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If d is a decimal, is d ≥ 1.55?

(1) When d is rounded to the nearest tenth, the result is 1.6

(2) When d is rounded to the nearest integer, the result is 2

I am struggling to solve this question on the basis of "if d is a decimal". Can someone explain what does this mean please and then the solution as well?

"If D is a decimal" = "if D is a real number". So D is a real number and we want to know if it is ≥ 1.55. Perhaps the best strategy here is to just pick numbers and see if we can prove the statements to be insufficient. Since this question is about number rounding, we should test the most extreme values that fit the statements.

(1) When D is rounded to the nearest tenth, the result is 1.6

If we are rounding up to 1.6, we would need to have a number in the form D = 1.5X, where X is the hundredths digit. To round up, it must be true that X ≥ 5, otherwise we would round down to 1.5 Therefore, it must be true that D ≥ 1.55 --> SUFFICIENT

(2) When d is rounded to the nearest integer, the result is 2

If we are rounding up to 2, we would need to have a number in the form D = 1.X, where X is the tenths digit. To round up, it must be true that X ≥ 5, otherwise we would round down to 1. Therefore, it must be true that D ≥ 1.5 If D = 1.5 the answer is NO. If D = 1.55 the answer is YES. --> INSUFFICIENT. The correct answer is A.

(1) When d is rounded to the nearest tenth, the result is 1.6

(2) When d is rounded to the nearest integer, the result is 2

I am struggling to solve this question on the basis of "if d is a decimal". Can someone explain what does this mean please and then the solution as well?

Doesn't statement 1 being sufficient or not depend on the rounding rules used for D? I.e. if D= 1.546 it is less than 1.55, but when rounded to the nearest tenth it would be 1.6.

Doesn't statement 1 being sufficient or not depend on the rounding rules used for D? I.e. if D= 1.546 it is less than 1.55, but when rounded to the nearest tenth it would be 1.6.

No, that's not correct.

Rounding is not cumulative, that is we are NOT rounding first to the hundredth and only then to the tenth. We are rounding directly to the tenth digit based on the hundredth digit. Thus, the only thing we are interested in when rounding to the nearest tenth is the hundredth digit, the only thing we are interested when rounding to the nearest hundredth is the thousandth digit, and so on. Thus rounded to the nearest tenth 1.546 is 1.5 not 1.6.

Rounding rules

Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.

Example: 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

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