The answer is E.
Answer: E
Question: If each digit in the set A = {1, 2, 3, 4, 5, 6} is used exactly once, in how many ways can the digits be arranged?
Options:
A)720
B)830
C)940
D)1050
E)1160
Rationale: 6! = 720
The answer is A.
Answer: A
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
Options:
A)7
B)9
C)11
D)12
E)15
Rationale: Explanation:
x/2 – x/3 = 6 => x =6
3 + 6 = 9
B)
Answer: B
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| =
Options:
A)ab-4+b
B)2b-ab-4
C)ab+4
D)ab-2b+5
E)4-ab
Rationale: Given: |ab| = ab and |a| = -a
Question: |b-3| + |ab-b| = ?
**** Looking at |ab| = ab tells us that a and b are either both positive or negative
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: a and b are both negative values
Let a=-1 and b=-1
|b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5
Test a) ab-4 = (-1)(-1)-4 = -5
Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7
Test c) ab+4 = 1 + 4 = 5
Answer: C
Answer: C
Question: There are 9 cities numbered 1 to 9.From how many cities the flight can start so as to reach the city 8 either directly or indirectly such that the path formed is divisible by 3.
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Start from 1: 1368, Start from 2: 2358, Start from 3: 378, Start from 4: 48, Start from 5: 528, Start from 6: 678, Start from 7: 78, Why start from 8???, Start from 9: 918. So flights can start from all 8 other cities.
ANSWER:B
Answer: B
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in
Options:
A)144 mins
B)140 mins
C)136 mins
D)132 mins
E)None of these
Rationale: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/36
=>4/x=1/36
x=36∗4=144mins
Answer: Option A
Answer: A