{"id":159900,"date":"2023-09-18T15:19:41","date_gmt":"2023-09-18T09:49:41","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=159900"},"modified":"2023-09-18T15:19:44","modified_gmt":"2023-09-18T09:49:44","slug":"each-of-the-letters-in-the-figure-below-represents-a-unique-integer-from-1-to-9","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/each-of-the-letters-in-the-figure-below-represents-a-unique-integer-from-1-to-9\/","title":{"rendered":"Each of the letters in the figure below represents a unique integer from 1 to 9"},"content":{"rendered":"\n

Q. Each of the letters in the figure below represents a unique integer from 1 to 9. The letters are positioned in the figure such that each of (A+B+C), (C+D+E), (E+F+G) and (G+H+K) is equal to 13. Which integer does E represent?<\/p>\n\n\n\n

A<\/td>B<\/td>C<\/td> <\/td><\/tr>
 <\/td>D<\/td><\/tr>
E<\/td>F<\/td>G<\/td><\/tr>
 <\/td>H<\/td><\/tr>
K<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

(A) 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (C) 6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (D) 7<\/p>\n\n\n\n

Ans: 4<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

(A + B + C) + (C + D + E) + (E + F + G) + (G + H + K) = A + B + 2C + D + 2E + F + 2G + H + K = 13 + 13 + 13 + 13 = 52\u00a0 \u2026\u2026(i) <\/p>\n\n\n\n

2.\u00a0A + B + C + D + E + F + G + H = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45\u00a0\u00a0\u00a0\u2026\u2026(ii) <\/p>\n\n\n\n

Subtracting (ii) from (i) we get, C + E + G = 7 <\/p>\n\n\n\n

We have C + D + E = 13 <\/p>\n\n\n\n

(C + D + E) –\u00a0(C + E + G) = 6 <\/p>\n\n\n\n

\u21d2\u00a0D – G = 6 <\/p>\n\n\n\n

Also,\u00a0(E + F + G) –\u00a0(C + E + G) = 6 <\/p>\n\n\n\n

\u21d2\u00a0F – C = 6 <\/p>\n\n\n\n

\u2234\u00a0D – G = F – C = 6 <\/p>\n\n\n\n

Possible values for (F, C) and (D, G) are (9, 3), (8, 2) and (7, 1). <\/p>\n\n\n\n

If\u00a0 (F, C) = (9, 3), then E + F + G = 13 would mean either E or G must be equal to 3 (only possibility for (E, G) = (1, 3) or (3, 1)) which is not possible as C is\u00a0equal to 3 for the selected set of conditions.<\/p>\n\n\n\n

Similarly, (D, G) cannot be (9, 3). <\/p>\n\n\n\n

Thus, the possibility of (9, 3) is ruled out. <\/p>\n\n\n\n

Now, Case 1:\u00a0(D, G) = (7, 1) and (F, C)\u00a0= (8, 2) <\/p>\n\n\n\n

Then, C + D + E =\u00a0 2 + 7 + E = 13 <\/p>\n\n\n\n

Case 2: (F, C) = (7, 1) and (D,G)\u00a0= (8, 2) <\/p>\n\n\n\n

Then, C + D + E = 1 + 8 + E = 13 <\/p>\n\n\n\n

Both cases give us E = 4. <\/p>\n\n\n\n

Hence, 4 is the correct answer.<\/p>\n","protected":false},"excerpt":{"rendered":"

Q. Each of the letters in the figure below represents a unique integer from 1 to 9. The letters are positioned in the figure such that each of (A+B+C), (C+D+E), (E+F+G) and (G+H+K) is equal to 13. Which integer does E represent? A B C     D E F G   H K (A) […]<\/p>\n","protected":false},"author":419,"featured_media":159901,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5141],"tags":[5140],"offerexpiration":[],"class_list":["post-159900","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/159900","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=159900"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/159900\/revisions"}],"predecessor-version":[{"id":159902,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/159900\/revisions\/159902"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/159901"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=159900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=159900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=159900"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/offerexpiration?post=159900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}