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Data Sufficiency: The Question Stem - What is the Issue?

Danny purchased a number of grease pumps of only two possible variants: $5 pumps and $25 pumps. If the ratio between the number of $5 pumps purchased and the number of $25 pumps purchased is 13:7, how many $5 grease pumps did Danny buy? >(1) The total purchase price of the grease pumps Danny bought was less than $400. >(2) The total purchase price of the grease pumps Danny bought was greater than $200.
Incorrect. [[snippet]] According to Stat. (1), the total price of the grease pumps Danny bought was less than $400. Since the statement sets a relatively low cap on the total price of the equipment, calculate the possible total prices that comply to the given ratio, and check which of those scenarios result in a total price less than $400. Had there been exactly __thirteen__ $5 pumps and __seven__ $25 pumps, the price of the entire purchase would have been >$$\text{Total} = (13\times \$5) + (7\times \$25) = \$65+\$175 = \$240$$. This is below the price cap imposed by the statement and therefore possible. Had there been __twenty-six__ $5 pumps and __fourteen__ $25 pumps, the total price would have been exactly twice $240 since the number of pumps was multiplied by 2. Hence, twenty-six $5 pumps and fourteen $25 pumps would cost >$$\text{Total} = 2\times \$240= \$480$$. This is greater than the $400 dollar price limit and therefore impossible. Needless to say, any greater number of pumps would result in an even greater total cost. It follows that the only possible scenario is thirteen $5 pumps and seven $25 pumps, meaning that Stat. (1) is sufficient. **Stat.(1) → S → AD**.
Incorrect. [[snippet]] According to Stat.(2), the total price of the grease pumps Danny bought was greater than $200. Had there been exactly __thirteen__ $5 pumps and __seven__ $25 pumps, the price of the entire purchase would have been >$$\text{Total} = 13\times \$5+7\times \$25 = \$65+\$175 = \$240$$, which is greater than $200, so this scenario is possible. However, the number of pumps could also be 26 and 14, or any other pair of numbers complying to the 13:7 ratio. Any such set of numbers would lead to a price greater than $240, and thus greater than $200, and would therefore comply to the statement. Hence, the statement is insufficient. **Stat.(2) → IS → ACE**.
Incorrect. [[snippet]] According to Stat. (1), the total price of the grease pumps Danny bought was less than $400. Since the statement sets a relatively low cap on the total price of the equipment, calculate the possible total prices that comply to the given ratio, and check which of those scenarios result in a total price less than $400. Had there been exactly __thirteen__ $5 pumps and __seven__ $25 pumps, the price of the entire purchase would have been >$$\text{Total} = (13\times \$5) + (7\times \$25) = \$65+\$175 = \$240$$. This is below the price cap imposed by the statement and therefore possible. Had there been __twenty-six__ $5 pumps and __fourteen__ $25 pumps, the total price would have been exactly two times $240 since the number of pumps would be multiplied by 2. Hence, twenty-six $5 pumps and fourteen $25 pumps would cost >$$\text{Total} = 2\times \$240= \$480$$. This is greater than the $400 dollar price limit and therefore impossible. Needless to say, any greater number of pumps would result in an even greater total cost. It follows that the only possible scenario is thirteen $5 pumps and seven $25 pumps, meaning that Stat. (1) is sufficient. **Stat.(1) → S → AD**. Therefore, answer choice C is eliminated.
Incorrect. [[snippet]] According to Stat.(2), the total price of the grease pumps Danny bought was greater than $200. Had there been exactly __thirteen__ $5 pumps and __seven__ $25 pumps, the price of the entire purchase would have been >$$\text{Total} = 13\times \$5+7\times \$25 = \$65+\$175 = \$240$$, which is greater than $200, so this scenario is possible. However, the number of pumps could also be 26 and 14, or any other pair of numbers complying to the 13:7 ratio. Any such set of numbers would lead to a price greater than $240, and thus greater than $200, and would therefore comply to the statement. Hence, the statement is insufficient. **Stat.(2) → IS → ACE**.
According to Stat.(2), the total price of the grease pumps Danny bought was greater than $200. We've already seen that thirteen $5 pumps and seven $25 pumps cost $240, which is greater than $200, so this scenario is possible. However, the number of pumps could also be 26 and 14, or any other pair of numbers complying to the 137 ratio. Any such set of numbers would lead to a price greater than $240, and thus greater than $200, and would therefore comply to the statement. Hence, the statement is insufficient. **Stat.(2) → IS → A**.
Correct. [[snippet]] According to Stat. (1), the total price of the grease pumps Danny bought was less than $400. Since the statement sets a relatively low cap on the total price of the equipment, calculate the possible total prices that comply to the given ratio, and check which of those scenarios result in a total price less than $400. Had there been exactly __thirteen__ $5 pumps and __seven__ $25 pumps, the price of the entire purchase would have been >$$\text{Total} = (13\times \$5) + (7\times \$25) = \$65+\$175 = \$240$$. This is below the price cap imposed by the statement and therefore possible. Had there been __twenty-six__ $5 pumps and __fourteen__ $25 pumps, the total price would have been exactly two times $240 since the number of pumps would be multiplied by 2. Hence, twenty-six $5 pumps and fourteen $25 pumps would cost >$$\text{Total} = 2\times \$240= \$480$$. This is greater than the $400 dollar price limit and therefore impossible. Needless to say, any greater number of pumps would result in an even greater total cost. It follows that the only possible scenario is thirteen $5 pumps and seven $25 pumps, meaning that Stat. (1) is sufficient. **Stat.(1) → S → AD**.
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.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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