divelab/Sys2Bench huggingface dataset:
Question: Suresh invested a sum of Rs. 15000 at 9 percent per annum Simple interest and Rs. 12000 at 8 percent per annum compound interest for a period of 2 years. What amount of interest did Suresh earn in 2 years?
Options:
A)4496.8
B)4596.8
C)4696.8
D)4796.8
E)4896.8
Rationale: S.I = PTR/100
S.I =15000*9*2/100
S.I= 2700
C.I =P(1+r/100)^n -P
C.I= 12000(1+8/100)^2-12000
C.I=1996.8
total amount in 2 years
as interest = S.I +C.I
= 2700+1996.8
=4696.8
ANSWER:C
Answer: C
Question: Anish borrowed 15000 at the rate of 12% and an other amount at the rate of 15% for two years. The total interest paid by him was 9000. How much did he borrow?
Options:
A)32,000
B)33,000
C)30,000
D)35,000
E)None of these
Rationale: Let x be the other amount
\ 3x⁄10 + 3600 = 900 ⇒ x = 18000
\ total borrowed sum = 33000
Answer B
Answer: B
Question: Let A represent a set of four distinct prime numbers. If the sum of the numbers in A is even and x is a member of A, then what is the least possible value that x can be?
Options:
A)1
B)2
C)3
D)5
E)7
Rationale: We are told that A is a set of four distinct prime numbers, and the sum of the numbers in A is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of A must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
Answer: C
Question: An eight-digit telephone number consists of exactly two zeroes. One of the digits is repeated thrice. Remaining three digits are all distinct. If the first three digits (from left to right) are 987, then find the probability of having only one 9, one 8 and one 7 in the telephone number.
Options:
A)1/18
B)1/20
C)1/10
D)5/47
E)5/45
Rationale: Explanation :
Case A: There is only one 9, one 8 and one 7 in the number.
Hence there has to be one digit from {1,2,3,4,5,6} repeated thrice.
Total number of ways in which such a number can exist is :
=>6C1×5!/(3!×2!).
=60.
Case B: One of the three digit {9,8,7} is repeated thrice.
Hence, there will be one digit from {1,2,3,4,5,6}.
Total number of ways in which such a number can exist:
=>3C1×6C1×5!/(3!×2!).
=>540
Total possible telephone numbers:
=60+540=600.
Hence the required Probability is 60/600 = 1/10.
Answer : C
Answer: C
Question: A room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
Options:
A)10
B)15
C)17
D)19
E)21
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 7 meters and 20 centimeters = 720 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 720 and 432 = 144
Thus, the number of square tiles required = (720 x 432 ) / (144 x 144) = 5 x 3 = 15
Answer: B
Answer: B
Question: The ratio of Rita's age to her mother's age is 3:8. The difference of their ages is 35 years. The ratio of their ages after 4 years will be:
Options:
A)7:12
B)5:12
C)38:43
D)42:47
E)52:47
Rationale: Rita age=3x
mother's age=8x
their difference = 8x-3x=35
x=7
therefore Rita's current age=21
mother's current age=56
4 years hence their ratio of ages will be 25:60
ans is 5:12
ANSWER:B
Answer: B
Question: City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)57
B)57.5
C)58.2
D)59
E)62
Rationale: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Answer: B
Question: In how many W ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
Options:
A)6
B)12
C)18
D)24
E)30
Rationale: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning W= 24 - 6 = 18
Answer: C
Answer: C
Question: What is the least integer greater than –1+0.5?
Options:
A)–2
B)–1
C)0
D)1
E)2
Rationale: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.
First, let's take care of the Arithmetic:
(-1) + (0.5) = -0.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -1 to -0.5).
Next, the question asks for the LEAST integer that is GREATER than -0.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -0.5 is 0.
Final Answer:
C
Answer: C
Question: A watch was sold at a loss of 8%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)2876
C)1977
D)1167
E)2711
Rationale: 92%
104%
--------
12% ---- 140
100% ---- ? => Rs.1167
Answer: D
Answer: D
Question: 25 x 10 + 25 x 11 = ?
Options:
A)725
B)720
C)600
D)525
E)None of them
Rationale: =25 x (10+11) (by distributive law)
=25 x 21
=525
Answer is D
Answer: D
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
Options:
A)288
B)277
C)299
D)500
E)278
Rationale: P - 340 = (P*4*8)/100
P = 500
Answer:D
Answer: D
Question: If x-y=8, which of the following must be true?
I. If x is positive, y must be positive
II. If x is negative, y must be negative
III.Both x and y are positive
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E
A) I only
B) II only
C) III only
D) I and II
E) II and III
Answer B
Answer: B
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 18 kmph, 17 kmph, and 16 kmph respectively. What is the ratio of the time taken by B to than taken by D?
Options:
A)5:16
B)5:17
C)9:8
D)8:9
E)None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D = 16 : 18 = 8 : 9.
Answer : D
Answer: D
Question: If 5x = 6y and xy ≠ 0, what is the ratio of 1/5*x to 1/8*y ?
Options:
A) 48/25
B) 36/25
C) 6/5
D) 5/6
E) 25/36
Rationale: 5x = 6y => x/y = 6/5
1/5*x to 1/8*y = x/y * 8/5 = (6/5)*(8/5)=48/25
Ans: A
Answer: A
Question: What is the next number of the following sequence
3,7,13,21,?
Options:
A)22
B)31
C)41
D)35
E)42
Rationale: 2^2-1=3
3^2-2=7
4^2-3=13
5^2-4=21
6^2-5=31
ANSWER:B
Answer: B
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 40 percent off the suggested retail price. If, during a special sale, an additional 5 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $500 before any discount?
Options:
A)$130.00
B)$285.00
C)$200.00
D)$258.00
E)$210.00
Rationale: Original price : 500 $
Max first discount = -40%
Thus : 500âˆ—(1âˆ’40/100)=300
Second discount on the discounted price = -20%
Thus : 300âˆ—(1âˆ’5/100)=285
Answer B.
Answer: B
Question: Find the total average marks of all the students in 2 separate classes, if the average marks of students in the first class of 39 students is 45 and that of another class of 35 students is 70.
Options:
A)55.8
B)51.8
C)53.8
D)56.8
E)52.8
Rationale: Sum of the marks for the class of 39 students = 39 * 45 = 1755
Sum of the marks for the class of 35 students = 35 * 70 = 2450
Sum of the marks for the class of 74 students =1755+2450=4205
Average marks of all the students = 4205/74
= 56.8
Answer:D
Answer: D
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Options:
A)87 kmph
B)68 kmph
C)14 kmph
D)76 kmph
E)57 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1)
= 3/1 = 3:1
Speed of the stream
= 42/3 = 14 kmph.
Answer:C
Answer: C
Question: Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 29. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
Options:
A)1
B)13
C)15
D)21
E)47
Rationale: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.
What does this imply?If the sum of the first n terms of the sequence is n
Since number of terms will definitely be positive, we are looking for a positive sum.
19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on
Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...
Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.
Answer (D)
Answer: D
Question: What percent of 60 is 25?
Options:
A)60%
B)50%
C)42%
D)25%
E)10%
Rationale: The phrasing of the question is difficult for some students. "What percent of 60 is 25?" is the same question as "25 is what percent of 60?" Many students find this later way of phrasing the question easier to work with.
If X is Y percent of Z, then X/Z=Y/100; For example, 10 is 50% of 20; X = 10, Y = 50, and Z = 20
Similarly, if you wanted to know what percent of 100 is 50, you would intuitively know that it is 50% since it is 50/100 or 50 per cent (literally, per 100).
Applying this logic to the problem at hand: 25/60= .42 = 42%
Thus, 25 is 42% of 60
If this way of solving the problem is difficult to conceptualize, consider another approach. It should be clear that 30 is 50% (or 1/2) or 60. Since 25 is less than 30, 25 must be less than 50% of 60. This means that any answer that is not less than 50% is wrong.
Since 25% is 1/4 and 1/4 of 60 is 15 (since 15*4=60), 25% is too small. By process of elimination, the answer is 42%
Answer C
Answer: C
Question: In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $847,000 invested in preferred stocks, what is the total amount of money invested in the fund?
Options:
A)$1,974,000
B)$2,538,000
C)$3,264,000
D)$3,826,000
E)$4,235,000
Rationale: Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 847---
Fund = 5 * 847---
Here, we can avoid the math and simply look at 5 * 7 -> 35. Only option E has 35 in it.
Answer (E).
Answer: E
Question: If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 16
Options:
A)8
B)18
C)64
D)16
E)26
Rationale: f(3)=2*3+2=8
now put this value again in the function
f(8)=2*8+2=18
ANSWER:B
Answer: B
Question: When a number is multiplied by 13,it will become greater to 105 by an amount with which it is lesser to105 by now. What is the number
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: no is 105-x, then
(105-x)*13 = 105+x
1365 -13 x =105+x
14x = 1260
x= 1260/14 =90
so number is 105-90 = 15
ANSWER:D
Answer: D
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Options:
A)1 : 3
B)3 : 2
C)3 : 4
D)3 : 5
E)None of these
Rationale: let length of trains are x and y
so speed of the trains will be x/27 and y/17 respectively.
now to cross each other time taken=23 second,
so (x+y)/((x/27)+(y/17))=23
(27*17)(x+y)/17x+27Y=23
so, ((x/y)+1)/17(x/y)+27=23/27*17
(x/y)+1=(23x/27y)+23/17
4*(x/27)=6*(y/17)
so,(x/27):(y/17)=3:2
so ratio of speed of the train will be 3:2
ANSWER:B
Answer: B
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 30% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
Options:
A)25%
B)30%
C)50%
D)55%
E)75%
Rationale: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.3N
x = 0.75N
The percentage of rooms which permit smoking is 1 - 0.75 = 25%
The answer is A.
Answer: A
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
Options:
A)1/2
B)3/4
C)3/7
D)3/11
E)4/7
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
A)
Answer: A
Question: If y is an integer, then the least possible value of |23 - 8y| is
Options:
A)5
B)2
C)3
D)4
E)1
Rationale: We know that 8y is a multiple of 8, so let’s first look at the multiples of 8 closest to 23. We have “16” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 2y = 16, y is 2 and when 3y = 24, y is 5. Let’s start with letting y = 4.
|23-8(2)|
|23-16|
|7| = 7
Next, let’s let y equal 3.
|23-8(3)|
|23-24|
|-1| = 1
We see that the smallest possible value of |23-8y| is 1.
Answer E.
Answer: E
Question: A sum of money lent out at S.I. amounts to a total of $590 after 2 years and to $815 after a further period of 5 years. What was the initial sum of money that was invested?
Options:
A)$490
B)$500
C)$510
D)$520
E)$530
Rationale: S.I for 5 years = $815 - $590 = $225
The S.I. is $45/year
S.I. for 2 years = $90
Principal = $590 - $90 = $500
The answer is B.
Answer: B
Question: Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 18kmph. For how many minutes does the bus stop per hr
Options:
A)12 min
B)11 min
C)13 min
D)20 min
E)40 min
Rationale: Due to stoppages,it covers 36km less.
time taken to cover 36 km is [36/54 *60] min = 40min
Answer is E.
Answer: E
Question: It takes one machine 7 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
Options:
A)a) 7/12
B)b) 1 1/2
C)c) 1 5/7
D)d) 3 1/2
E)e) 2 6/11
Rationale: RT = W
Given:
R = 1/7 + 1/4 = 11/28
T = ?
W = 1
T = 1 / (11/28) = 28/11 = 2 6/11
Answer: E
Answer: E
Question: A train 260 m long passed a pole in 26 sec. How long will it take to pass a platform 650 m long?
Options:
A)91 sec
B)89 sec
C)54 sec
D)27 sec
E)22 sec
Rationale: Speed = 260/26 = 10 m/sec.
Required time = (260 + 650)/10
= 91 sec.
Answer: A
Answer: A
Question: The compound ratio of 5:6, 3:2 and 4:5?
Options:
A)1:9
B)1:7
C)1:2
D)1:1
E)1:4
Rationale: 5/6 * 3/2 * 4/5
= 1/1
=1:1
Answer: D
Answer: D
Question: A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning ?
Options:
A)22
B)24
C)28
D)26
E)29
Rationale: Let the average score of 19 innings be x.
Then, 18x+98/19=x+4
The average score after 20th innings
= x + 4 = 22 + 4 = 26
Answer D
Answer: D
Question: 2/3rd of the boys and 3/4th of the girls of a school participate in a function. If the no.of participating students is 550, out of which 150 are girls, what is the total no.of students in the school?
Options:
A)400
B)460
C)800
D)880
E)900
Rationale: Let total number of boys be x and total number of girls be y. y=400=>x = 600and^= I50=>y = 200 Now, x + y = 800
C
Answer: C
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 161?
Options:
A)2670
B)2980
C)3550
D)4030
E)4540
Rationale: 100 + 102 + ... + 160 =
100*31 + (2+4+...+60) =
100*31 + 2*(1+2+...+30) =
100*31 + 2(30)(31)/2 =
100*31 + 30*31 = 130(31) = 4030
The answer is D.
Answer: D
Question: Arun started a business investing Rs. 45,000. After three months. Pramod joined him with a capital of Rs.60,000. If at the end of one year, the total profit from the business is Rs.26,000, what would be Pramod's share in it?
Options:
A)Rs.10,000
B)Rs.14,000
C)Rs.13,000
D)Rs.16,000
E)None of these
Rationale: ( arun)45000*12 : (pramod)60000*9 =>>(45*12) : (60*9) ==> (arun) 1: (pramod) 1
pramod's share is >> 26000 * 1/(1+1)=>13000
ANSWER:C
Answer: C
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got
Options:
A)55%
B)56%
C)57%
D)58%
E)None of these
Rationale: Explanation:
Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
Option C
Answer: C
Question: 1^23×1^23+2^8×2^8+2×123×2^8=?
Options:
A)454621
B)123545
C)343566
D)325456
E)128513
Rationale: 1+256*256+246*256
128513
E
Answer: E
Question: Marge has W candies, where W is an integer such that 20 < W< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
Options:
A) 0
B) 1
C) 2
D) 3
E) 4
Rationale: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.
This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47
If she divides the candies among 6 children, she will have 1 candy remaining.
this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49
ONLY 37 is common, so candies are 37 in number..
if 37 is divided in 7 kids, remainder W= 2
C
Answer: C
Question: If Rs.2800 yields a simple of Rs.480 in 3 Years, calculate the percentage rate?
Options:
A)11.6%
B)10%
C)14.6%
D)12.6%
E)13.6%
Rationale: 480 = (2400*2*R)/100
R = 10%
Answer: B
Answer: B
Question: The sum of two consecutive number is 97. Which is the larger number?
Options:
A)42
B)49
C)44
D)45
E)46
Rationale: Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=97
2x+1=97
2x=96
x=48
Therefore larger number is x+1=49
ANSWER:B
Answer: B
Question: The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: The question basically asks how many minutes it takes for a population to increase by factor 50(50,000 / 1,000 = 50).
Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:
2^x >= 50, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^6 = 64, i.e. the population has to double 6 times.
Since it takes the population 2 minutes to double once it takes 6*2 minutes = 12 minutes to double nine times.
Thus, solution B = 12 is correct.
Answer: B
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)10
B)18
C)20
D)22
E)24
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,
Then 30 ~ 40 = 10
===> 1 -----> 10
===> 2 -----> 20
C
Answer: C
Question: Here are some words translated from an artificial language.
hapllesh means cloudburst
srenchoch means pinball
resbosrench means ninepin
Which word could mean "cloud nine"?
Options:
A)leshsrench
B)ochhapl
C)haploch
D)haplresbo
E)ochhase
Rationale: Hapl means cloud; lesh means burst; srench means pin; och means ball; and resbo means nine. Leshsrench (choice a) doesn't contain any of the words needed for cloud nine. We know that och means ball, so that rules out choices b and c. When you combine hapl (cloud) with resbo (nine), you get the correct answer
Answer:D
Answer: D
Question: N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N?
Options:
A)23
B)28
C)4
D)1
E)25
Rationale: If the remainder is same in each case and remainder is not given, HCF of the differences of the numbers is the required greatest number
6905 - 1305 = 5600
6905 - 4665 = 2240
4665 - 1305 = 3360
Hence, the greatest number which divides 1305, 4665 and 6905 and gives the same remainder, N
= HCF of 5600, 2240, 3360
= 1120
Sum of digits in N
= Sum of digits in 1120
= 1 + 1 + 2 + 0
= 4
Answer is C
Answer: C
Question: If A,B,C,D,E,F,G,H,I,J are in an decreasing Arithmetic Progression as such. Then Which of the following operations will result in either mean or the median being modified.
A) A is replaced by J
B) A and H are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and D are removed
Options:
A)1) A and B
B)2) A and E
C)3) A,B,E
D)4) All of them
E)5) None of them
Rationale: Here answer will be (C).
There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. Other changes will affect the mean and median.
Answer: C
Answer: C
Question: The perimeter of an isosceles right triangle is 10 + 10 sq rt 2. What is the length of the hypotenuse of the triangle?
Options:
A)5
B)6
C)7.07
D)8
E)9
Rationale: side of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 =10 + 10 Sqrt2 or,
a. ( 2+ sqrt2) = 10(1 + sqrt2), a= 10*(1+sqrt2)/2+sqrt2 =10*2.414/3.414 =0.707*10 then hypotenuse = 7.07
C
Answer: C
Question: The relationship between quantities m and n is expressed by the equation 10m = 5(n - 42). If the difference between the two chosen values of n is 30, what is the difference in the corresponding values of m?
Options:
A)30/11
B)42/11
C)60/11
D)150/11
E)15
Rationale: Another Simple way
10m=5(n-42)
Assume n = 42 to make one side equal to 0
then 10m=0
and m = 0
Repeat it by assuming n as 42+30 i.e 72
10m= 5(72-42)
10m=150
m=150/10
diff = 15 - 0 = 15
Answer : E
Answer: E
Question: A women walking at 5 Kmph reaches her office 8 minutes late. If she walks at 9 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
Options:
A)2 1/5 Km
B)3 Km
C)4 1/3 Km
D)5 Km
E)5 1/3 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 5*9/2 * 16/60
= 45/2 * 16/60
= 3 Km
B)
Answer: B
Question: On a map, 3.5 inches represent 35 miles. How many miles approximately is the distance if you measured 127 centimeters assuming that 1-inch is 2.54 centimeters?
Options:
A)515
B)500
C)525
D)530
E)535
Rationale: 1 inch = 2.54 cm
3.5 inch = 2.54 * 3.5 cm
8.89 cm = 35 miles
127 cms = 35/8.89*127= 500 miles
Answer : B
Answer: B