divelab/Sys2Bench huggingface dataset:
Question: Paul buys his co-workers donuts 24 glazed, 12 creme-filled and 6 with sprinkles. The glazed donuts cost $0.75 each, the creme-filled donuts cost $1.00 each, and the sprinkle covered donuts cost $0.50 each. What is the average cost Paul paid for each donut?
Options:
A)70 cents
B)75 cents
C)79 cents
D)80 cents
E)1 dollar
Rationale: Explanation:
24 12 6
0.75 1.00 0.50
$18 + $12 + $3 = $33/42 = $0.79
C
Answer: C
Question: How many positive integers less than 100 have a remainder of 6 when divided by 13?
Options:
A)2
B)7
C)6
D)9
E)10
Rationale: We have to include 6 also.As 13*0 + 6 =6
If somebody says to divide 6 by 13 ,we will be telling we have 0 quotient and remainder as 6.
Answer is C
Answer: C
Question: If the price of a certain computer increased 30 percent from d dollars to 377 dollars, then 2d =
Options:
A)540
B)570
C)619
D)649
E)580
Rationale: Before Price increase Price = d
After 30% Price increase Price = d+(30/100)*D = 1.3d = 377 (Given)
i.e. d = 377/1.3 = $290
i.e. 2d = 2*290 = 580
Answer: option E
Answer: E
Question: For any number x, x* is defined as the greatest positive even integer less than or equal to x. What is the value of 5.2 – 5.2*?
Options:
A)0.2
B)1.2
C)1.8
D)2.2
E)4.0
Rationale: Since x* is defined as the greatest positive even integer less than or equal to x, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).
Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2
Answer: B.
Answer: B
Question: The compound ratio of 5:6, 3:2 and 4:5?
Options:
A)1:8
B)1:6
C)1:2
D)1:1
E)1:7
Rationale: 5/6 * 3/2 * 4/5
= 1/1
1:1
Answer: D
Answer: D
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 40% alcohol, is?
Options:
A)2.25
B)4.25
C)5.25
D)6.25
E)7.25
Rationale: 4.5 4.5
40% 60%
40% ----- 4.5
60% ------? => 6.75 - 4.5 = 2.25 ml
ANSWER:A
Answer: A
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
Options:
A)180
B)128
C)276
D)297
E)236
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer:A
Answer: A
Question: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum Q of all possible 2-digit remainders for x/y?
Options:
A)560
B)616
C)672
D)728
E)784
Rationale: ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
Q=8(2+3+4....+12)=616
Answer: B
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 6x km.
Options:
A)40kmph
B)45kmph
C)48kmph
D)50kmph
E)55kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 6x/(x/8)
= 48 kmph
Answer:C
Answer: C
Question: If a#b = ab – b + b^2, then 3#8 =
Options:
A)80
B)8
C)15
D)21
E)35
Rationale: Solution -
Simply substitute 3 and 8 in equation in the place of a and b respectively.
3#8 = 3*8 - 8 + 8^2 = 24 - 8 + 64 = 80. ANS A
Answer: A
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
Options:
A)76
B)28
C)26
D)20
E)27
Rationale: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is
= 28
Answer:B
Answer: B
Question: A survey is conducted on 800 people from a city. It is found that 6 1% of people surveyed speakHindi, 54.5% people speak Bangla and 37.5% of them speak English. 16.5% people can speak only Hindi and Bangla, 14.5% people can speak only Hindi and English and 6% people can speak only Bangla and English. Answer the following questions based on this information.
How many people are there who can speak only Hindi ?
Options:
A)172
B)174
C)176
D)178
E)179
Rationale: Explanation :
x + y + z + k = 800 - (132 + 116 + 48) = 504 .....(i)
x + k = 488 - (132 + 116) = 240 .....(ii)
y + k = 436 - (132 + 48) = 256 ......(iii)
z + k = 300 - (116 + 48) = 136 .....(iv)
(eqn ll + lll + IV) - eqn (l) gives
2k = (240 + 256 + 136) - 504
2k = 632 - 504 = 128 ∴ k = 64
x = 240 - 64 = 176
y = 256 - 64 = 192
z = 136 - 64 = 72
Answer : Option C
Answer: C
Question: An engine moves at the speed of 60 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 4 coaches are attached speed decreases to 48 kmph.What will be the speed of train when 36 coaches are attached.
Options:
A)24
B)28
C)20
D)32
E)40
Rationale: 1.
No. of coaches =4
sqr root=2
speed decreases by 12
12=k*2
k=6
No. of coaches=36
swr root=6
decrease=6*6=36
New speed=60-36=24
A
Answer: A
Question: Divide 5679 by 7 and find out remainder and quotient ?
Options:
A)901, 5
B)811, 2
C)921, 7
D)805, 4
E)951, 20
Rationale: dividend = divisor * quotient + remainder ===> 5679 = 7 * 811 + 2 ===> remainder = 2 and quot = 811 Ans - B
Answer: B
Question: If a and b are different values and a – b = 3(√a - √b), then in terms of b, a equals:
Options:
A)√b
B)b
C)b - 2√b + 1
D)b - 6√b + 9
E)b^2 – 2b√b + b
Rationale: (√a)^2 - (√b)^2 = 3(√a - √b) -----> ( √a + √b) ( √a - √b) = 3(√a - √b) -------> √a + √b = 3, so
√a = 3 - √b, square both sides and solve.
Answer is D.
Answer: D
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
Options:
A)119
B)125
C)772
D)662
E)812
Rationale: D = 90 * 5/18 * 5
= 125 m
Answer:B
Answer: B
Question: A train passes a station platform in 38 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)180 m
B)200 m
C)270 m
D)320 m
E)None
Rationale: Sol.
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 metres.
Then, x + 300 / 38 = 15 ⇔ x + 300 = 570 ⇔ x = 270 m.
Answer C
Answer: C
Question: The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 220, how many such sequences can be formed?
Options:
A)29
B)17
C)25
D)33
E)50
Rationale: Four consecutive odd numbers: k-2, k, k+2, k+4
Three consecutive even numbers: n-2, n, n+2
k-2+k+k+2+k+4=n-2+n+n+2
4k+4=3n
4(k+1)=3n
k+1=(3/4)n
k=(3/4)n-1
All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:
We know,
101<n<220
104<=n<=216
Count=(216-104)/4+1=212/4+1=28+1=29
Ans: 29.
Answer: A
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
Options:
A)20
B)22
C)25
D)24
E)26
Rationale: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.
ANSWER B
Answer: B
Question: What is the sum of all the multiples of 10 between 0 and 75?
Options:
A)500
B)620
C)450
D)340
E)280
Rationale: The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280.
Final Answer:
E
Answer: E
Question: P,Q and R together earn Rs.1890 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
Options:
A)s.40
B)s.70
C)s.90
D)s.100
E)s.120
Rationale: Explanation :
Amount Earned by P,Q and R in 1 day = 1890/9 = 210 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120	---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130	---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-210 = 40
=>Amount Earned by R in 1 day = 40
Answer : Option A
Answer: A
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 4 runs. His new average is:
Options:
A)64 runs
B)66 runs
C)68 runs
D)70 runs
E)72 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 4
= 11x + 44 = 10x + 108
= x = 64.
New average = (x + 4) = 68 runs.
Answer:C
Answer: C
Question: During a recent track meet, Peter ran x meters of the 100 meter dash in 6 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
Options:
A)6z/x
B)6zx
C)6x/z
D)6/xz
E)xz/6
Rationale: Speed of Peter = x/6 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/6) = 6z/x
Option A
The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: A
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 36 days and B in 18 days, then C alone can do it in?
Options:
A)1
B)7
C)8
D)9
E)6
Rationale: C = 1/4 - 1/36 – 1/18 = 1/6 => 6 days'
Answer: E
Answer: E
Question: An article is bought for Rs.980 and sold for Rs.788, find the loss percent?
Options:
A)16%
B)19%
C)17%
D)13%
E)12%
Rationale: 980 ---- 192
100 ---- ? => 19%
Answer:B
Answer: B
Question: A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
Options:
A)11 hrs
B)8 hrs 5 min
C)7 hrs 45 min
D)9 hrs 20 min
E)None of these
Rationale: Explanation :
Given that time taken for riding both ways will be 2 hours lesser than
The time needed for waking one way and riding back
From this, we can understand that
Time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
Answer : C
Answer: C
Question: Which of the following is between 14/19 and 19/23?
Options:
A)1/3
B)3/8
C)1/2
D)5/8
E)7/9
Rationale: I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:
1) I estimate 14/19 to be ~3/4+ (approximately slightly greater than 3/4)
2) I estimate 19/23 to be ~4/5+ (approximately slightly greater than 4/5)
3) So now I'm looking for an answer choice that is .75 < x < .80
It should be pretty easy to identify which answer choices are less than .75 (or 3/4) if you have had practice with fractions.
A) clearly wrong - it's less than 3/4
B) also clearly wrong - it's less than 3/4
C) also clearly wrong - it's less than 3/4
D) also clearly wrong - it's less than 3/4
I would just stop here and select E. But to verify:
E) 7/9 ~ .77 which is greater than .75 and less than .80
Answer: E
Question: The diameter of a cylindrical tin is 8cm and height is 5 cm. Find the volume of the cylinder?
Options:
A)33
B)45
C)66
D)80
E)21
Rationale: r = 4 h = 5
π * 4 * 4 * 5 = 80 π cc
Answer:D
Answer: D
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent
Options:
A)90%
B)40%
C)100%
D)75%
E)25%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
Answer: C
Question: Which of the following could be the value of x, if |14x – 56| = 196?
Options:
A)-14
B)-18
C)-10
D)10
E)1/4
Rationale: |14x – 56| = 196
=> 14x - 56 = 196
or 14x - 56 = -196
=> 14x = 252 or 14x = -140
=> x = 18 or x = -10
Answer C
Answer: C
Question: What is the remainder when 54487^(42787035) is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: We need to find the units digit of the number.
The units digit of powers of seven repeats 7, 9, 3, and 1 cyclically.
Since 42787035 has the form 4a + 3, the units digit is 3.
Then the remainder when dividing by 5 is 3.
The answer is D.
Answer: D
Question: How many pieces of 85 cm length can be cut from a rod of 42.5 meters long?
Options:
A)50
B)40
C)30
D)20
E)10
Rationale: Number of pieces = 4250/85=850/17=50
Answer is A.
Answer: A
Question: What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits?
Options:
A)53978
B)53916
C)53961
D)56781
E)None of these
Rationale: Explanation:
The greatest 5 digit number that can be formed using the given digits = 74320
The smallest 5 digit number that can be formed using the given digits = 20342
.: The required difference = 74320 - 20342 = 53978
Answer: Option A
Answer: A
Question: How many ounces of a 60% salt solution must be added to 60 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?
Options:
A)16.67
B)30
C)50
D)60
E)70
Rationale: let x=ounces of 60% salt solution to be added
.2*60+.6x=.4(60+x)
x=60
Answer D
Answer: D
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
Options:
A)30, 40
B)25, 30
C)50, 60
D)20, 40
E)35, 45
Rationale: Explanation:
Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
ANSWER IS A
Answer: A
Question: If -4 < x < 4 and -6 < y < 3, which of the following specifies all the possible values of xy?
Options:
A)-42 < xy < 21
B)-42 < xy < 24
C)-28 < xy < 18
D)-24 < xy < 24
E)-24 < xy < 24
Rationale: The least value of xy is a bit more than 4*(-6)=-24 and the largest value of xy is a bit less than (-4)*(-6)=24.
Therefore -24 < xy < 24.
Answer: D.
Answer: D
Question: 9.009/2.002 =
Options:
A)4.05
B)4.50045
C)4.501
D)4.5045
E)4.5
Rationale: 9.009/2.002 = 9009/2002 = 9(1001)/2(1001) = 9/2 = 4.5
The answer is E.
Answer: E
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 33 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
Options:
A)154.
B)172.
C)186.
D)98.
E)142.
Rationale: All of them catch fishes in relation to number 33....
2/3*33+2*33+2*1.5*33*2/3=154
Answer is A
Answer: A
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a even number written on it?
Options:
A)1/12
B)1/10
C)1/8
D)1/42
E)5/9
Rationale: Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same)
P(+ on 1st pick) = 5/10
P(+ on 2nd pick) = 4/9
P(+ on 3rd pick) = 3/8
P(+ on 4rd pick) = 2/7
5/10*4/9*3/8*2/7=1/42
D
Answer: D
Question: If a man crosses a 800 m long street in 5 minutes. What is his speed?
Options:
A)7 km/hr
B)7.1 km/hr
C)7.2 km/hr
D)8 km/hr
E)9.6 km/hr
Rationale: distance = 800 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=800/300=2.67m/s=2.67×18/5 km/hr=9.6 km/hr
E
Answer: E
Question: A number exceeds by 40 from its 3/8 part. Then the number is?
Options:
A)A)32
B)B)24
C)C)64
D)D)40
E)E)45
Rationale: x – 3/8 x = 40
x = 64
ANSWER:C
Answer: C
Question: 1/0.06 is equal to
Options:
A)25.5
B)16.7
C)25
D).25
E)None of these
Rationale: Explanation:
1/0.06 = (1 * 100)/6 = 100/6 = 16.7
Option B
Answer: B
Question: AQ + CD = AAA, where AQ and CD are two-digit numbers and AAA is a three digit number; A, Q, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
Options:
A) 1
B) 3
C) 7
D) 9
E) Cannot be determined
Rationale: Since AQ and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.
So, A=1 and we have 1Q+CD=111
Now, C can not be less than 9, because no two-digit integer with first digit 1 (1Q<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1Q<111).
Hence C=9.
Answer: D.
Answer: D
Question: The sum of three consecutive numbers is 87. The greatest among these three numbers is :
Options:
A)22
B)24
C)26
D)30
E)44
Rationale: Sol.
Let the numbers be x, x + 1 and x + 2.
Then, x + (x + 1) + (x + 2) = 87 ⇔ 3x = 84 ⇔ x = 28.
Greatest number = (x + 2) = 30.
Answer D
Answer: D
Question: P and Q started a business investing Rs 50000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
Options:
A)12:5
B)17:3
C)10:6
D)17:7
E)10:3
Rationale: Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 50000:15000
= 50:15
= 10:3
Option E
Answer: E
Question: Having scored 98 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?
Options:
A)28
B)27
C)26
D)22
E)24
Rationale: Explanation :
Let the average score of the first 18 innings be n
18n + 98 = 19(n+4)=> n = 22
So, Average score after 19th innings = x+4 =26.
Answer : C
Answer: C
Question: Bradley owns b video game cartridges. If Bradley’s total is one-eighth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
Options:
A)33b / 4
B)35b / 4
C)37b / 4
D)39b / 4
E)41b / 4
Rationale: b = Bradley’s total
8b = Andrew’s total
b/4 = Charlie’s total
The total number of cartridges is:
b + 8b+ b/4 = (4b + 32b + b) / 4 = 37b / 4
The answer is C.
Answer: C
Question: What is 2 3/4 - 1 2/5 divided by 2/3 - 1/3 ?
Options:
A)17/36
B)36/17
C)7/6
D)27/20
E)51/44
Rationale: 2 3/4 - 1 2/5 = 11/4 - 7/5 = (55 - 28 )/20 = 27/20
2/3 - 1/3 = (6-3)/3 = 3/3 = 1
So 27/20/1 = 27-20
Answer - D
Answer: D
Question: There are 4 magazines lying on a table; 2 are fashion magazines and the other 2 are sports magzines. If 1 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?
Options:
A)1
B)1/2
C)1/4
D)1/6
E)1/8
Rationale: 1- (2c1/4c1) = 1-1/2 = 1/2
Answer: B
Answer: B
Question: We bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $373. How many math books did we buy?
Options:
A)23
B)27
C)31
D)35
E)39
Rationale: M + H = 80
H = 80 - M
4M + 5H = 373
4M + 5*(80 - M) = 373
M = 27
The answer is B.
Answer: B
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 W 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 W will be 8 - 5 = 3
And answer B
Answer: B
Question: Joan and Karl each bought a TV and the sum of their purchases was $500. If twice of what Joan paid was $40 more than what Karl paid, what did Joan pay for her TV?
Options:
A)$165
B)$170
C)$175
D)$180
E)$185
Rationale: J+K=500 so K=500-J
2J=K+40
2J=(500-J)+40
3J=540
J=180
The answer is D.
Answer: D
Question: Sakshi can do a piece of work in 20 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
Options:
A)15
B)16
C)18
D)25
E)10
Rationale: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 20 : x ⇒ x = (20x4/5) ⇒ x = 16 days.
Hence,Tanya takes 16 days is complete the work.
Answer B
Answer: B
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
Options:
A)508
B)500
C)800
D)570
E)503
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
Answer:B
Answer: B
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.0
B)1.9
C)1.6
D)1.5
E)1.1
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: D
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer T between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
Options:
A)12
B)15
C)17
D)T=18
E)20
Rationale: Since we are concerned with integers between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Answer: D
Question: How many of the integers between 45 and 105 are even ?
Options:
A)21
B)30
C)11
D)10
E)9
Rationale: Number start between 45 to 105 is 60 numbers
half of them is even..which is 30
ANSWER:B
Answer: B
Question: John takes 15 hours to complete a certain job, while Bill takes only 5 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?
Options:
A)2 hours, 5 minutes
B)2 hours, 40 minutes
C)3 hours, 20 minutes
D)3 hours, 45 minutes
E)4 hours, 10 minutes
Rationale: The rate of John plus Bill is 1/15 + 1/5 = 4/15 of the job completed per hour.
If Steve worked at the same rate as John, the rate would be 4/15 + 1/15 = 1/3
The slowest possible time would be 3 hours.
If Steve worked at the same rate as Bill, the rate would be 4/15 + 1/5 = 7/15
The fastest possible time would be 15/7 hours = 2 hours + 1/7 hours.
The actual time is somewhere between these two extreme points.
The answer is B.
Answer: B
Question: A manâ€™s current age is (2/5) of the age of his father. After 5 years, he will be (1/2) of the age of his father. What is the age of father at now?
Options:
A)40
B)25
C)38
D)50
E)39
Rationale: Let, fatherâ€™s current age is A years.
Then, Manâ€™s current age =[ (2/5)A ]years.
Therefore, [ (2/5)A + 5 ]= (1/2)(A + 5)
2(2A + 25) = 5(A + 8)
A = 25
B
Answer: B
Question: If the numbers 1 to 97 are written on 97 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
Options:
A)1/50
B)1/25
C)1/97
D)1
E)2
Rationale: There are 25 primes, 71 composite numbers from 1 to 97. The number
which is neither prime nor composite is 1.
Therefore, required probability = 1/97.
ANSWER:C
Answer: C
Question: Express 30 mps in kmph?
Options:
A)122
B)108
C)110
D)150
E)100
Rationale: 30 * 18/5 = 108 kmph
Answer: B
Answer: B
Question: Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
Options:
A)21 cm
B)19 cm
C)32 cm
D)18 cm
E)28 cm
Rationale: 93 + 123 + 153 = a3 => a = 18
ANSWER:D
Answer: D