divelab/Sys2Bench huggingface dataset:
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
Options:
A)4
B)8
C)9
D)10
E)12
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: B
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 5m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Options:
A)54
B)32
C)75
D)20
E)11
Rationale: A/8 = 5 * 5 => A = 5 * 5 * 8
x * 2x = 5 * 5 * 8
x = 10 => 2x = 20
Answer:D
Answer: D
Question: Given 2 numbers; 8 and q, the LCM and HCF of both numbers is 72 and 1 respectively. Find q?
Options:
A)3
B)5
C)6
D)9
E)7
Rationale: HCF x LCM = Product of Numbers
1 x 72 = 8 x q
q = (1 x 72) / 8
other number = 9
ANSWER : D
Answer: D
Question: Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4≤ X≤ 5 and 6≤ y≤ 16. How many different triangles with these properties could be constructed?
Options:
A)110
B)1100
C)9900
D)10000
E)12100
Rationale: total values for x=10;y=11
x1,y1=10*11.......................coordinates of 1st pnt
x2,y2=9*1(y2=y1)............... coordinates of 2nd pnt y coordinates will be same as that of 1st pnt bcoz it is parallel to x axis
x3,y3=1*10(x2=x3)..........coordinates of 3rd pt. x coordinates will be same as that of 2nd point bcoz to make a right angle it has to be parallel to y axis
tot ways=10*11*9*1*1*10=9900
ANS:C
Answer: C
Question: What is the dividend. divisor 16, the quotient is 6 and the remainder is 2
Options:
A)86
B)87
C)88
D)89
E)90
Rationale: C = d * Q + R
C = 16 * 6 + 2
C = 86 + 2
C = 88
Answer: C
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
Options:
A)1.44%
B)1.74%
C)1.84%
D)1.47%
E)1.24%
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by
= [(profit%)(loss%)]/100
= (12)(12)/100 % = 1.44%
Answer:A
Answer: A
Question: Three hundred students at College Q study a foreign language. Of these, 120 of those students study French, and 170 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from
Options:
A)10 to 40
B)50 to 90
C)60 to 100
D)60 to 110
E)70 to 110
Rationale: 120 students study French
180 students do not study French
170 students study Spanish
130 students do not study Spanish
90 students study neither French nor Spanish
180-130=50
180-90=90
B. 50 to 90
Answer: B
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 22 seconds. The ratio of their speeds is?
Options:
A)3/7
B)3/2
C)3/5
D)3/1
E)5/5
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 22
==> 27 x + 17 y = 22x + 22 y ==> 5 x = 5 y ==> x/y
= 5/5.
Answer: E
Answer: E
Question: The heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4. Find the ratio of their volumes.
Options:
A)1:14
B)12:4
C)9:6
D)1:7
E)9:32
Rationale: Let the radii of their bases be r and R and their heights be h and 2h respectively.
Then,(2r/2R)=(3/4)  R=(4/3)r.
 Ratio of volumes = (((1/3)r2h)/((1/3)(4/3r)2(2h)))=9: 32.
ANSWER E 9:32
Answer: E
Question: If a - b = 5 and a2 + b2 = 34, find the value of ab.
Options:
A)A)4.5
B)B)12
C)C)15
D)D)18
E)E)20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 34 - 25 = 9
ab = 4.5.
Answer: A
Answer: A
Question: Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
Options:
A)150
B)160
C)170
D)180
E)190
Rationale: Let the 1st paycheck be x (integer).
Dawson got a weekly raise of $ 160.
So after completing the 1st week she will get $ (x+160).
Similarly after completing the 2nd week she will get $ (x + 160) + $ 160.
= $ (x + 160 + 160)
= $ (x + 320)
So in this way end of every week her salary will increase by (B)$ 160.
Answer: B
Question: $500 will become $1000 in 6 years find the rate of interest?
Options:
A)A)16.67%
B)B)20%
C)C)25%
D)D)30%
E)E)50%
Rationale: SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*6 =16.67%
Answer is A
Answer: A
Question: Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?
Options:
A)0
B)2
C)4
D)5
E)6
Rationale: Solution:
The average of the elements in the original set S is: (0+2+4+5+9) /5 =20 /5 =4.
If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,
(0+2+5+9) /4=16 /4 =4.
Answer: Option C
Answer: C
Question: A man swims downstream 72 km and upstream 45 km taking 12 hours each time; what is the speed of the current?
Options:
A)1.125
B)1.128
C)1.126
D)1.123
E)1.121
Rationale: 72 --- 12 DS = 6
? ---- 1
45 ---- 12 US = 3.75
? ---- 1 S = ?
S = (6 - 3.75)/2 = 1.125
Answer:A
Answer: A
Question: If y is a positive even integer, and n and m are consecutive integers, then (n - m)^y/(m - n)^y =
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: y= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^y)/((m-n)^y)= ((n-m)/(m-n))^y = (-1)^y
Since we are raising the difference of n and m to power y , which is even , the answer will be 1 .
Answer D
Answer: D
Question: A car traveled 75% of the way from town A to town B at an average speed of 60 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?
Options:
A)10
B)20
C)25
D)30
E)37.5
Rationale: Total distance = 100 miles (easier to work with %)
75% of the distance = 75 miles
25% of the distance = 25 miles
1st part of the trip → 75/60 = 1.25
2nd part of the trip → 25/S = t
Total trip → (75+25)/40 = 1.25 + t » 100/40 = 1.25 + t » 2.5 = 1.25 + t » t = 1.25
Back to 2nd part of the trip formula: 25/S = 1.25 » S = 20
Ans B
Answer: B
Question: Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?
Options:
A)440/455
B)412/455
C)434/455
D)449/455
E)438/455
Rationale: Total ways of selecting 3 dots out of 15 is 15C3 = 455 If 3 dots are collinear then triangle may not be formed. Now look at the above diagram. If we select any 3 dots from the red lines they may not form a triangle. They are 3 x 5C3 = 30. If we select the three letters from blue lines, they may not form a triangle. They are in total 5 ways. Also there are 6 others lines which don't form a triangle. Also another two orange lines. Total = 30 + 5 + 6 + 2 = 43. So we can form a triangle in 455 - 43 = 412. So answer could be 412/455.
ANSWER:B
Answer: B
Question: If f(2, 7) = 57 and f(1, 6) = 37, what is the value of f(3, 10)?
Options:
A)107
B)127
C)147
D)None of these
E)Cannot be determined
Rationale: Solution:
The function f(a, b) = a3 + b2
f(2, 7) therefore is = 23 + 72 = 8 + 49 = 57 and
f(1, 6) = 13 + 62 = 1 + 36 = 37.
Therefore, f(3, 10) = 33 + 102 = 27 + 100 = 127.
Answer B
Answer: B
Question: Usually the room tariff in this hotel is higher. At present, it is low because of the ______ season.
a. peak
Options:
A)PINK
B)bkue
C)orancge
D)off
E)iwww
Rationale: Explanation:
Because of the Off season.
Answer:D
Answer: D
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Options:
A)5/6
B)5/9
C)5/4
D)5/2
E)5/1
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9
Answer: B
Answer: B
Question: How many seconds will a 650 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 48 km/hr?
Options:
A)25
B)45
C)54
D)44
E)48
Rationale: Speed of train relative to man = 48- 3 = 45 km/hr.
= 45 * 5/18 = 25/2 m/sec.
Time taken to pass the man = 650 * 2/25 = 54 sec.
Answer: C
Answer: C
Question: What will be the compound interest on Rs. 25000 after 3 years at the rate of 12 % per annum
Options:
A)Rs 10123.20
B)Rs 10123.30
C)Rs 10123.40
D)Rs 10123.50
E)None of these
Rationale: Explanation:
(25000×(1+12/100)3)
=>25000×28/25×28/25×28/25
=>35123.20
So Compound interest will be 35123.20 - 25000
= Rs 10123.20
Option A
Answer: A
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)192 km
B)162 km
C)172 km
D)168 km
E)112 km
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer:B
Answer: B
Question: If a and b are prime numbers, which of the following CANNOT be (x + y)?
Options:
A)5
B)9
C)13
D)16
E)23
Rationale: All answer choices but E are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.
Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.
Answer: E.
Answer: E
Question: Two 6 faced dice are thrown together. The probability that all the three show the same number on them is?
Options:
A)1/32
B)1/6
C)1/33
D)1/38
E)1/34
Rationale: The three dice can fall in 6 * 6 = 36 ways.
Hence the probability is 6/36
= 1/6
Answer: B
Answer: B
Question: 12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c?
Options:
A)1 / 2
B)1 / 3
C)1 / 4
D)1 /6
E)1 / 12
Rationale: 6a/100 = 12
a = 200
12b/100 = 6
b = 50
c = b/a = 50 / 200 = 1/4
The answer is C.
Answer: C
Question: Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
Options:
A)900
B)980
C)1200
D)1240
E)1400
Rationale: Amount received by sanjay.
4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1400.
E
Answer: E
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
Options:
A)20:15:18
B)20:15:16
C)20:15:12
D)20:15:11
E)20:15:15
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: C
Question: In how many way the letter of the word "APPLE" can be arranged
Options:
A)20
B)40
C)60
D)80
E)90
Rationale: Explanation:
Friends the main point to note in this question is letter "P" is written twice in the word.
Easy way to solve this type of permutation question is as,
So word APPLE contains 1A, 2P, 1L and 1E
Required number =
=5!/1!∗2!∗1!∗1!=5∗4∗3∗2!/2!=60
Option C
Answer: C
Question: Jar A has 16% more marbles than Jar B . What percent of marbles from Jar A need to be moved into Jar B so that both jars have equal marbles?
Options:
A)5%
B)7%
C)9%
D)11%
E)13%
Rationale: An easy way to solve this question is by number plugging. Assume there are 100 marbles in Jar B then in Jar A there will be 116 marbles. Now, for both jars to have equal marbles we should move 8 marbles from A to B, which is 8/116=~7% of A.
Answer: B.
Answer: B
Question: If green means red, red means white, white means blue, blue means orange and orange means green, what is the colour of snow ?
Options:
A)Blue
B)Green
C)Yellow
D)Red
E)Pink
Rationale: Explanation:
The colour of snow is 'blue' and as given 'White' means Blue'.
so, the snow is 'blue'.
Answer: A
Answer: A
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
Options:
A)288
B)327
C)585
D)972
E)271
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer: C
Answer: C
Question: A sum fetched total simple interest of 4016.25 at the rate of 13 p.c.p.a. in 5 years. What is the sum?
Options:
A)6178.85
B)8032.5
C)4462.5
D)8900
E)None of these
Rationale: Let the sums be P.
Now, 65% of P = 4016.25
or, P = 6178.85
Answer A
Answer: A
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 21 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
Options:
A)25
B)32
C)36
D)58
E)61
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
21 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 44
b = 33
Number of freshmen who take Art = 33 + 20 + 5 = 58
Answer D
Answer: D
Question: If 1/2 of a pencil is blue, 1/8 of the remaining is red and the remaining 3/8 is white, what is the total length of the pencil?
Options:
A)5
B)3
C)1
D)4
E)2
Rationale: Blue is 1/2 but can also be written as 4/8Red is 1/8White is 3/84/8+1/8+3/8= 8/8=1Answer is C) 1
Answer: C
Question: Look at this series: 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, ... What number should come next?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
The answer is C.
Answer: C
Question: In a party attended by 13 persons, each clinch their glass with every other. How many glass clinches?
Options:
A)51
B)52
C)78
D)54
E)55
Rationale: Total no. of person = 11
Total no. of glass clinches = n(n-1)/2
=13*12/2
= 78
ANSWER:C
Answer: C
Question: Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 6 km/hr and 12 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)28 sec
B)37 sec
C)17 sec
D)60 sec
E)27 sec
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 200 / (6+ 12)5/18 = 300* 18 / 18 * 5 = 60 seconds.
Answer : D
Answer: D
Question: 4 shepherds were watching over the flocks and they were commenting on how many sheep they each had. If ram had 3 more sheep than he would have one less than rahul. wheras akar has the same number as the other 3 shepherds put togeher. If john had 3 less sheep he would have exactly trile the number of ram. If they were evenly distributed if they would each have 11 seep how many sheep did ram have?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: akar has=ram+rahul+john
after evenly distribution each has 11. so, total no. is 44
so, akar has=22 & ram+rahul+john=22 also ram=rahul-4 & john-3=3*ram solving these we get the sol.
ANSWER:B
Answer: B
Question: Reduce
368/575 to the lowest terms.
Options:
A)30/25
B)28/29
C)27/29
D)16/25
E)17/28
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 575 which is 23
Step2: Divide both by 23, we will get the answer 16/25
Option D
Answer: D
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
A. 15 kmph B. 10 kmph
Options:
A)12.9 kmph
B)28.8 kmph
C)28.9 kmph
D)12.5 kmph
E)29.9 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Answer: D
Question: What is the two-digit number?
I. Sum of the digits is 7.
II. Difference between the number and the number obtained by interchanging the digits is 9.
III. Digit in the ten's place is bigger than the digit in the unit's place by 1.
Options:
A)I and II
B)II and III
C)I and III only
D)All
E)I and II as well as I and III
Rationale: Answer: Option E
Explanation:
Let the tens and units digit be x and y respectively.
I. x + y = 7.
II. (10x + y) - (10y + x) = 9 x - y = 1.
III. x - y = 1.
Thus, I and II as well as I and III give the answer.
Correct answer is (E).
Answer: E
Question: A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 15 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)
Options:
A)1650
B)2750
C)3850
D)4950
E)6050
Rationale: The distance the sound traveled to the man is 15*330 = 4950 meters
The answer is D.
Answer: D
Question: Distance between A and B is 36 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 2 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 1 mph, in the second hour it was 1.25 mph, in the third hour it was 1.5 mph, and so on. Where will they meet each other?
Options:
A) 12 miles away from A
B) 12 miles away from B
C) after 6 hours from start
D) after 12 hours from start
E) midway between A and B
Rationale: Since the question asks where A and B will meet each other, we know the answer will involve distance and location.
In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of A (assuming guy who starts from A is A) is 2 mph and distance is 36 miles. So this means that A would take a total of 36/2 = 18 hours to cover the distance from A to B. So, if B's speed were also 2, both A and B would travel for 9 hours to meet in the middle.
B has uniform speed per hour so its average will be the simple average of all speeds: 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5...
and 2 is actually right in the middle of the 9 speeds, implying both A and B have the same average speed.
The correct answer is (E).
Answer: E
Question: If the personal income tax rate is lowered from 42% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $42400?
Options:
A)$3500
B)$5000
C)$4240
D)$7000
E)$10000
Rationale: Saving = (42-32)% of 42400 = 4240.
Answer:C
Answer: C
Question: The number 523hbc is divisible by 7,8,9. Then what is the value of h*b*c
Options:
A)504
B)532
C)210
D)180
E)280
Rationale: LCM of 7, 8 and 9 is 504, thus 523hbc must be divisible by 504.
523hbc=523000+hbc
523000 divided by 504 gives a remainder of 352.
Hence, 352hbc=k*504.
k=1 hbc=152 --> h*b*c=10
k=2 hbc=656 --> h*b*c=180
As hbc is three digit number k can not be more than 2.
Two answers? Well only one is listed in answer choices, so D.
Answer: D.
Answer: D
Question: Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm?
Options:
A)225 cm2
B)150 cm2
C)127 cm2
D)177 cm2
E)187 cm2
Rationale: 1/2 * 30(9 + 6)
= 225 cm2
Answer: A
Answer: A
Question: In the xy-plane, the point (3, 1) is the center of a circle. The point (3, -2) lies inside the circle and the point (-2, 1) lies outside the circle. If the radius r of the circle is an integer, then r =
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: An easy way to solve this question will be just to mark the points on the coordinate plane.
You'll see that the distance between the center (3, 1) and the point inside the circle (3, -2) is 3 units
(both points are on x=3 line so the distance will simply be 1-(-2)=3)
So the radius must be more than 3 units.
The distance between the center (3,1) and the point outside the circle (-2,1) is 5 units
(both points are on y=1 line so the distance will simply be 3-(-2)=5)
So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4.
Answer: C.
Answer: C
Question: How long does a train 165 meters long running at the rate of 90 kmph take to cross a bridge 660 meters in length?
Options:
A)28
B)27
C)33
D)18
E)12
Rationale: T = (660 + 165)/90 * 18/5
T = 33
Answer: C
Answer: C
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
Options:
A)50
B)26
C)28
D)69
E)17
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
Answer: A
Question: A reduction of 44% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
Options:
A)2.3
B)8.3
C)7.3
D)3.3
E)1.3
Rationale: Explanation:
40*(44/100) = 17.6 --- 64
? --- 12 => Rs.3.30
Answer: D
Answer: D
Question: Sum of the squares of 3 no. is 52 and the sum of their products taken two at a time is 72. Find the sum?
Options:
A)18
B)21
C)13
D)16
E)14
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 52 + 2* 72
a + b + c = âˆš196 = 14
Answer E
Answer: E
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an even number.
2. Y^(X + Y) is not an integer.
3. X^Y is a positive number.
Options:
A)2 only.
B)3 only.
C)1 and 3 only.
D)2 and 3 only.
E)1, 2 and 3.
Rationale: Statement I is not TRUE
Statement II is TRUE
Statement III is not TRUE
Answer : A
Answer: A
Question: How many times digit 5 is used while writing numbers from 100 to 1000?
Options:
A)648
B)300
C)252
D)225
E)290
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 5 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 290. Hence E.
Answer: E
Question: fill in ht blank:(a) the point with coordinates (0,0) is called ____ of a rectangular coordinate system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___
Options:
A)(a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y
B)(a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y
C)(a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
D)(a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for z
E)none of the above
Rationale: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer (C)
Answer: C