divelab/Sys2Bench huggingface dataset:
Question: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 400 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
Options:
A)1.58%
B)1.98%
C)10%
D)15%
E)19%
Rationale: I think there is a typo in question.
It should have been "By weight Liquid 'X ' makes up..... "
Weight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B
When 400gms of A and 700gms of B is mixed :
Weight of Liquid X = (0.8 * 400)/100 + (1.8* 700)/100 = 15.8gms
% of Liquid X in resultant mixture = (15.8/1000) *100 = 1.58%
A
Answer: A
Question: 2 cow’s and 8 goats are brought for Rs.1400. If the average price of a goat be Rs.60. What is the average price of a cow.
Options:
A)Rs. 480
B)Rs.960
C)Rs.960
D)Rs. 460
E)Rs. 560
Rationale: Explanation:
Average price of a goat = Rs.60
total price of 8 goats = 8*60 = Rs.480
But total price of 2 cows and 8 goats = Rs. 1400
Total price of 2 cows is = 1400 - 480
= 980
Average price of a cow = 980/2
= Rs. 460
Answer: Option D
Answer: D
Question: A courtyard is 30 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
Options:
A)22877
B)24000
C)20000
D)27999
E)17799
Rationale: Number of bricks =Courtyard area/1 brick area
=(3000×1600/20×10)=24000
Answer: B
Answer: B
Question: Length of train is 130 meters and speed of train is 45 km/hour. This train can pass a bridge in 30
seconds, then find the length of the bridge.
Options:
A)230 meters
B)235 meters
C)240 meters
D)245 meters
E)None of these
Rationale: ExplanaƟon:
Let the length of bridge is X [as always we do :)]
Speed of train is = 45*(5/18) m/sec = 25/2 m/sec
Time = 30 seconds
Total distance = 130+x
We know Speed = distance/Ɵme
so,
130+x30=252=>2(130+x)=750x=245 meters
So length of the bridge is 245 meters
Answer:D
Answer: D
Question: 7.515/10.02 =
Options:
A) 0.35
B) 0.3505
C) 0.3509
D) 0.351
E) 0.75
Rationale: 7.515 / 10.02
7.515 / 1002 = 7.5
move the comma two places to the left as we have 2 decimal places from the divisor: 0.75. Answer: E
Answer: E
Question: If p/7 = r/2 and r = 0.75s, what is the ratio of p to r to s?
Options:
A)2 : 3 : 4
B)8 : 12 : 9
C)21 : 6 : 8
D)6 : 4 : 3
E)12 : 8 : 3
Rationale: p/7=r/2, r=0.75s, what is p:r:s?
we get p/r=7/2 and r/s=3/4, so
7/3*3/2 and 2/2*3/4
21/6 and 6/8
C
Answer: C
Question: A man sells a horse for Rs.200 and loses something, if he had sold it for Rs.620, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)140
B)162
C)160
D)150
E)71
Rationale: CP = SP + 1CP = SP - g
200 + x = 620 - 2x
3x = 420 => x = 140
Answer:A
Answer: A
Question: (4300331)-?=2535618
Options:
A)1865113
B)1775123
C)1764713
D)1675123
E)None of them
Rationale: Let 4300331-x=2535618
then x=4300331-2535618
=1764713
Answer is C
Answer: C
Question: (2+0.0001)/(0.04+20)
The value of the expression above is closet to which of the following?
Options:
A)0.0001
B)0.001
C)0.1
D)1
E)10
Rationale: Notice that we need approximate value of the fraction.
Now, the nominator is very close to 2 and the denominator is very close to 20, hence the value of the fraction is very close to 2/20=0.1.
Answer: C.
Answer: C
Question: The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages.
Options:
A)30%
B)32.50%
C)33 1/3%
D)40%
E)50%
Rationale: Explanation:
The gain is 4 out of 12 articles.
Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3%
Answer: Option C
Answer: C
Question: A borrowed some money at the rate of 5% p.a. for the first four years, 8% p.a.for the next 8 years and 10% p.a.for the period beyond 12 years If the total interest paid by him at the end of 14 years is 41600, how much money did he borrow?
Options:
A)40,000
B)50,000
C)62,000
D)45,000
E)None of these
Rationale: Let the sum be x. Then,
(x×4×5/100)+(x×8×8/100)+(x×2x10/100)=41600
⇒ 20x + 64x + 20x = (41600 × 100)
⇒ 104x = 4160000
⇒ x = 40000.
Answer A
Answer: A
Question: A batsman makes a score of 85 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
Options:
A)40
B)50
C)62
D)45
E)35
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+85 = 11x
x = 85-50 = 35
Answer is E
Answer: E
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 1/2 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
Options:
A)4/7
B)5/7
C)8/11
D)7/12
E)11/15
Rationale: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (x/2)(3y/4) = 3xy/8
The total number of boxes is xy + 3xy/8 = 11xy/8
The fraction loaded by the day crew is xy / (11xy/8) = 8/11
The answer is C.
Answer: C
Question: There are 10 red balls, 10 blue balls, 15 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
Options:
A)10
B)23
C)43
D)41
E)16
Rationale: The worst case scenario would be if we pick 9 red balls, 9 blue balls, 14 (?) balls and 8 black balls. In this case we'll have 11+9+14+8=40 balls and still won't have all the balls of one color. The next 41rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: D.
Answer: D
Question: If 25% of x is 30 less than 15% of 1500, then x is?
Options:
A)872
B)738
C)837
D)780
E)83
Rationale: 25% of x = x/4 ; 15% of 1500
= 15/100 * 1500 = 225
Given that, x/4 = 225 - 30
=> x/4 = 195 => x = 780.
Answer:D
Answer: D
Question: If Jesse flips a coin five times in a row, what is the probability that the result will be heads at least 3 times?
Options:
A)21/128
B)29/128
C)35/128
D)1/16
E)1/2
Rationale: Question : Atleast 3 heads in 5 flip.
The total outcome of flip is = 2^5 = 32
For any Coins problem write the ask in the shown format.
HHHTT
HHHHT
HHHHH
Once you have written in the above mentioned format the answer is pretty straight.
HHHTT = [5!]/3!*2! = 10
HHHHT = [5!]/4! = 5
HHHHH = [5!]/[5!] = 1
Sum = 10+5+1 = 16/32 = 1/2
Answer - E
Answer: E
Question: How many 3 digits number are there which sum of digits is equal to 16.
Options:
A)63
B)64
C)65
D)66
E)67
Rationale: 100-200=4;
200-300=5;
---------
---------
700-800=10;
800-900=9;
900-999=8;
Total= 66
ANSWER:D
Answer: D
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)12%
C)22%
D)24%
E)21
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds. The ratio of their speeds is:
Options:
A)3 : 1
B)3 : 2
C)2 : 7
D)3 : 25
E)3 : 4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 47 x meters, and length of the second train = 38 y meters. (47 x + 37 y) / (x + y) = 40 ==>
47 x + 38 y = 40x + 40 y ==> 7x = 2 y ==> x/y = 2/7
Answer: Option C
Answer: C
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 14 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
Options:
A)80%
B)105%
C)120%
D)112%
E)138%
Rationale: 0,112R = x/100*0.1R
Answer D
Answer: D
Question: What is the largest integer n such that
n2- 38/n + 1
is an integer?
Options:
A)36
B)38
C)72
D)76
E)None of these
Rationale: Doing the long division algebraically, we get a quotient of n-1 with a remainder of
-37. In order for the division to give an integer, n+1 must divide -37 evenly. So n+1 = 37,
and n = 36.
correct answer A
Answer: A
Question: If 135*s is a perfect square then s can be which of the following numbers?
Options:
A)15
B)35
C)54
D)105
E)150
Rationale: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 135 are 3 *3 *3 *5
1)15 = 3 * 5
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice A completes the pairing of 3, 5 . It adds a3, a5, and a7to the prime factors of 135 (3*3*3*5) and makes it a perfect square. A
Answer: A
Question: Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X?
Options:
A)30%
B)35%
C)40%
D)45%
E)50%
Rationale: The volume of the mixture be X+Y.
0.3X +0.4Y=0.36(X+Y)
X=2Y/3
X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%.
The answer is C.
Answer: C
Question: Grace has 18 jellybeans in her pocket. She has 10 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Options:
A)4
B)8
C)12
D)13
E)15
Rationale: The worst scenario is when she takes 10 red and 4 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.
Answer: E.
Answer: E
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability Q that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
Options:
A)15/64
B)30/64
C)1/2
D)1/4
E)52/64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days Q= 15/64
Ans A it is.
Answer: A
Question: Of the 15 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department?
Options:
A)10
B)20
C)30
D)40
E)45
Rationale: This is ratio problem solving question.
I will prefer to use RMV box.
R M V
Sales 2 5 10
Other 1 5 5
Total 3 5 15
Answer is 10. i.e A
Answer: A
Question: In how many ways can five boys, three girls and a teacher sit in a row such that all boys sit together?
Options:
A)A)10000
B)B)12100
C)C)14400
D)D)1097
E)E)2781
Rationale: Treat all boys as one unit. Now there are four students and a teacher and they can be arranged in 5! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements
= 5! * 5! = 120 * 120
= 14400.
Answer:C
Answer: C
Question: A motorcyclist goes from Nagpur to Delhi, a distance of 600 kms at an average of 60 kmph speed. Another man starts from Nagpur by car 5 Â½ hours after the first, and reaches Delhi Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:7
C)1:9
D)1:5
E)2:5
Rationale: T = 600/60 =10 h
T = 10 - 6 = 4
Time Ratio = 10:4= 5:2
Speed Ratio = 2:5
Answer: E
Answer: E
Question: A boatman can row 3 km against the stream in 20 minutes and return in 9 minutes. Find the rate of current ?
Options:
A)7/2 kmph
B)8/2 kmph
C)5.5 kmph
D)1/2 kmph
E)2/2 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/9 = 20 km/hr
Rate of current = (20-9)/2 = 5.5 km/hr.
Answer: C
Answer: C
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
Options:
A)3.2
B)3.4
C)3.6
D)3.8
E)4
Rationale: 3.6
Option 'C'
Answer: C
Question: A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
Options:
A)4%
B)61/4%
C)20%
D)25%
E)30%
Rationale: Let C.P. of 1 litre milk be Re. 1
Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.
CP of 1 lr = 100/125*1 = 4/5
Ratio of milk to water = 4/5:1/5 = 4:1
=20%
ANSWER C
Answer: C
Question: What is the least integer that is a sum of four different primes each greater than 20?
Options:
A)79
B)83
C)120
D)133
E)169
Rationale: Given integer must be a sum of 4 primes each greater than 20. Thus each prime must be odd.
Therefore sum of Odd + Odd + Odd + Odd = Even
Only Even option is 120
Therefore Ans: C
To verify
120 = 23 + 29 +31 +37
Answer: C
Question: Assisants are needed to prepare for preparation. Each helper can make either 2 large cakes or 35 small cakes/hour. The kitchen is available for 3hours and 20 large cakes and 700small cakes are needed. How many helpers are required?
Options:
A)9
B)10
C)13
D)16
E)18
Rationale: 20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.
B
Answer: B
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
Options:
A)9%loss
B)8%loss
C)3%loss
D)2%loss
E)1%loss
Rationale: (30*30)/100
= 9%loss
Answer: A
Answer: A
Question: If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
Options:
A)Rs.(xy/d)
B)Rs.(yd/x)
C)Rs.(y/d)
D)Rs.(xd)
E)Rs.(x/d)
Rationale: Cost of x metres = Rs. d.
Cost of 1 metre = Rs.	d/x
Cost of y metres = Rs.(d/x)* y= Rs.(yd/x)
Answer is B.
Answer: B
Question: 1370 , 1320 , 1070 , -180 ?
Options:
A)-6440
B)-6680
C)-6480
D)-5480
E)-4480
Rationale: 1370-1320=50 -->50*5=250
1320-250=1070-->250*5=1250
1070-1250=-180-->1250*5=6250
-180-6250=-6430......so ans:-6480
ANSWER:C
Answer: C
Question: Golu started from his house towards North. After covering a distance of 8 km. he turned towards left and covered a distance of 6 km. What is the shortest distance now from his house?
Options:
A)10 km.
B)16 km.
C)14 km
D)2 km.
E)4 km.
Rationale: C-------------B
!
!
!
!
!
A
AB=8 Km BC=6Km
AC=sqrtof(8^2+6^2)
AC=10KM
ANSWER:A
Answer: A
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)49 sec
B)50 sec
C)48 sec
D)43 sec
E)32 sec
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer:C
Answer: C
Question: If the speed of a man is 45 km per hour, then what is the distance traveled by him in 30 seconds ?
Options:
A)275m
B)360m
C)375 m
D)420 m
E)440 m
Rationale: The distance traveled in 30 sec = 45*(5/18) *30 =375m
ANSWER:C
Answer: C
Question: A car travelling 5/7th of its actual speed covers 42 km in 1 hr 40 min 48 sec. what is the actual speed of the car?
Options:
A)22
B)35
C)27
D)10
E)18
Rationale: Explanation:
Let the Actual Speed = x
It is travelling with 5/7 of its actual speed = 5x/7.
Converting the time into seconds = 3600 + 2400 + 48 seconds.
Covers a distance with speed = 42/(3600 + 2400 + 48)
= 424048424048 × 3600 = 25 kph
Given 5x75x7 = 25 kph
So Actual Speed = 25 × (7/5) = 35 kph
Answer:B
Answer: B
Question: In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least one coin of at least three types of coins must be included?
Options:
A)78
B)103
C)118
D)131
E)221
Rationale: This question is similar to determining the number of ways using one of each type of coin, but allows the exclusion of one type.
I. Case I = Four Quarters (100 cents)
Subcase 1= 4 Q, 1 D (110 cents) not allowed as this exceeds $1.05.
Subcase 2= 4 Q, 0 D (100 cents) not allowed since it does not allow for both nickels and pennies.
Case I does not allow any ways.
II. Case II = Three Quarters (75 cents)
This allows for two, one, or zero dimes. Three dimes would bring us up to $1.05, and we wouldn't have room for any pennies or nickels.
Subcase 1 = 3 Q, 2 D (95 cents)
1) one nickel (N) and 5 pennies (P)
2) 2 N and 0 P
3) 0 N and 10 P
Subcase 2 = 3 Q, 1 D (85 cents)
4) 4 N and 0 P
5) 3 N and 5 P
6) 2 N and 10 P
7) 1 N and 15 P
8) 0 N and 20 P
Subcase 3 = 3 Q, 0 D (75 cents)
(5 ways) we could have 1-5 nickels
Case II allows for a total of 13 ways.
III. Case III = Two Quarters (50 cents)
This allows for 0-5 dimes.
Subcase 1 = 2 Q, 5 D (100 cents)
(2 ways) we could have 0-1 nickel
Subcase 2 = 2 Q, 4 D (90 cents)
(4 ways) we could have 0-3 nickels
Subcase 3 = 2 Q, 3 D (80 cents)
(6 ways) we could have 0-5 nickels
Subcase 4 = 2 Q, 2 D (70 cents)
(8 ways) we could have 0-7 nickels
Subcase 5 = 2 Q, 1 D (60 cents)
(10 ways) we could have 0-9 nickels
Subcase 6 = 2 Q, 0 D (50 cents)
(10 ways) we could have 1-10 nickels
Case III allows for a total of 40 ways
IV. Case IV = One Quarter (25 cents)
This allows for 0-7 dimes
Subcase 1 = 1 Q, 7 D (95 cents)
(3 ways) we could have 0-2 nickels
Subcase 2 = 1 Q, 6 D (85 cents)
(5 ways) we could have 0-4 nickels
Subcase 3 = 1 Q, 5 D (75 cents)
(7 ways) we could have 0-6 nickels
Subcase 4 = 1 Q, 4 D (65 cents)
(9 ways) we could have 0-8 nickels
Subcase 5 = 1 Q, 3 D (55 cents)
(11 ways) we could have 0-10 nickels
Subcase 6 = 1 Q, 2 D (45 cents)
(13 ways) we could have 0-12 nickels
Subcase 7 = 1 Q, 1 D (35 cents)
(15 ways) we could have 0-14 nickels
Subcase 8 = 1 Q, 0 D (25 cents)
(15 ways) we could have 1-15 nickels
Case IV allows for a total of 78 ways.
IV. Case V = Zero Quarters (0 cents)
This allows for 1-9 dimes
Subcase 1 = 0 Q, 9 D (90 cents)
(2 ways) we could have 1-2 nickels
Subcase 2 = 0 Q, 8 D (80 cents)
(4 ways) we could have 1-4 nickels
Subcase 3 = 0 Q, 7 D (70 cents)
(6 ways) we could have 1-6 nickels
Subcase 4 = 0 Q, 6 D (60 cents)
(8 ways) we could have 1-8 nickels
Subcase 5 = 0 Q, 5 D (50 cents)
(10 ways) we could have 1-10 nickels
Subcase 6 = 0 Q, 4 D (40 cents)
(12 ways) we could have 1-12 nickels
Subcase 7 = 0 Q, 3 D (30 cents)
(14 ways) we could have 1-14 nickels
Subcase 8 = 0 Q, 2 D (20 cents)
(16 ways) we could have 1-16 nickels
Subcase 9 = 0 Q, 1 D (10 cents)
(18 ways) we could have 1-18 nickels
Case V allows for a total of 90 ways.There's no other case, because we have to have at least one quarter or one dime. The total over the cases equals
Total = 0 + 13 + 40 + 78 + 90 =221 ways.
OA =(E)
Answer: E
Question: What is the sum of all digits for the number 10^28 - 44?
Options:
A)233
B)245
C)257
D)270
E)285
Rationale: 10^28 is a 29-digit number: 1 followed by 28 zeros.
10^28 - 44 is a 28-digit number: 26 9's and 56 at the end.
The sum of the digits is 26*9+5+6=245.
The answer is B.
Answer: B
Question: 8 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
Options:
A)1:2
B)1:3
C)2:1
D)2:3
E)None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 8x + 2y = 4(x+y)
=> 4x = 2y
=> x/y = 2/4
=> x:y = 1:2
Option A
Answer: A
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 14 mat-weavers in 14 days?
Options:
A)25
B)19
C)39
D)61
E)49
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	14 :: 4 : x
Days	4:14
4 * 4 * x = 14 * 14 * 4
x =	(14 * 14 * 4)/(4 x 4)
x = 49.
Answer is E.
Answer: E
Question: If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true?
I. xa= y
II. y = 1
III. a and y are prime integers.
Options:
A) None
B) I only
C) II only
D) III only
E) I and II
Rationale: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2).
I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2);
II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2);
III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2).
Answer: A.
Answer: A
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 3. Their L.C.M. is
Options:
A)48
B)22
C)56
D)27
E)36
Rationale: Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 3.
So, the numbers 9 and 12.
L.C.M. of 9 and 12 = 36.
Answer: Option E
Answer: E
Question: A girl sitting in a train which is travelling at 40 kmph observes that a goods train travelling in a opposite direction, takes 12 seconds to pass him. If the goods train is 1120 m long, find its speed.
Options:
A)295
B)296
C)297
D)298
E)299
Rationale: Relative speed = (1120/12)m/s = (1120/12)*(18/5) = 336 kmph
speed of goods train = 336-40 = 296 kmph
Answer is B
Answer: B
Question: There are 32 students in a class. Nine of those students are women. What percent are men? (round to the nearest tenth)
Options:
A)70.9%
B)71.9%
C)72.9%
D)73.9%
E)74.9%
Rationale: Total 100% 32
Men 23
Women 9
32-9=23
x/100=23/32
Multiply the opposites:
100 x 23 = 2300
Divide by the remaining number:
71.87/2300.00
32
71.9%(rounded to nearest tenth)
correct answer B
Answer: B
Question: There are 20 states in a certain country and every pair of them is connected by a road way. How many road ways are there?
Options:
A)22
B)277
C)288
D)266
E)2A1
Rationale: Answer:A
Answer: A
Question: At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?
Options:
A)24min
B)14min
C)74min
D)54min
E)44min
Rationale: In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5
Answer: A
Answer: A
Question: If (x + 1)(x + 3) = x^2 + x, what is a possible value of x?
Options:
A) 2
B) 3
C) -1/3
D) -3
E) -1
Rationale: Rearranging the given expression:
(x + 1)(x + 3) = x^2 + x
i.e. x^2 + 4x + 3 = x^2 + x
i.e. 3x = -3
i.e. x = -3/3 = -1
Answer: Option E
Had it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible.
Answer: E
Question: In how many ways can 4 black and 4 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
Options:
A)144
B)24
C)576
D)48
E)16
Rationale: 4 black chess pieces can be arranged in 4! ways and 4 white pieces can be arranged in 4! ways.
W_W_W_W
Number of ways = 4!*4! = 24 * 24 = 576
Answer C
Answer: C
Question: The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is z, then
Options:
A)x = y + z
B)2x = y + z
C)x = 2y + z
D)x = y + 2z
E)None of these
Rationale: Explanation:
X =((3y+3z)/6)
or
2X= y + z
Option B
Answer: B
Question: The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 406 lbs, how much does substance x weigh?
Options:
A)68
B)76
C)84
D)92
E)110
Rationale: x:y=4:6
if the ratio is halevd then x:y=2:6
The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.
x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)
so x:y:z= 12:36:10
and we know x + y + z = 406 lbs
from the ratio of x ,y and z we have x=12k y=36k z=10K
put it in the equation we have 12k+36k+10k=406
k=7
Hence x=12(7)=84
Ans C
Answer: C