mathewhe/aqua_rat huggingface dataset:
Question: In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 1/4
(E) 3/4
Rationale: (1/2)G=(1/3)(B+G)
3G=2B+2G
G=2B
B/G=1/2.
The answer is A.
Answer: (A) 1/2
Question: The length and the breadth of a rectangle are in the ratio of 3 : 2 respectively. If the sides of the rectangle are extended on each side by 1 metre, the ratio of length to breadth becomes 10 : 7. Find the area of the original rectangle in square metres.
(A) 256
(B) 150
(C) 280
(D) Data inadequate
(E) None of these
Rationale: Let the length and breadth be l and b respectively.
l⁄b = 3⁄2 or l = 3⁄2b .....(i)
l+1/b+1=10/7 or 7l - 10b = 3 .....(ii)
From eq. (i)
10.5b – l 0b = 6 or, 0.5b = 3 or, b = 6 and l = 9
Area = l × b = 6 × 9 = 54 m2
Answer E
Answer: (E) None of these
Question: If m > 0 and x is m/10 of y, then, in terms of m, y=?x
(A) a) 100m
(B) b) 1/100m
(C) c) 1/m
(D) d) 100/m
(E) e) 10,000/m
Rationale: x= m/10 * y
So y= 10/m * x
So y= (100/m)/10 * x
D
Answer: (D) d) 100/m
Question: The ratio of boys to girls in Class A is 5 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
(A) 8
(B) 7
(C) 10
(D) 11
(E) 12
Rationale: Since it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.
so ans can either be 8 0r 12.
With 8 as answer - no of girls = 8
With 12 as answer - no of girls = 12
Now Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5.
So we are looking for number of girls in B to be divisible by 5.
With 8 as answer -> Girls = 8-2 = 6. (Not possible)
With 12 as answer -> Girls = 12-2 = 5.
So, answer = 7. ( B)
Answer: (B) 7
Question: According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 29, by how much does the temperature in degrees Celsius (C) increase?
(A) 9
(B) 15
(C) 47
(D) 48 3/5
(E) 59
Rationale: You can plug in values.
C = 5/9*(F-32)
F=32 --> C=0;
F=32+29=61 --> C=5/9*29=16.11.
Increase = 16.11 degrees.
Answer: B.
Answer: (B) 15
Question: Find a a prime number from the options below.
(A) 86
(B) 87
(C) 88
(D) 89
(E) 90
Rationale: Clearly, 89 is a prime number.
D
Answer: (D) 89
Question: If an integer x is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that x(x + 1)(x + 2) will be divisible by 8?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/4
(E) 5/8
Rationale: I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 8 = Integer, therefore we have 48 / 96 numbers divisible by 8
O E O / 8 = Not Integer
We cannot forget multiples of 8 from 1 to 96
We have 12 numbers that are multiple of 8
Therefore, 48/96 + 12/96 = 60/96 = 5/8
answer : E
Answer: (E) 5/8
Question: 9 friends are living in 9 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 9 parking spots. In how many ways can they park their cars so that exactly 7 people park their cars in the spots allotted to them?
(A) 24
(B) 36
(C) 48
(D) 60
(E) 72
Rationale: 9C7 = 36
The remaining 2 people in each case will be parked in each other's parking spots.
The answer is B.
Answer: (B) 36
Question: Machine A can print one lakh books in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All the three machines start job at 9.00 am. A breaks down at 11.00 am and the other two machines finish the job. Approximately at what time will the job be finished?
(A) 12.00 noon
(B) 1.30 pm
(C) 1.00 pm
(D) 11.30 am
(E) None of these
Rationale: Part of print done by A, B and C in 2 hours = 2(1⁄8 + 1⁄10 + 1⁄12) = 37⁄60
Remaining = 1 - 37⁄60 = 23⁄60
If B and C print together, then they can print in 10×12/10+12
Therefore, remaining part can be printed by
B and C in 10×12/22×23/60 ≈ 2 hrs.
Hence, the job will be finished at
9 am + 2 + 2 = 1.00 p.m.
Answer C
Answer: (C) 1.00 pm
Question: A coin is tossed 5 times, Probability of getting
head exactly 3 times is:
(A) 0.3125
(B) 0.4125
(C) 0.5125
(D) 0.6125
(E) 0.7125
Rationale: coin tossed 5 times so 2*2*2*2*2=32
getting heads only in 3 times=HHHHH,HHHHT,HHHTT,HHTTH,HTTHH,TTHHH,THHHT,THHTH,THTHH,HTHTH=10
PROBABILITY=10/32=0.3125.
ANSWER:A
Answer: (A) 0.3125
Question: In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 150 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
(A) 40 ml
(B) 100/3 ml
(C) 30 ml
(D) 20/3 ml
(E) 10 ml
Rationale: There are 0.3*100=30 ml of element X in the initial solution.
We need X to be 1/3rd of 150 ml in the resulting solution, so 50 ml. Thus out of 50 ml of solution added, 20 must be X (in order it to become 50 ml) ans the remaining 30 must be Y.
Answer: C
Answer: (C) 30 ml
Question: A milk man makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase?
(A) 30
(B) 40⁄3
(C) 22
(D) 10
(E) None of these
Rationale: Let profit per litre = 20
So, C.P. /litre = 100
S.P. / litre = 120
On adding 10% water to the milk
C.P. / 9⁄10 litre = 100
S.P. / 9⁄10 litre = 120
S.P / litre = 120×10/9=400/3
⇒ Profit / litre = 400⁄3 - 100 = 33.33
% by which profit increases = 33.33 – 20 = 13.3
Answer B
Answer: (B) 40⁄3
Question: What least number must be added to 696, so that the sum is completely divisible by 20 ?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: If we divide 696 by 20 remainder is 16
20 - 16 =4
Answer : B
Answer: (B) 4
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
(A) Rs.17
(B) Rs.12
(C) Rs.15
(D) Rs.29
(E) Rs.19
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6
= Rs.15.
Answer:C
Answer: (C) Rs.15
Question: Replace the ? by the correct Mathematics symbol to make the expression true 15 ? 3 ? 3 ? 5 = 20
(A) 15 ÷ 3 x 3 - 5 = 20
(B) 15 + 3 ÷ 3 + 5 = 20
(C) 15 x 3 + 3 + 5 = 20
(D) 15 x 3 ÷ 3 + 6 = 20
(E) 15 x 3 ÷ 3 + 5 = 20
Rationale: Answer : E
Answer: (E) 15 x 3 ÷ 3 + 5 = 20
Question: Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.
(A) √3:1
(B) √7:1
(C) √2:1
(D) 2:1
(E) 3:1
Rationale: Explanation:
Let their heights be h and 2h and radii be r and R respectively then.
πr2h=πR2(2h)
=>r2/R2 = 2h/h
=2/1
=>r/R = √2/1
=>r:R = √2:1
ANSWER IS C
Answer: (C) √2:1
Question: How many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
(A) 14
(B) 13
(C) 12
(D) 8
(E) 10
Rationale: The number = 2a + 3b < 20
When a = 1, b = 1, 2, 3, 4, 5 -> 2a = 2; 3b = 3, 6, 9-> the number = 5, 8, 11 --> 3 numbers
when a =2, b = 1,2,3-> ....--> 3 numbers
when a =3, b = 1,2,3,4 --> ....--> 2 numbers
Total number is already 8. Look at the answer there is no number greater than 8 --> we dont need to try any more
Answer must be D
Answer: (D) 8
Question: If [x] is the greatest integer less than or equal to x, what is the value of [-2.6]+[1.4]+[2.7]?
(A)  0
(B)  1
(C)  2
(D)  6
(E)  7
Rationale: You are asked what the closest lesser integer value to [x] is.
[-2.6] = -3.0
[1.4] = 1.0
[2.7] = 2.0
Therefore , answer is: -3.0 + 1.0 + 2.0 = 0.0
Option A.
Answer: (A)  0
Question: A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 11
(B) 49
(C) 88
(D) 65
(E) 22
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 ==> x
= 49 km/hr.
Answer:B
Answer: (B) 49
Question: What is the remainder when 1201 × 1202 ×1203 × 1204 is divided by 6?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The remainders when dividing each number by six are: 1, 2, 3, and 4.
The product is 1*2*3*4 = 24
The remainder when dividing 24 by 6 is 0.
The answer is A.
Answer: (A) 0
Question: What is the perimeter of a square field whose diagonal is 8√2?
(A) 82 m
(B) 32 m
(C) 27 m
(D) 26 m
(E) 76 m
Rationale: 4a = 32 m
Answer: B
Answer: (B) 32 m
Question: A person buys an article at $1200. At what price should he sell the article so as to make a profit of 40%?
(A) 1670
(B) 1600
(C) 1680
(D) 1900
(E) 1230
Rationale: C
1680
Cost price = $1200
profit = 40% of 1200 = $480
Selling price = Cost price + Profit
= 1200 + 480 = 1680
Answer: (C) 1680
Question: There is a sufficient food for 200 men for 20 days after 15 days 100 men leave the place. For how many days will the rest of the food last for the rest of the men?
(A) 10 days
(B) 5 days
(C) 15 days
(D) 12 days
(E) 10 days
Rationale: Explanation:
After 13 days , 100 men left,
Therefore 5 days*200 men =x days*100men
X = 10 days
Answer: Option A
Answer: (A) 10 days
Question: Nelly made a part payment of $875 toward buying a brand new refrigerator, which represents 25% of the total cost of the refrigerator, how much remains to be paid?
(A) $2225
(B) $2782
(C) $1625
(D) $2629
(E) $2625
Rationale: Explanation:
Let's start with what the total price of the refrigerator would be. If 25% is equal to $875 then 100% equals $x. We just have to multiply $875 by 4 to get total amount=$3500. Out of this amount we then need to deduct the amount already paid which was $875 so we have $3500-$875=$2625
Answer: Option E
Answer: (E) $2625
Question: If 2^(2w) = 8^(w−4), what is the value of w?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: 2^(2w) = 8^(w−4)
2^(2w) = 2^(3*(w−4))
2^(2w) = 2^(3w-12)
Let's equate the exponents as the bases are equal.
2w = 3w-12
w = 12
The answer is D.
Answer: (D) 12
Question: Salesperson A's compensation for any week is $260 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?
(A) $6000
(B) $8000
(C) $10,000
(D) $12,000
(E) $14,000
Rationale: 260+0.06(x-1000) = 0.08x
0.02x = 200
x = $10,000
The answer is C.
Answer: (C) $10,000
Question: A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km per hour. Find the distance travelled on foot.
(A) 26 km
(B) 32 km
(C) 30 km
(D) 28 km
(E) None
Rationale: Total Time = 7hrs
Let the distance travelled by foot @ 8kmph be x kms
? distance travlled by bicycle @ 16kmph be (80-x)kms
ATQ. 7hr = x/8 + (80-x)/16
? 7 = (2x + 80 - x)/16
? x = 32kms
Answer: B.
Answer: (B) 32 km
Question: Express a speed of 30 kmph in meters per second?
(A) 10 mps
(B) 8 mps
(C) 9 mps
(D) 7 mps
(E) 12 mps
Rationale: 30 * 5/18
= 8 mps
Answer:B
Answer: (B) 8 mps
Question: Anusha, Banu and Esha run a running race of 100 meters. Anusha is the fastest followed by Banu and then Esha. Anusha, Banu and Esha maintain constant speeds during the entire race. When Anusha reached the goal post, Banu was 10m behind. When Banu reached the goal post Esha was 10m behind. How far was behind Anusha when the latter reached the goal post.
(A) 22
(B) 88
(C) 81
(D) 66
(E) 22
Rationale: By that time Anusha covered 100m, Bhanu covered 90m. So ratio of their speeds = 10 : 9
By that time Bhanu reached 100m, Esha covered 90m. So ratio of their speeds = 10 : 9
Ratio of the speed of all the three = 100 : 90 : 81
By that time Anusha covered 100m, Esha Covers only 81.
Answer:C
Answer: (C) 81
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 35% profit on the cost of the item?
(A) 18
(B) 21.6
(C) 22
(D) 22.5
(E) 27.7
Rationale: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 35% of the final price --> (final price)*0.65 = $18 --> (final price) = $27.7.
Answer: E.
Answer: (E) 27.7
Question: n^(n/2)=2 is true when n=2 in the same way what is the value of n if n^(n/2) =12?
(A) 12
(B) 6
(C) 14
(D) 16
(E) 10
Rationale: n^(n/2)=12Apply logN/2logn=log12nlogn=2log12=log12^2=log144Logn=log144Now apply antilogn= 144/nNow n=12ANSWER:A
Answer: (A) 12
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts five hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 3
(B) 4.5
(C) 4
(D) d) 10
(E) e) 5
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 5+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(5+T) = 40*T
T = 15 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*15/60 = 10 hrs
Time taken by A = 5+T = 5+15 = 20 hrs
Time taken by K = 10 hrs
So K starts 20-10 = 10 hrs after A. (answer D)
Answer: (D) d) 10
Question: What is the product of the greatest 2 digit multiple of 5 and the greatest 2 digit prime number?
(A) 9,310
(B) 9,408
(C) 9,506
(D) 9,603
(E) 9,702
Rationale: the greatest 2 digit multiple of 5: 95
the greatest 2 digit prime numebr: 97
97*98.
A)9,310
Answer: (A) 9,310
Question: How many possible ways are there to select 2 stocks at random from 11 stocks?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: 11C2 = 55
The answer is E.
Answer: (E) 55
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is ?
(A) 948
(B) 876
(C) 768
(D) 658
(E) 958
Rationale: P.W. = (100*T.D)/(R*T) = (100*168)/(14*2) = 600 Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768. Answer : C
Answer: (C) 768
Question: Ada's income is 60 percent more than Adelaide's income, and Adelaide's income is 50 percent less than Bella's income. What percent of Bella's income is Ada's income?
(A) 86%
(B) 30%
(C) 50%
(D) 90%
(E) 80%
Rationale: Bella's income = 100 (assume);
Adelaide's income = 50 (50 percent less than Bella's income);
Ada's income = 80 (60 percent more than Adelaide's income).
Thus, Ada's income (80) is 80% of Bella's income (100).
Answer: E
Answer: (E) 80%
Question: If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was
(A) Rs 1.56
(B) Rs 2.40
(C) RS 3.00
(D) Rs 3.80
(E) Rs 4.20
Rationale: first 1/5 mile costs = 1.00
remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14,
hence 14*0.20=2.80
total fare = 2.80 + 1.00 =3.80
ANSWER:D
Answer: (D) Rs 3.80
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 136, then the number of hens will be
(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 = 48
=> h + c = 48 ---(Equation 1)
number of feet = 136
=> 2h + 4c = 136
=> h + 2c = 68 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 68 - 48
=> c = 20
Substituting the value of c in Equation 1, we get
h + 20 = 48
=> h = 48 - 20 = 28
i.e., number of hens = 28
Answer : E
Answer: (E) 28
Question: Which of the following equations has a solution in common with x^2 + 14x + 33 = 0?
(A) 3x^2 - 5x - 2 = 0
(B) -x^2 - 3x + 28 = 0
(C) -x^2 - 2x + 99 = 0
(D) 3x^2 + 30x + 27 = 0
(E) none of the above
Rationale: Given : x^2 + 14x + 33 = 0 => (x+3) (x+11) = 0 => -3 and -11 are the roots..
A. 3x^2 - 5x - 2 = 0 => (x-2) (3x+1)
B. -x^2 - 3x + 28 = 0 => (-x+7) (x+4)
C. -x^2 - 2x + 99 = 0 => (x+11) (-x+9)
D. 3x^2 + 30x + 27 = 0 => (x+9) (3x+3)
None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.
So IMO "C" is correct answer... because it shares the one root (part of the solution), (-11), from the (x+11) portion of its simplification.
Answer: (C) -x^2 - 2x + 99 = 0
Question: The Q train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Q train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
(A) 1.8m
(B) 6m
(C) 7m
(D) 9m
(E) 12m
Rationale: The reason it is failing for you is that you chose incorrect numbers. If the question says it Q took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.
If you take such numbers you can solve problem.
AB = 7, BC=5
Therefore
AB-BC = 2
But from question, AB-BC =m
=> m=2
Now total distance = AB+BC= 12
Substitute 12 to get answer in terms of m
Total distance =12 =6m
Ans B
Answer: (B) 6m
Question: There are 16 teams divided in 4 groups. Every team from each group will play with each other once. The top 2 teams will go to the next round and so on the top two teams will play the final match. Minimum how many matches will be played in that tournament?
(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
Rationale: In each group, total matches played = 4C24C2 = 6.
So total matches played in the first round = 6 × 4 = 24
Now top two teams from each group progress to the next round. Now these 8 teams are pooled into 2 groups. Total matches played in the second round = 6 × 2 = 12
Now 4 teams progress to the next round. Total matches played in the third round = 6
From this round, 2 teams progress to the next round. And final will be played between them.
Total matches = 24 + 12 + 6 + 1 = 43
Answer:A
Answer: (A) 43
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 48
(B) 50
(C) 64
(D) 70
(E) 80
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: There are 16 bees in the hive , then 8 more fly. How many bees are there in all?
(A) 7
(B) 33
(C) 12
(D) 24
(E) 25
Rationale: 16+8=24 . Answer is D.
Answer: (D) 24
Question: Two boys starts from the same place walking at the rate of 4 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 10.5 km apart?
(A) 8
(B) 5
(C) 7
(D) 9
(E) 6
Rationale: Explanation:
Relative speed = 5.5 - 4 = 1.5 kmph (because they walk in the same direction)
distance = 10.5 km
time = distance / speed=10.5/1.5=7 hr
Answer :C
Answer: (C) 7
Question: A cistern 5m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49 m2
(B) 42.5 m2
(C) 53.5 m2
(D) 55 m2
(E) 57 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 5 x 1.25) + 5 x 4] m2
= 42.5 m2.
Answer: Option B
Answer: (B) 42.5 m2
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
(A) 22
(B) 27
(C) 88
(D) 76
(E) 16
Rationale: Sum of the 10 numbers = 230
If each number is increased by 4, the total increase =
4 * 10 = 40
The new sum = 230 + 40 = 270 The new average = 270/10 = 27.
Answer: B
Answer: (B) 27
Question: If n is an integer, then the least possible value of |48 - 7n| is?
(A) 1
(B) 0
(C) 5
(D) 4
(E) 2
Rationale: |48 - 7n| represents the distance between 48 and 7n on the number line. Now, the distance will be minimized when 7n, which is multiple of 7, is closest to 48. Multiple of 7 which is closest to 48 is 49 (for n = 7), so the least distance is 1: |48 - 49| = 1.
Answer: A.
Answer: (A) 1
Question: If 24 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
(A) 276
(B) 350
(C) 425
(D) 512
(E) 648
Rationale: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.
The number of ways to select 2 lines from 24 lines is 24C2 = 276
The answer is A.
Answer: (A) 276
Question: A password for a computer uses eight digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
(A) 1/32
(B) 1/16
(C) 1/8
(D) 2/5
(E) 1/256
Rationale: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 × 10 × 10× 10 × 10 × 10 = 100,000,000 possible combinations.
Prime numbers constitute 2, 3, 5, 7, 11, 13 and 17. In addition to zero, this is 5 total possibility for each digit. So the number of satisfactory variants is 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 . So the probability is 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/256.
The right answer is choice (E).
Answer: (E) 1/256
Question: Evaluate 100 / .25
(A) 400
(B) 510
(C) 500
(D) None of these
(E) 506
Rationale: Explanation:
100/.25 = 10000/25 = 400
Option A
Answer: (A) 400
Question: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in five hours, what fraction of the room can Joseph paint in 20 minutes?
(A) 1/5x
(B) x/(x-3)
(C) (x-5)/15x
(D) x/(x-5)
(E) (x-5)/x
Rationale: Let J be Joseph's rate per hour.
1/x + J = 1/5 of a room per hour
J = 1/5 - 1/x, of a room per hour
In 20 minutes, Joseph can paint 1/3*(1/5-1/x) = 1/15-1/3x = (x-5)/15x
The answer is C.
Answer: (C) (x-5)/15x
Question: A start walking from a place at a uniform speed of 7 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.
(A) 4.7 kmph
(B) 7.6 kmph
(C) 4 kmph
(D) 7 kmph
(E) 5.3 kmph
Rationale: Distance covered by A in 30 min = 1 Km
B covers extra 1km in 1 hour 48 minutes (9/5 hr)
i.e. Relative speed of B over A = 1/(9/5) = 5/9
So the speed of B = Speed of A + 5/9
= 7 + 5/9
= 7.55
Answer B
Answer: (B) 7.6 kmph
Question: In 1 hour, a boat goes 5 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is :
(A) 3 km/hr.
(B) 2 km/hr.
(C) 6 km/hr.
(D) 8 km/hr.
(E) 5 km/hr.
Rationale: Speed in still water = 1/2(5 + 5) km/hr
= 5 km/hr. ANSWER :E
Answer: (E) 5 km/hr.
Question: In 1950, Richard was 4 times as old as Robert. In 1955, Richard was 3 times as old as Robert. In which year was Richard 1.6 times as old as Robert?
(A) 1960
(B) 1965
(C) 1970
(D) 1975
(E) 1990
Rationale: In 1950: Ri = 4 Ro -------------- eq1
In 1955: Ri +5 = 3(Ro+5)---------eq2
Thus in 1950, solving eq1 and eq2
1950 Ro= 10 , Ri =40
1990 Ro= 50 , Ri =80 =1.6 times
Thus Ans:E
Answer: (E) 1990
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 19
(B) 10
(C) 14
(D) 17
(E) 15
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: B
Answer: (B) 10