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In that particular one it just is anal about how you right it. Some of the questions it wants one word per box while others require two. "Ready Front" or "close interval" are examples. This is once again just a failure of SSD to be tested properly so it fails to work properly even when you are correct.
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∙ 11y ago
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What is the sum of all prime numbers between 1 and 100 that are simultaneously one greater than a multiple of 4 and one less than a multiple of 5?
118 Start with the numbers that are 1 less than a multiple of 5. This produces, 4, 9, 14, 19, 24,...,89, 94, 99 Clearly the sequence 4, 14, 24 etc has to be a multiple of 4 or 2 greater than a multiple of 4 so these do not apply. This leaves 9,19,29,39,49,59,69,79,89,99. The prime numbers within this group are, 19, 29, 59, 79 & 89. The numbers that are 1 greater than a multiple of 4 are 29 & 89. 29 + 89 = 118. Using Modular Arithmetic we have : x ≡ 1 (mod4), x = -1 ≡ 4 (mod5) so we can write that, x = 5n + 4... (where n is a positive integer) Thus, 5n + 4 ≡ 1 (mod4) : 5n ≡ -3 ≡ 1 (mod4) : 4n + n ≡ n ≡ 1 (mod4) Consequently n = 1,5,9,13,17... As, x = 5n + 4 , then x = 9, 29, 49, 69, 89. Of these, only 29 & 89 are prime numbers. Hence, 29 + 89 = 118
