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# Data Sufficiency: Yes/No Basic Technique

In a sequence of \$\$N\$\$ consecutive integers, are there exactly two multiples of 8? >(1) \$\$N=18\$\$ >(2) The first integer in the sequence is not a multiple of 8.
Incorrect. [[snippet]] Stat. (1): Plug in for the integers in the set, such as the integers between 1 and 18, inclusive. In this case, there are exactly _two_ multiples of 8 in the set (8 and 16), so the answer is "Yes." However, is this always true, for any number? Plug in a DOZEN F case, such as the integers between 0 and 17, inclusive (the "Z" stands for Zero). Now there are _three_ multiples of 8 (0, 8, and 16) in the set, so the answer is "No." Overall, that's a "Maybe," so **Stat.(1) → Maybe → IS → BCE**.
Stat. (1)+(2): Combined, the two statements limit your plug-ins to sets of 18 consecutive integers beginning with an integer that is not a multiple of 8. Again, plug in the integers between 1 and 18 to get _two_ multiples of 8. Now think of a DOZEN F case to get a "No" answer, such as the set of integers between -1 and 16, inclusive. This set satisfies the terms set in both statements, yet yields _three_ multiples of 8 (0, 8, and 16). This is still "Maybe," so **Stat.(1+2) → Maybe → IS → E**.
Incorrect. [[snippet]] Stat. (1): Plug in for the integers in the set, such as the integers between 1 and 18, inclusive. In this case, there are exactly _two_ multiples of 8 in the set (8 and 16), so the answer is "Yes." However, is this always true, for any number? Plug in a DOZEN F case, such as the integers between 0 and 17, inclusive (the "Z" stands for Zero). Now there are _three_ multiples of 8 (0, 8, and 16) in the set, so the answer is "No." Overall, that's a "Maybe," so **Stat.(1) → Maybe → IS → BCE**. Stat. (2): Alone, this statement allows plugging in all integers between 1 and 18, inclusive, yielding _two_ multiples of 8 (8 and 16). However, since the number of terms isn't determined in Stat. (2), the set could include, for example, only three integers (such as 1, 2, and 3), yielding _zero_ multiples of 8. Overall, that's a "Maybe," so **Stat.(2) → Maybe → IS → CE**.
Incorrect. [[snippet]] Stat. (1)+(2): Combined, the two statements limit your plug-ins to sets of 18 consecutive integers beginning with an integer that is not a multiple of 8. Plug in the integers between 1 and 18 to get _two_ multiples of 8 and an answer of "Yes." Now think of a DOZEN F case to get a "No" answer, such as the set of integers between -1 and 16, inclusive. This set satisfies the terms set in both statements, yet yields _three_ multiples of 8 (0, 8, and 16) and an answer of "No." This is still "Maybe," so **Stat.(1+2) → Maybe → IS → E**.
Incorrect. [[snippet]] Stat. (2): Alone, this statement allows plugging in all integers between 1 and 18, inclusive, yielding _two_ multiples of 8 (8 and 16) and an answer of "Yes." However, since the number of terms isn't determined in Stat. (2), the set could include, for example, only three integers (such as 1, 2, and 3), yielding _zero_ multiples of 8 and an answer of "No." Overall, that's a "Maybe," so **Stat.(2) → Maybe → IS → ACE**.
Correct. [[snippet]] Stat. (1): Plug in for the integers in the set, such as the integers between 1 and 18, inclusive. In this case, there are exactly _two_ multiples of 8 in the set (8 and 16), so the answer is "Yes." However, is this always true, for any number? Plug in a DOZEN F case, such as the integers between 0 and 17, inclusive (the "Z" stands for Zero). Now there are _three_ multiples of 8 (0, 8, and 16) in the set, so the answer is "No." Overall, that's a "Maybe," so **Stat.(1) → Maybe → IS → BCE**. Stat. (2): Alone, this statement allows plugging in all integers between 1 and 18, inclusive, yielding _two_ multiples of 8 (8 and 16). However, since the number of terms isn't determined in Stat. (2), the set could include, for example, only three integers (such as 1, 2, and 3), yielding _zero_ multiples of 8. Overall, that's a "Maybe," so **Stat.(2) → Maybe → IS → CE**.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.