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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.
  • a)
    (1)
  • b)
    (2)
  • c)
    (3)
  • d)
    (2) & (3)
  • e)
    (1), (2), & (3)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
j = ab.pqrDecimal j is represented as above, with digits a, b, p, q an...
Given: j = ab.pqr
  • 0 ≤ a, b, p, q, r ≤ 9
Also, p + q = 3
  • 0 ≤ p ≤ 3 and 0 ≤ 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,
  • 6 ≤ r ≤ 9
((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
  • j/10 = a.bpqr
Let’s round j/10 to the nearest thousandths:
  • Step R1 -Marking the digit at the thousandths place: a.bpqr
  • Step R2 -The digit on q’s right is r.
  • Step R3 – Since r > 5, we will add 1 to q.
  • Step R4 – a.bpqr will be rounded to a.bp(q+1)0.
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
  • 100j = abpq.r
Let’s round 100j to the nearest tens:
  • Step R1 -Marking the digit at the tens place: abpq.r
  • Step R2 -The digit on p’s right is q.
  • Step R3 – Since q < 5, we will keep p as it is. (Note that in fact q < 4.)
  • Step R4 – abpq.r will be rounded to abp0.0
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
  • 1000j = abpqr
Let’s round 1000j to the nearest thousands:
  • Step R1 -Marking the digit at the thousands place: abpqr.
  • Step R2 -The digit on b’s right is p.
  • Step R3 – Since p < 5, we will keep b as it is. (Note that in fact p < 4.)
  • Step R4 – abpqr will be rounded to ab000
Conclusion: Statement (3) is TRUE.
 Overall Conclusion: Only statements (2) and (3) are true.
Answer: Option (D)
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j = ab.pqrDecimal 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.a)(1)b)(2)c)(3)d)(2) & (3)e)(1), (2), & (3)Correct answer is option 'D'. Can you explain this answer?
Question Description
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