mathewhe/aqua_rat huggingface dataset:
Question: CP of 2 buffaloes are Rs30,000. By selling 1 at a loss of 15% and other at a profitof 19%, he foundthat SP of both buffaloes is the same. Find the CP of each?
(A) Rs. 8,500
(B) Rs.10,500
(C) Rs.11,000
(D) Rs.11,500
(E) Rs.12,500
Rationale: Let the C.P of 1st buffalo = x
∴C.P of 2nd buffalo = 30,000 - x
S.P of 1st buffalo = ( 100 - loss% )
------------------- x C.P
100
S.P = 100 - 15x
-----------= 85x/ 100
100
S.P of 2nd buffalo = ( 100 - Profit%)
--------------------- x C.P
100
S.P = (100 + 19)(30,000- x) 119(30,000 -x)
-------------------- = ----------------
100 100
S.P of 1st buffalo = S.P of 2nd buffalo
85x/ 100 = 119 ( 30,000 - x)/ 100
⇒ 85x = 119(30,000 - x)
⇒ 85x = 3,570,000 - 119x
⇒ 85x + 119 x = 3,570,000
⇒ 204x = 3,570,000
⇒ x = 3,570,000 / 204
⇒ x = Rs.17,500
C.P of 1st buffalo = Rs.17,500
C.P of 2nd buffalo = 30,000 - 17,500 = Rs.12,500
E
Answer: (E) Rs.12,500
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 1. If p is any prime number then f(p)=
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.
Answer: A.
Answer: (A) p-1
Question: There was a grandmother in a village that had a grandchild. Upon asking her grandchild’s age she told that she is as older as many days old as her daughter’s age in weeks and as many days as her own age in years. The sum of the ages of three is 130. Then how old is the child?
(A) 127
(B) 117
(C) 137
(D) 147
(E) 157
Rationale: let the ages be a,b and c of grandmother,daughter and granddaughter respectively.
we have 3 equations as:
52b=365c
and a=365c
also,a+b+c=130
solving this,i m getting age of granddaughter about 127 days.
ANSWER:A
Answer: (A) 127
Question: How many different positive numbers smaller than 2∗10^8 can be formed using the digits 1 and 2 only?
(A) 256
(B) 510
(C) 512
(D) 766
(E) 6561
Rationale: Any combination of number starts with digit "2" is greater than 2*10^8
Total possible combinations with 1 and 2 = 2^9
Total possible combinations with 2 as starting digit = 2^8
Numbers smaller than 2*10^8 can be formed = 2^9 - 2^8
= 2^8(2-1)
= 256.
Answer : A
Answer: (A) 256
Question: In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 15 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?
(A) 124
(B) 135
(C) 146
(D) 157
(E) 168
Rationale: Initially the number of gold coins and silver coins is 2k and 6k.
After adding gold coins, the number of coins is 3k and 6k.
Thus k = 15 and the total number of coins is 9k = 135.
The answer is B.
Answer: (B) 135
Question: Given that p/q < 1, and both p and q are positive integers, which one of the following must be greater than 1?
(A) p/q^2
(B) p^2/q
(C) p^2/q^2
(D) q/p
(E) √(p/q)
Rationale: Since p/q is a fraction q must always be > 1
Given -
Which one of the following must be greater than 1
We can get the result one only when the denominator in p/q ( Which is less than 1 ) becomes numerator..
Among the given options only (D) has the required characteristic we are looking for...
Hence answer will be (D)
Answer: (D) q/p
Question: A , B , C start a business each investing Rs 20,000 . After 5 month A withdraws Rs 5000, B withdraws Rs 4000 & C invests Rs 6000 more . At the end of the year, a total profit of Rs 69900 was recorded . Find the share of A
(A) 20600
(B) 20700
(C) 20500
(D) 20400
(E) None of these
Rationale: Explanation :
A : B : C = (20000*5 +15000*7) : (20000*5 +16000*7) : (20000*5 +26000*7)
= (20*5 + 15*7) : (20*5 + 16*7) : (20*5 + 26*7)
= 205 : 212 : 282
A's share = 69900 * 205/(205+212+282) = 69900*205/699 = 20500. Answer : Option C
Answer: (C) 20500
Question: A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 224 customers. How many more new tables than original tables does the restaurant have?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: If all the tables seated 4, the number of customers could be 4*40 = 160.
224-160 = 64, so 64/2 = 32 tables must be new tables seating 6 people.
The number of tables seating 4 people is 40-32 = 8.
The number of new tables is 32-8 = 24 more than the number of old tables.
The answer is D.
Answer: (D) 24
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates?
(A) 56
(B) 120
(C) 210
(D) 1120
(E) 6720
Rationale: 8 total employees 5 potential executives. = 8!/5!3! = 56
Those 5 executives are made up of P, T, W,W,W. Use an anagram grid here to determine the total here. = 5!/3! = 20.
Multiply 56 by 20 and your answer is 1120.
ANS:D.
Answer: (D) 1120
Question: In a box, there are 8 red, 5 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
(A) 2/3
(B) 8/21
(C) 3/7
(D) 9/22
(E) 8/19
Rationale: Explanation:
Total number of balls = (8 + 5 + 6) = 19
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/19.
Answer: Option E
Answer: (E) 8/19
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment R that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
(A) a. 3/5
(B) b.2/3
(C) c.7/10
(D) d.3/4
(E) e.4/5
Rationale: X(10) --- Net(0) --- R(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Answer: (A) a. 3/5
Question: What is the total surface area in square meters of a rectangular solid whose length is 10 meters, width is 9 meters, and depth is 6 meters?
(A) 400 m2
(B) 404 m2
(C) 408 m2
(D) 401 m2
(E) 412 m2
Rationale: Surface Area of a cuboid = 2(lb+bh+lh) = 2(10*9+9*6+10*6)=2(90+54+60)=2*204=408 m2
Answer : C
Answer: (C) 408 m2
Question: An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
(A) 28,000 degrees / second
(B) 58,000 degrees / second
(C) 18,000 degrees / second
(D) 38,000 degrees / second
(E) 88,000 degrees / second
Rationale: 3000 revolutions / minute
= 3000*360 degrees / 60 seconds
= 18,000 degrees / second
correct answer C
Answer: (C) 18,000 degrees / second
Question: The list price of an article is Rs.70. A customer pays Rs.61.74 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 8%
(B) 7%
(C) 10%
(D) 2%
(E) 4%
Rationale: Explanation:
70*(90/100)*((100-x)/100) = 61.74
x = 2%
Option D
Answer: (D) 2%
Question: Find the area of circle whose radius is 5m?
(A) 78.57
(B) 81.54
(C) 71.77
(D) 72.88
(E) 72.98
Rationale: 22/7 * 5 * 5
= 78.57
Answer:A
Answer: (A) 78.57
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $33. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) xy/297
(B) 11xy/3
(C) 3xy/11
(D) 297/(xy)
(E) 297xy
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 33 / (xy/9) = 297/(xy).
The answer is D.
Answer: (D) 297/(xy)
Question: Find the number of ways in which 3 different beads can be arranged to form a necklace.
(A) 30
(B) 20
(C) 1
(D) 60
(E) 80
Rationale: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,3 beads can be arranged to form a necklace in(3-1)! /2ways
= 2/2 = 1 way
Answer is C
Answer: (C) 1
Question: Of the 30 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?
(A) 15
(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 10 20
Other 1 10 10
Total 3 10 30
Answer is 20. i.e B
Answer: (B) 20
Question: If y is 80% greater than x, than x is what % less than y?
(A) 20
(B) 25
(C) 33 1/3
(D) 44 4/9
(E) 80
Rationale: Let x = 100
So y = 180
We want percentage change.
So, (100-180)/180
= -44.44%
= 44 4/9% lesser than y.
Hence option (D).
Answer: (D) 44 4/9
Question: Look at this series: 26, 24, 20, 18, 14, __What number should come next?
(A) 10
(B) 12
(C) 13
(D) 17
(E) 15
Rationale: This series is alternatively subtracted first 2 is subtracted, then 4 is subtracted then 2, and so on.
Answer is option B (12)
Answer: (B) 12
Question: If x^2 = y^3 , where x and y are non negative and non zero integers, what is the greatest possible value of x and y from options below?
(A) x=27 , y=7
(B) x=27, y=9
(C) x=25, y=5
(D) x=9, y=3
(E) x=121, y=11
Rationale: A. x=27 y=7 729 = 343 wrong
B. x=27, y=9 729 = 729 right
C. x=25, y=5 625 = 125 wrong
D. x=9, y =3 81 = 27 wrong
E. x=121, y =11 14641 = 1331 wrong
answer is B.
Answer: (B) x=27, y=9
Question: A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?
(A) 7
(B) 8
(C) 4
(D) 2
(E) 9
Rationale: 70 * (10/100) = 7
Wine Water
87 1/2% 12 1/2%
87 1/2% ------- 63
12 1/2% -------? => 9-7=2
Answer: D
Answer: (D) 2
Question: In a sample of patients at an animal hospital, 30 percent are cats and 60 percent are not dogs. What fraction of those patients who are not cats are dogs?
(A) 1/7
(B) 1/3
(C) 2/5
(D) 3/5
(E) 4/7
Rationale: Given :60% are not dogs, so 40% are dogs.
Cats are 30% so 70% are not cats.
Question is dogs to not cats=40/70 = 4/7
Answer is E
Answer: (E) 4/7
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.45, b = 3.05, and c = 3.76, what is y – x?
(A) -0.1
(B) 0.4
(C) 0.05
(D) 0.1
(E) 0
Rationale: To find x, we first sum a, b, and c, then round to the tenths place. 5.45 + 3.05 + 3.76 = 12.26, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 3.0 + 3.8 = 12.2.
We are looking for y - x, which gives us 12.2 - 12.2 = 0, or answer choice E.
Answer: (E) 0
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
(A) 37 min
(B) 55 min
(C) 47 min
(D) 67 min
(E) 45 min
Rationale: C
47 min
Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer: (C) 47 min
Question: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I can have to pack and distribute?
(A) 25
(B) 37
(C) 54
(D) 65
(E) 50
Rationale: Explanation : . The required number will be obtained by taking LCM of 2, 3 and 4 and adding 1 into it. The number so obtained is 25.
Answer A
Answer: (A) 25
Question: In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 20m
(B) 25m
(C) 22.5m
(D) 9m
(E) None of these
Rationale: Explanation:
Distance covered by B in 9 sec. =(100/45 x 9)m = 20m
A beats B by 20 metres.
Answer: A
Answer: (A) 20m
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7
(B) 6
(C) 8
(D) 2
(E) 4
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55
= 6 sec.
AnswerB
Answer: (B) 6
Question: Two trains leave the train station at the same time. One train, on the blue line, heads east- while the other, on the red line, heads west. If the train on the blue line averages 40km/hr and the other train averages 40 km/hr- how long will it take for the trains to be 100 Km apart?
(A) 2 hours
(B) 2.25 hours
(C) 1 hour
(D) 1.25 hours
(E) Not enough information
Rationale: Each train is averaging 40 Km/Hour in an opposite direction. After 1 hour, they will be 80 Km apart, and after 1.25 hours, they will be 100 Km apart. (80*1.25=100)
Answer is D
Answer: (D) 1.25 hours
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $46 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
(A) $5
(B) $10
(C) $14
(D) $16
(E) $28
Rationale: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $46
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 46
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 46
i.e. x = 30
i.e. Fixed Monthly Charge, y = 16
Answer: Option
D
Answer: (D) $16
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 8.30 a.m.?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 2
Rationale: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour SO 2 times in 1/2 hour
Time duration from 8 am to 8.30 am = 0.5 hour
Hence they cross each other 2 times before 8.30 am
Answer is E
Answer: (E) 2
Question: The ratio of the ages of three people is 4:6:7. Eight years ago, the sum of their ages was 78. Find their present ages.
(A) 12,18,21
(B) 16,24,28
(C) 20,30,35
(D) 24,36,42
(E) 28,42,49
Rationale: Let the present ages be 4x, 6x, 7x.
(4x-8) + (6x-8) + (7x-8) = 78
17x = 102
x = 6
Their present ages are 24, 36, and 42.
The answer is D.
Answer: (D) 24,36,42
Question: When a number is first increased by 20% and then reduced by 20%, The number is:
(A) Does not change
(B) Decreases by 4%
(C) Increases by 4%
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Formula = AFTER INCREASED 20%*AFTER REDUCED 20%/TOTAL 100%
= 120*80/100 = 94 %
= Decreases by 4%
Answer: Option B
Answer: (B) Decreases by 4%
Question: The L.C.M. of 2 numbers is 48. The numbers are in the ratio 2:3. Find their sum?
(A) 36
(B) 40
(C) 48
(D) 32
(E) 56
Rationale: Let the numbers be 2x and 3x
L.C.M. = 6x
6x = 48
x = 8
The numbers are = 16 and 24
Required sum = 16+24 = 40
Answer is B
Answer: (B) 40
Question: If T is an integer greater than 6, which of the following must be divisible by 3?
(A) T(T+1)T-4)
(B) N(N+2)(N-1)
(C) N(N+3)(N-5)
(D) N(N+4)(N-2)
(E) N(N+5)(N-6)
Rationale: Now take T = 3k , T = 3k+1 T = 3k+2..put in all the choices. If by putting all the values of T we get it is divisible by 3, then it is correct answer choice.
A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: (A) T(T+1)T-4)
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre.
(A) $8250
(B) $8350
(C) $8650
(D) $8450
(E) $8500
Rationale: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $400
Hence, total cost
=5.5×3.75×400= $8250
A
Answer: (A) $8250
Question: A and B invests Rs.2000 and Rs.4000 in a business. After 8 months, A withdraws half of his capital and B withdraws three-fourth of his capital. In what ratio should they share the profits at the end of the year?
(A) 8:9
(B) 5:9
(C) 7:9
(D) 4:9
(E) 3:7
Rationale: A : B
(2000*8)+(1000*4) : (4000*8)+(1000*4)
20000 : 36000
5 : 9
Answer: B
Answer: (B) 5:9
Question: A certain business school has 500 students, and the law school at the same university has 800 students. Among these students, there are 30 sibling pairs consisting of 1 business student and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?
(A) 3/40000
(B) 3/20000
(C) 3/4000
(D) 9/400
(E) 6/130
Rationale: probability of selecting 1 student from Harvard's Business School---1/500
probability of selecting 1 student from Harvard's Law School---------1/800
probability that these two students are siblings----(1/500 * 1/800)
since there are 30 siblings, hence (1/500 * 1/800)*30.
3/40000
Answer:A
Answer: (A) 3/40000
Question: A and B participate in a 5000 m bicycle race which is being run on a circular track of 500 m. If the speed of A and B are 20 m/s and 10 m/s respectively, what is the distance covered by A when he passes B for
the seventh time ?
(A) 2500
(B) 2800
(C) 4000 m
(D) Situation is not possible
(E) None of these
Rationale: Track length = 500 m
Speed of A and B are 20m/s and 10 m/s respectively
Time taken by them to meet = length/ relative speed = 500/(20-10) 50 sec.
Time taken to meet for the 7th time = 7 *50 =350 sec ……..(1)
Total duration of race = total legth of race/ speed
= 500/20 = 250 sec ……..(2)
From (1) and (2) we can find out that 7th time meeting is not possible.
Answer: D
Answer: (D) Situation is not possible
Question: The function f(K) represents the number of ways that prime numbers can be uniquely summed to form a certain number K such that K = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Lets start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: D
Answer: (D) 7
Question: Average age of students of an adult school is 44 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
(A) 1200
(B) 180
(C) 360
(D) 240
(E) None of these
Rationale: Explanation :
Let the original no. of students be x.
According to situation, 44x + 120*32 = (x + 120)36 ⇒ x = 60
So, Required no. of students after joining the new students
= x + 120 = 180
Answer : B
Answer: (B) 180
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7000?
(A) s. 4991
(B) s. 5991
(C) s. 6001
(D) s. 6991
(E) s. 7991
Rationale: total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009.
Reqd.sale=Rs.[(7000*6)-34009]
= Rs.(42000-34009)
= Rs.7991.
ANSWER:E
Answer: (E) s. 7991
Question: If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 600. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 615. What is the value of X?
(A) 8000
(B) 6000
(C) 5000
(D) 4000
(E) 3000
Rationale: Simple way to solve this question is to use options.
From SI, we know that X*y=30,000.
Now, put the value of X = 6000, we will have y = 5%
To calculate CI,
Now, we know 1st year Amount= 6000+5% of 6000= 6300.
2nd year, Amount = 6300 + 5% of 6300 =6615
We can see after 2 years Interest = 6615-6000= 615. hence, it satisfies the question. Hence B is the correct answer
Answer: (B) 6000
Question: If |z|/w = 6,which of the following must be true?
(A) z = -6w
(B) z = 6w
(C) z^2 = 36w^2
(D) z^2 = 36w^3
(E) z^3 = 216w^3
Rationale: |z|/w = 6.
|z| = 6w.
Then z = 6w or -6w and so z^2 = 36w^2.
The answer is C.
Answer: (C) z^2 = 36w^2
Question: Find the third proportional to 10 and 30?
(A) 10
(B) 60
(C) 80
(D) 90
(E) 20
Rationale: Formula = Third proportional = (b × b)/a
A = 10 and B = 30
(30 x 30)/ 10 = 900/10= 90
D
Answer: (D) 90
Question: A woman has $99999 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her nine children?
(A) 2
(B) 1
(C) 0
(D) 3
(E) 4
Rationale: To find the least amount the woman should add to her saving account to split the money evenly among her 9 children,
she needs to make the total divisible by 9
Simply add the individual digits of the total = 9+9+9+9+9 = 45
45 divided by 9 = 5 so answer is 0
Correct Option : D
Answer: (D) 3
Question: Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
(A) 75 × 8 ÷ 6
(B) 98 ÷ 2.5 + 15.2 × 4
(C) √225 – 5 × 2(2)
(D) 76 × 1.5 – 5.5 × 2.6
(E) 48 × 1.2 + 127.2 ÷ 3
Rationale: Check all options one by one.
(a) 75×8/6=100
(b) 98⁄2.5 + (15.2 × 4) = 100
(c) (15 × 8) – (5 × 4) = 100
(d) (76 × 1.5) – (5.5 × 2.6) = 99.7
(e) (48 × 1.2) + 127.2⁄3 = 100
Answer D
Answer: (D) 76 × 1.5 – 5.5 × 2.6
Question: Baby Isabel plays with blocks. Each block is 5.6 inches tall. She has a collection of 38 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?
(A) 212.8"
(B) 90.8"
(C) 206.2"
(D) 120"
(E) 151.7"
Rationale: 5.6"*38=212.8". Answer is A.
Answer: (A) 212.8"
Question: The sum of the ages of 5 children born at the intervals of years each is 50 years. What is the age of the youngest child?
(A) 6 years
(B) 8 years
(C) 10 years
(D) 12 years
(E) 14 years
Rationale: Let the ages of the children be x, (x + 2), (x + 4), (x + 6) and (x +8) years.
Then, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 50
5x = 30 => x = 6.
Age of youngest child = x = 6 years.
ANSWER:A
Answer: (A) 6 years
Question: A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
(A) 10 years
(B) 8 years
(C) 6 years
(D) 12 years
(E) 13 years
Rationale: Explanation:
Let the sum be Rs.1 which becomes Rs.2 after 4 years
⇒ 2 = 1(1 + R/100 )4 --- (equation 1)
Let the sum of Rs.1 becomes Rs.8 after n years
⇒ 8 = 1(1 + R/100)n --- (equation 2)
⇒ (2)3 = 1(1+R/100)n
⇒ [1(1+R/100)4]3 = 1(1+R/100)n (âˆµ replaced 2 with the value in equation 1) (1 + R/100)12 = (1+R/100)n
⇒ n = 12
i.e., the sum amounts to 8 times in 12 years
Answer: Option D
Answer: (D) 12 years
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 5 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: To get 40 points as end of season we need another 35 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
Option B=7*3 + 8*1=29
Option C=8*3+7*1=31
Option D=9*3+6*1=33
Option E=10*3+5*1=35
hence option E-10
Answer: (E) 10
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 12
(B) 24
(C) 48
(D) 60
(E) 50
Rationale: Answer: Option C
Explanation:
Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
ANSWER C
Answer: (C) 48