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On Sunday, a farmer brought two types of fruit to the market: apples and pears. During the day, the farmer sold 1/7 of the apples he had brought. If the farmer sold at least 1 apple and at least 1 pear that day, did the farmer bring more than 105 pieces of fruit to the market?
(1) The number of apples the farmer sold that day was 15/16 as many as the number of apples he sold on Saturday.
(2) During the day, the number of apples the farmer sold was 6/7 as many as the number of pears he sold.
(1) The number of apples the farmer sold that day was 15/16 as many as the number of apples he sold on Saturday.
(2) During the day, the number of apples the farmer sold was 6/7 as many as the number of pears he sold.
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13 Mar 2026, 02:15
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GMAT Club Official Solution:
On Sunday, a farmer brought two types of fruit to the market: apples and pears. During the day, the farmer sold 1/7 of the apples he had brought. If the farmer sold at least 1 apple and at least 1 pear that day, did the farmer bring more than 105 pieces of fruit to the market?
Firstly, note that on Sunday, the farmer sold 1/7 of the apples he had brought, so (apples brought on Sunday) = 7 * (apples sold on Sunday).
(1) The number of apples the farmer sold that day was 15/16 as many as the number of apples he sold on Saturday.
This implies that:
(apples sold on Sunday) = 15/16 * (apples sold on Saturday);
(apples sold on Sunday) / (apples sold on Saturday) = 15/16.
Hence, (apples sold on Sunday) must be a multiple of 15.
Since (apples brought on Sunday) = 7 * (apples sold on Sunday), (apples brought on Sunday) must be a multiple of 7 * 15 = 105. Therefore, the total number of fruit he brought (apples + pears) must be at least 105 + 1 = 106 (since he sold at least 1 pear then he must have brought at least 1 pear). Sufficient.
(2) During the day, the number of apples the farmer sold was 6/7 as many as the number of pears he sold.
This implies that:
(apples sold on Sunday) = 6/7 * (pears sold on Sunday);
(apples sold on Sunday) / (pears sold on Sunday) = 6/7.
Hence, (apples sold on Sunday) must be a multiple of 6. Since (apples brought on Sunday) = 7 * (apples sold on Sunday), (apples brought on Sunday) must be a multiple of 7 * 6 = 42.
If the farmer sold 6 apples and 7 pears, then he brought 7 * 6 = 42 apples and could have brought 7 pears, for a total of 49 pieces of fruit (not more than 105).
However, if the farmer sold 18 apples and 21 pears, then he brought 7 * 18 = 126 apples and must have brought at least 21 pears, for a total of at least 147 pieces of fruit (more than 105). Not sufficient.
Answer: A.
On Sunday, a farmer brought two types of fruit to the market: apples and pears. During the day, the farmer sold 1/7 of the apples he had brought. If the farmer sold at least 1 apple and at least 1 pear that day, did the farmer bring more than 105 pieces of fruit to the market?
Firstly, note that on Sunday, the farmer sold 1/7 of the apples he had brought, so (apples brought on Sunday) = 7 * (apples sold on Sunday).
(1) The number of apples the farmer sold that day was 15/16 as many as the number of apples he sold on Saturday.
This implies that:
(apples sold on Sunday) = 15/16 * (apples sold on Saturday);
(apples sold on Sunday) / (apples sold on Saturday) = 15/16.
Hence, (apples sold on Sunday) must be a multiple of 15.
Since (apples brought on Sunday) = 7 * (apples sold on Sunday), (apples brought on Sunday) must be a multiple of 7 * 15 = 105. Therefore, the total number of fruit he brought (apples + pears) must be at least 105 + 1 = 106 (since he sold at least 1 pear then he must have brought at least 1 pear). Sufficient.
(2) During the day, the number of apples the farmer sold was 6/7 as many as the number of pears he sold.
This implies that:
(apples sold on Sunday) = 6/7 * (pears sold on Sunday);
(apples sold on Sunday) / (pears sold on Sunday) = 6/7.
Hence, (apples sold on Sunday) must be a multiple of 6. Since (apples brought on Sunday) = 7 * (apples sold on Sunday), (apples brought on Sunday) must be a multiple of 7 * 6 = 42.
If the farmer sold 6 apples and 7 pears, then he brought 7 * 6 = 42 apples and could have brought 7 pears, for a total of 49 pieces of fruit (not more than 105).
However, if the farmer sold 18 apples and 21 pears, then he brought 7 * 18 = 126 apples and must have brought at least 21 pears, for a total of at least 147 pieces of fruit (more than 105). Not sufficient.
Answer: A.
General Discussion
05 Mar 2026, 07:41
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Statement 1:
15/16 sold
Hmm it means the number of total sold here would be a multiple of 16 AND
no.of apples sold on sunday is 15x
Keep this
We also know from stem 1/7th was sold meaning the total number of apples actually
is a multiple of both 15 and 7!
LCM(15,7)=105
And we also know atleast 1 pear was sold that day so 106 total fruits were brought to the market MINIMUM
106>105
Therefore SUFFICIENT
Statement 2:
Similar logic on applying we notice that:
6*7=42 and since we can have a value under 105, there will 100% be cases above 100 as there are no contraints there
Hence INSUFFICIENT
Answer: Option A IMO
15/16 sold
Hmm it means the number of total sold here would be a multiple of 16 AND
no.of apples sold on sunday is 15x
Keep this
We also know from stem 1/7th was sold meaning the total number of apples actually
is a multiple of both 15 and 7!
LCM(15,7)=105
And we also know atleast 1 pear was sold that day so 106 total fruits were brought to the market MINIMUM
106>105
Therefore SUFFICIENT
Statement 2:
Similar logic on applying we notice that:
6*7=42 and since we can have a value under 105, there will 100% be cases above 100 as there are no contraints there
Hence INSUFFICIENT
Answer: Option A IMO
Bunuel
