Number System
-
Sum of three fractions is 2 11 24
On dividing the largest fraction by the smallest fraction 7/6 is obtained which is 1/3 greater than the middle fraction. The smallest fraction is
-
View Hint View Answer Discuss in Forum
Let the three fractions be p, q and r, where p < q < r.
According to the question,r = 7 ⇒ r = 7 p p 6 6
Again, middle fraction= q = 7 − 1 = 7 − 2 = 5 6 3 6 6
Correct Option: B
Let the three fractions be p, q and r, where p < q < r.
According to the question,r = 7 ⇒ r = 7 p p 6 6
Again, middle fraction= q = 7 − 1 = 7 − 2 = 5 6 3 6 6 ∴ p + q + r = 2 11 24 ⇒ p + 5 + 7 p = 59 6 6 24 ⇒ p + 7p = 59 − 5 6 24 6 ⇒ 6p + 7p = 59 − 20 = 39 6 24 24 ⇒ 13p = 39 ×6 = 39 24 4 ⇒ p = 39 = 3 4 × 13 4
- Find the greatest among the following given numbers.
(3)1/3, (2)1/2, 1, (6)1/6
-
View Hint View Answer Discuss in Forum
LCM of 3, 2 and 6 = 6
Now we can apply and we can write as below
∴ (3)1/3 = (32)1/6 = (9)1/6
21/2 = (23)1/6 = (8)1/6
11/6 = 1
(6)1/6 = (6)1/6Correct Option: D
LCM of 3, 2 and 6 = 6
Now we can write as below
∴ (3)1/3 = (32)1/6 = (9)1/6
21/2 = (23)1/6 = (8)1/6
1 = (1)1/6
(6)1/6 = (6)1/6
Clearly we can see that power 1/6 is same for all the base numbers. So the number which has greatest base with be greatest among these all number.
∴ (9)1/6 = (3)1/3 is the greatest number.
- The least number of five digits which has 123 as a factor is
-
View Hint View Answer Discuss in Forum
The smallest number of 5 digits = 10000
Remainder on dividing 10000 by 123 = 37Correct Option: B
The smallest number of 5 digits = 10000
Remainder on dividing 10000 by 123 = 37
∴ Required number
= 10000 + (123 – 37) = 10086
- The sum of the digits of a two-digit number is 14 and the difference between the two digits of the number is 2. What is the product of the two digits of the two-digit number ?
-
View Hint View Answer Discuss in Forum
Let be the ten's digit be P and unit's digit be Q.
The two-digit number = 10P + Q
(where, P > Q)
According to the question,
P + Q = 14 ......(i)
and P - Q = 2 .......(ii)Correct Option: B
Let be the ten's digit be P and unit's digit be Q.
The two-digit number = 10P + Q
(where, P > Q)
According to the question,
P + Q = 14 ......(i)
and P - Q = 2 .......(ii)
solving Eqs. (i) and (ii), we get
P = 8 and Q = 6
∴ Required product = 8 x 6 = 48
- The sum of the four consecutive even numbers is 284. What would be the smallest number.
-
View Hint View Answer Discuss in Forum
Let four consecutive even numbers are P, P + 2, P + 4 and P + 6
According to the question,
P + P + 2 + P + 4 + P + 6 = 284Correct Option: C
Let four consecutive even numbers are P, P + 2, P + 4 and P + 6
According to the question,
P + P + 2 + P + 4 + P + 6 = 284
⇒ 4P + 12 = 284
⇒ 4P = 284 - 12 = 272
∴ P = 272/4 = 68
