What is the value of x/10 , when it is rounded to the nearest hundredth digit? Take the value of x as 194.283.
What is the approximate value of the expression
Given p = 5.369 and q = 7.4y5. When q is rounded to the nearest hundredth digit, it is equal to 7.5. Find p + q.
Correct Answer : c
Explanation : q is nearest to 7.5
that means 7.450 ≤ 7.4 ≤ 7.499
P = 5.369
Q = 7.450
Adding P + Q
= 5.369 + 7.450
= 12.819
For Q = 7.499
P = 5.369
Adding P + Q
= 5.369 + 7.499
= 12.868
12.819 < P+Q < 12.868
According to options, 12.864 lies between 12.819 and 12.868
What is the value of 47.xy9 when it is rounded to the nearest integer? It is also known that x > y.
The expression 32045 × 643 ÷ 15987 is approximately equal to:
Step 1: Question statement and Inferences
We need to find the approximate value of 32045 × 643 ÷ 15987
As all the answer options have zero in unit and tens digit
We can round all the numbers to hundreds place
Step 2: Finding required values
Rounding 32045 to hundreds = 32000
Rounding 643 to hundreds = 600
Rounding 15987 to hundreds = 16000
Step 3: Calculating the final answer
32045 × 643 ÷ 15987 ≃ 32000 * 600/16000 = 1200
Answer: Option (C)
What is the approximate value of N, if N is equal to 33% of 3.683 × 42.198 ÷ 20.679?
Step 1: Question statement and Inferences
We have to find approximate value of 33% of 3.683 × 42.198 ÷ 20.679
Step 2: Finding required values
As we have to find the approximate value.
Rounding to the units digit:
Step 3: Calculating the final answer
Let’s simplify the expression
The final answer
Answer: Option (C)
When rounded to the nearest hundredths digit, the number p becomes 6.72. What is the hundredths digit of p?
(1) The thousandths digit of p is 3.
(2) The sum of the hundredths and the thousandths digits of p is 5
Steps 1 & 2: Understand Question and Draw Inferences
We are given a number p. We have to find the hundredths digit of p.
Let’s say p = a.bcde (Here a, b, c, d and e are digits)
We are given that on rounding to the hundredths digit, p becomes 6.72
So, by comparing the form a.bcde with 6.72, we conclude that:
a = 6, b = 7 and:
If d ≥ 5, then c = 1
If d < 5, then c = 2
We need to find the value of c.
Step 3: Analyze Statement 1
Statement 1 says: The thousandths digit of p is 3.
So, the number a.bcde = a.bc3e
That is, d = 3
From the condition above, this clearly implies that c = 2
Thus, Statement 1 alone is sufficient to answer the question: what is the value of c?
Step 4: Analyze Statement 2
Statement 2 says: The sum of the hundredths and the thousandths digits of p is 5
That is, c + d = 5
We have inferred that:
If d ≥ 5, then c = 1
In this case, the sum of c + d will range from 6 to 10, inclusive
We also inferred that
If d < 5, then c = 2
This means, if d = 0, 1, 2, 3 or 4, then c = 2
Out of these possible values of d, we see that if d = 3, then c = 2 and the condition given in Statement 2 (that c + d = 5) is also fulfilled.
Therefore, using Statement 2, we can deduce that:
c = 2
Thus, Statement 2 alone is sufficient to find the value of c.
Step 5: Analyze Both Statements Together (if needed)
This step is not needed as we get a unique value for c in both steps 3 and 4.
Answer: Option (D)
If r, s, and t are the tenths, hundredths, and the thousandths digit respectively of decimal d = 26.rst, is t – 4 positive?
(1) If 10d were rounded to the nearest tenths, the result would be 260.3
(2) s is even
Step 1 & 2 – Understand the question and draw inferences from the question statement.
Given: d = 26.rst
To find: If t – 4 > 0
We need to find if t – 4 > 0
i.e. if t > 4
Thus, we need to find if 5 ≤ t ≤ 9
Step 3 – Analyze Statement 1 Independently
Statement 1 – If 10d were rounded to the nearest tenths, the result would be 260.3
d = 26. rst
Let’s round 10d to the nearest tenths:
Marking the digit at the tenths place: 26r.st
The digit on s’s right is t
i. If t ≥ 5, we will add 1 to s.
ii. If t < 5, we will keep s as it is
Therefore, 26r. st may be rounded to 26r.s0 (if t < 5) or 26r.(s+1)0 (if t ≥ 5)
Comparing this with the number 260.3, we get:
Thus, information provided in Statement 1 is not sufficient to arrive at a unique answer.
Step 4 – Analyze Statement 2 Independently
Per Statement 2, s is even.
However, to answer the given question, we need to find if 5 ≤ t ≤ 9
Thus, information provided in Statement 2 is not sufficient to arrive at a unique answer.
Step 5 – Analyze Both Statements Together
Per Statement 1, we have:
s = 2, if t ≥ 5 and s = 3, if t < 5
Per Statement 2, we have:
s is even.
Combining both statements, we have s = 2
Since t is a digit, t cannot be greater than 9.
Therefore statement 1 and statement 2 together are sufficient to arrive at a unique answer.
Answer: Option (C)
If a = 3.78xy7 and b = 1.37486, where x and y are positive digits, what is the value of a + b?
(1) If a and b are rounded to nearest thousandths digit, then a + b = 5.162
(2) If a and b are rounded to nearest tenthousandths digit, then a + b = 5.1622
Steps 1 & 2: Understand Question and Draw Inferences
We are given that:
a = 3.78xy7 (Here, x and y are positive digits)
b = 1.37486
We have to find the value of a + b.
Now, to find the sum of a and b, first we need to find the values of x and y so that we can determine the value of a. Since we already have the value of b, we can then add both of them and find a + b.
So, the question here is what is the value of a?
Step 3: Analyze Statement 1
Statement 1 says: If a and b are rounded to nearest thousandths digit, then a + b = 5.162
So, we know that:
(Rounded value of a to nearest thousandths place) + (Rounded value of b to nearest thousandths place) = 5.162 ……………… (1)
Now, we can’t find the rounded value of a, but we can find the rounded value of b to nearest thousandths place.
Now, let’s round b to the nearest thousandths:
By putting the rounded value of b in equation (1):
(Rounded value of a to nearest thousandths place) + 1.375 = 5.162
(Rounded value of a to nearest thousandths place) = 5.162 – 1.375 = 3.787
So, the rounded value of 3.78xy7 to the nearest thousandths place = 3.787
This means,
If y ≥ 5, then x = 6
If y < 5, then x = 7
Thus, we are not able to determine a unique value of x and y each.
Hence, statement 1 is not sufficient to answer the question: What is the value of a?
Step 4: Analyze Statement 2
Statement 2 says: If a and b are rounded to nearest tenthousandths digit, then a + b = 5.1622
(Rounded value of a to nearest tenthousandths place) + (Rounded value of b to nearest tenthousandths place) = 5.1622 ……………… (2)
Let’s round b to the nearest tenthousandths:
By putting the rounded value of b in equation (2):
(Rounded value of a to nearest tenthousandths place) + 1.3749 = 5.1622
(Rounded value of a to nearest tenthousandths place) = 5.1622 – 1.3749 = 3.7873
So, the rounded value of 3.78xy7 to the nearest tenthousandths place = 3.7873
Now, let’s round a to the nearest tenthousandths:
So, the value of y = 2.
Thus, a = 3.78x27
Also, by comparing 3.7873 to 3.78x27 we get to know that the value of x is 7.
Thus, we know that the value of a is 3.78727.
So, statement 2 alone is sufficient to answer the question: What is the value of a?
Step 5: Analyze Both Statements Together (if needed)
Since statement 2 alone is sufficient to answer the question, we don’t need to perform this step.
Answer: Option (B)
j = ab.pqr
Decimal j is represented as above, with digits a, b, p, q and r. If p + q = 3 and q + r = 9, which of the following statements are true?
(1) If j/10 were rounded to the nearest thousandths, the result would contain the digit q.
(2) If 100j were rounded to the nearest tens, the result would contain the digit p.
(3) If 1000j were rounded to the nearest thousands, the result would contain the digit b.
Given: j = ab.pqr
Also, p + q = 3
((p, q) may be (0,3), (1, 2), (2, 1) or (3, 0))
Also given that q + r = 9
We already concluded from the above that 0 ≤ q ≤ 3,
((q, r) may be (0, 9), (1, 8), (2, 7) or (3, 6))
Now, let’s analyze the given statements:
Statement I: If j/10 were rounded to the nearest thousandths, the result would contain the digit q
j = ab.pqr
Let’s round j/10 to the nearest thousandths:
Conclusion: Statement (1) is FALSE.
Statement II: If 100j were rounded to the nearest tens, the result would contain the digit p
j = ab.pqr
Let’s round 100j to the nearest tens:
Conclusion: Statement (2) is TRUE.
Statement III: If 1000j were rounded to the nearest thousands, the result would contain the digit b.
j = ab.pqr
Let’s round 1000j to the nearest thousands:
Conclusion: Statement (3) is TRUE.
Overall Conclusion: Only statements (2) and (3) are true.
Answer: Option (D)
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